Ultrasonic flow rate metering

Abstract

A method for an ultrasonic time-of-flight flow meter (1) includes driving an ultrasonic transducer (2, 3) using a first waveform <semantics>(V1(t))<annotation encoding="application / x-tex">(V_1(t))< / annotation>< / semantics> for a first duration <semantics>(Δt1)<annotation encoding="application / x-tex">(\Delta t_1)< / annotation>< / semantics>, the first waveform <semantics>(V1(t))<annotation encoding="application / x-tex">(V_1(t))< / annotation>< / semantics> configured to cause oscillation (21) of the ultrasonic transducer (2, 3), The method also includes driving the ultrasonic transducer (2, 3) using a second waveform <semantics>(V2(t))<annotation encoding="application / x-tex">(V_2(t))< / annotation>< / semantics> for a second duration <semantics>(Δt2)<annotation encoding="application / x-tex">(\Delta t_2)< / annotation>< / semantics>. There is a discontinuity between the first waveform <semantics>(V1(t))<annotation encoding="application / x-tex">(V_1(t))< / annotation>< / semantics> and the second waveform <semantics>(V2(t))<annotation encoding="application / x-tex">(V_2(t))< / annotation>< / semantics>. The second waveform <semantics>(V2(t))<annotation encoding="application / x-tex">(V_2(t))< / annotation>< / semantics> and the second duration <semantics>(Δt2)<annotation encoding="application / x-tex">(\Delta t_2)< / annotation>< / semantics> are configured to maintain a voltage <semantics>(Vt−(t))<annotation encoding="application / x-tex">(V_t - (t))< / annotation>< / semantics> across the ultrasonic transducer (2, 3) within a predetermined range <semantics>(Vh,VI)<annotation encoding="application / x-tex">(V_h, V_I)< / annotation>< / semantics>.

Description

Ultrasonic flow rate metering Field of the invention The present invention relates to methods of ultrasonic flow rate metering using time- of-flight measurements, and flow rate meters employing the methods. Background Ultrasonic flow rate meters have been constructed which measure a flow velocity of a liquid or gas based on time-of-flight measurements. Typically, a pair of ultrasonic transducers is arranged at opposite ends of a flow tube having a known length. Alternatively, a pair of ultrasonic transducers may be arranged spaced apart along the length of a flow tube by a distance, the ultrasonic transducers arranged at angles to the flow tube such that ultrasound may pass between the pair by reflecting from an internal wall or reflector of the flow tube. By obtaining time-of-flight measurements between the ultrasonic transducers both with, and against, the flow direction of the liquid or gas, a difference may be obtained which relates to the flow velocity of the liquid or gas. For example, US 2013 / 080,081 A1 describes a fluid flow meter which estimates the velocity of water or another fluid flowing through a pipe by comparing measurements of the water velocity to one or more pre-determined templates. The fluid flow meter may collect measurement signals from one or more flow sensors (e.g., ultrasonic transducers), estimate the fluid velocity or flow rate by comparing the measurement signals to the template(s), and either store the comparison results in local memory, transmit the results to a remote memory or server, or both. The use of variable frequency, or "chirp", excitation signals for ultrasonic transducers has been reported, see for example "Excitation signal's influence on ultrasonic transit time flow meter's performance", L Svilainis, P Kabisius, A Aleksandrovas and A Chaziachmetovas, IOP Conference Series, Materials Science and Engineering, Volume 42, conference 1, DOI: 10.1088 / 1757-899X / 42 / 1 / 012047. Summary According to a first aspect of the invention, there is provided a method for an ultrasonic time-of-flight flow meter. The method includes driving an ultrasonic transducer using a first waveform for a first duration, the first waveform configured to cause oscillation of the ultrasonic transducer. The method also includes driving the ultrasonic transducer using a second waveform for a second duration. There is a discontinuity between the first waveform and the second waveform. The second waveform and the second duration are configured to maintain a voltage across the ultrasonic transducer within a predetermined range. The first waveform may include two or more distinct sub-waveforms, each sub- waveform of the first waveform configured to cause oscillation of the ultrasonic transducer. The second waveform may include two or more distinct sub-waveforms, each sub-waveform of the second waveform configured, in combination with the overall second duration, to maintain the voltage across the ultrasonic transducer within the predetermined range. An ultrasonic time-of-flight flow meter may include first and second ultrasonic transducers spaced apart along a fluid flow path. The first and second ultrasonic transducers may be configured such that a transmission path between the first and second ultrasonic transducers has a component in a direction parallel to the fluid flow path. The fluid flow path may be defined by a flow tube. The first and second ultrasonic transducers may be arranged at opposed ends of the flow tube. The first and second ultrasonic transducers may be oriented parallel to a flow direction oriented along the flow tube. The first and second ultrasonic transducers may be spaced apart along the length of the flow tube. The first and second ultrasonic transducers may be arranged at angles to the flow direction such that the transmission path between the first and second ultrasonic transducers includes at least one reflection from an internal wall of the flow tube. The first and second ultrasonic transducers may be arranged at angles to the flow direction such that the transmission path between the first and second ultrasonic transducers includes at least one reflection from a reflector element which is arranged within the flow tube, embedded in a wall of the flow tube, or integrally formed as part of a wall of the flow tube. The first and second ultrasonic transducers may be separated by a distance along the flow path. The method may include alternating between driving the first ultrasonic transducer according to the method and receiving a signal using the second ultrasonic transducer, and driving the second ultrasonic transducer according to the method and receiving a signal using the first ultrasonic transducer. The first waveform may be configured to excite a recommended, or designed for, resonance of the driven ultrasonic transducer. The discontinuity may be a discontinuity in one or more of frequency, gradient of frequency with respect to time, pulse width, duty-cycle and / or phase of the first and second waveforms. The discontinuity may take the form of a deviation between the last cycle or half-cycle of the first waveform and the first cycle or half cycle of the second waveform, the deviation being one or more of about 10% of frequency, about 10% of period, about 10% of pulse width, about 10% of duty cycle and / or more than about <com:Math><semantics>π / 8<annotation encoding="application / x-tex">\pi / 8< / annotation>< / semantics>< / com:Math> of phase. The discontinuity may exist if the first waveform has a first fixed frequency and the second waveform has a second, different, fixed frequency. A discontinuity may exist if the first waveform is a first exponential chirp and the second waveform is a second, different, exponential chirp. A discontinuity may exist if the first waveform is a first linear chirp and the second waveform is a second, different, linear chirp. A discontinuity may exist if the first waveform is a first reciprocal chirp <com:Math><semantics>(1 / x)<annotation encoding="application / x-tex">(1 / x)< / annotation>< / semantics>< / com:Math> and the second waveform is a second, different, reciprocal chirp. A discontinuity may exist if the first waveform is selected from a first group consisting of a first fixed frequency waveform, the first exponential chirp, the first linear chirp or the first reciprocal chirp, and if the second waveform is selected from a second group consisting of a second fixed frequency waveform, the second exponential chirp, the second linear chirp or the second reciprocal chirp. A discontinuity factor, <com:Math><semantics>Df<annotation encoding="application / x-tex">D_f< / annotation>< / semantics>< / com:Math> may be defined as <com:Math><semantics>Df=(f(t1+δt)−f(t1−δt)) / f(t1−δt)<annotation encoding="application / x-tex">D_f = (f(t_1 + \delta t) - f(t_1 - \delta t)) / f(t_1 - \delta t)< / annotation>< / semantics>< / com:Math>, wherein <com:Math><semantics>f(t)<annotation encoding="application / x-tex">f(t)< / annotation>< / semantics>< / com:Math> is the frequency f at time t, <com:Math><semantics>ti<annotation encoding="application / x-tex">t_i< / annotation>< / semantics>< / com:Math> is the time at the end of the first waveform, and <com:Math><semantics>δt<annotation encoding="application / x-tex">\delta t< / annotation>< / semantics>< / com:Math> is a small increment of time, which may take values within the range 10 ns <com:Math><semantics>≤δt≤<annotation encoding="application / x-tex">\leq \delta t \leq< / annotation>< / semantics>< / com:Math> 10 µs. The small increment of time <com:Math><semantics>δt<annotation encoding="application / x-tex">\delta t< / annotation>< / semantics>< / com:Math> may preferably be about 100 ns. Alternatively, the discontinuity factor may be defined as <com:Math><semantics>Df=(f(t1+T(t1))−f(t1)) / f(t1)<annotation encoding="application / x-tex">D_f = (f(t_1 + T(t_1)) - f(t_1)) / f(t_1)< / annotation>< / semantics>< / com:Math>, in which <com:Math><semantics>f(t1)<annotation encoding="application / x-tex">f(t_1)< / annotation>< / semantics>< / com:Math> is the end frequency of the first waveform and <com:Math><semantics>T(t1)=1 / f(t1)<annotation encoding="application / x-tex">T(t_1) = 1 / f(t_1)< / annotation>< / semantics>< / com:Math> is the length of the final period of the first waveform. Whichever definition is used, a discontinuity may exist if the discontinuity factor is greater than or equal to 2. Whichever definition is used, a discontinuity may exist if the discontinuity factor is greater than or equal to 1. Whichever definition is used, a discontinuity may exist if the discontinuity factor is greater than or equal to 0.5. The second duration may be configured to be sufficiently long to allow an oscillation energy of the ultrasonic transducer to reduce to a level whereby the voltage across the ultrasonic transducer will remain within the predetermined range after the end of the second duration. The predetermined range may be a designed for driving voltage range of the ultrasonic transducer, or the designed for driving voltage range of the ultrasonic transducer plus an overvoltage tolerance. The predetermined range may be the designed for driving voltage of the ultrasonic transducer plus an overvoltage tolerance of ±5%, ±10% or <com:Math><semantics>±15%<annotation encoding="application / x-tex">\pm 15\%< / annotation>< / semantics>< / com:Math>. The predetermined range may be a rail-to-rail voltage of a further component which is connected to the ultrasonic transducer in series or in parallel, or the rail-to-rail voltage of the further component plus an overvoltage tolerance. The predetermined range may be the rail-to-rail voltage of the further component plus an overvoltage tolerance of <com:Math><semantics>±5%<annotation encoding="application / x-tex">\pm 5\%< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>±10%<annotation encoding="application / x-tex">\pm 10\%< / annotation>< / semantics>< / com:Math> or <com:Math><semantics>±15%<annotation encoding="application / x-tex">\pm 15\%< / annotation>< / semantics>< / com:Math>. The overvoltage tolerance of the further component may be ±1 mV, ±10 mV, ±200 mV or ±600 mV. The further component may be a switch, a multiplexer, an integrated circuit, and so forth. The method may prevent or reduce coupling between the ultrasonic transducer and one or more further ultrasonic transducers via intermediate components connecting the ultrasonic transducer to the one or more further ultrasonic transducers. For example, the method may prevent or reduce coupling between the first and second ultrasonic transducers. The predetermined range may be between and including -0.2 V to 3.5 V. The predetermined range may be between and including -0.2 V to 5.2 V. The first waveform may have a frequency spectrum in which a majority of the power is within one or more bandwidths corresponding to respective resonances of the ultrasonic transducer, and the second waveform may have a frequency spectrum in which a majority of the power is outside the one or more bandwidths corresponding to respective resonances of the ultrasonic transducer. The first waveform may have a frequency spectrum in which 50% or more, 60% or more, 70% or more, 80% or more, or 90% or more of the power is within the one or more bandwidths corresponding to respective resonances of the ultrasonic transducer. The second waveform may have a frequency spectrum in which 50% or more, 60% or more, 70% or more, 80% or more, or 90% or more of the power is outside the one or more bandwidths corresponding to respective resonances of the ultrasonic transducer. The first waveform may have a substantially constant base frequency. The second waveform may have a substantially constant base frequency. Depending upon the application, the term "substantially" may correspond to a tolerance of <com:Math><semantics>±5%<annotation encoding="application / x-tex">\pm 5\%< / annotation>< / semantics>< / com:Math>, or <com:Math><semantics>±10%<annotation encoding="application / x-tex">\pm 10\%< / annotation>< / semantics>< / com:Math>. The frequency of the first waveform may vary as a function of time. The frequency of the first waveform may vary linearly as a function of time. The frequency of the first waveform may vary exponentially as a function of time. The frequency of the first waveform may vary reciprocally as a function of time. The first waveform may take the form of a chirp. The frequency of the second waveform may vary as a function of time. The frequency of the second waveform may vary linearly as a function of time. The frequency of the second waveform may vary exponentially as a function of time. The frequency of the second waveform may vary reciprocally as a function of time. The second waveform may take the form of a chirp. The second waveform may have a phase shift of between and including <com:Math><semantics>π / 2<annotation encoding="application / x-tex">\pi / 2< / annotation>< / semantics>< / com:Math> to <com:Math><semantics>3π / 2<annotation encoding="application / x-tex">3\pi / 2< / annotation>< / semantics>< / com:Math> with respect to the first waveform, and the second duration may be insufficient to cause oscillation of the ultrasonic transducer in response to the second waveform. The second duration may be insufficient to generate significant oscillation of the ultrasonic transducer. The second duration may be configured such that a maximum amplitude of any voltage oscillation induced across the ultrasonic transducer following the end of the second waveform is less than or equal to 200 mV. The ultrasonic transducer may be a piezoelectric transducer. The method may be used to measure the flow rate of a liquid. The method may be used to measure the flow rate of a gas. The method may be used to measure the flow rate of water. The method may be used to measure the flow rate of natural gas. The method may be used to measure a flow rate used for fiscal metering purposes. According to a second aspect of the invention, there is provided an ultrasonic time-of- flight flow meter, including a first ultrasonic transducer and a second ultrasonic transducer spaced apart along a fluid flow path and configured such that a transmission path between the first and second ultrasonic transducers has a component in a direction parallel to the fluid flow path. The ultrasonic time-of-flight flow meter also includes a controller configured to drive the first and second ultrasonic transducers alternately. The controller is configured to drive the driven ultrasonic transducer using a first waveform for a first duration. The first waveform is configured to cause oscillation of the driven ultrasonic transducer. The controller is also configured to drive the driven ultrasonic transducer using a second waveform for a second duration. There is a discontinuity between the first waveform and the second waveform. The second waveform and the second duration are configured to maintain a voltage across the driven ultrasonic transducer within a predetermined range. The fluid flow path may be defined by a flow tube. The first and second ultrasonic transducers may be arranged at opposed ends of a flow tube. The first and second ultrasonic transducers may be oriented parallel to a flow direction oriented along the flow tube. The first and second ultrasonic transducers may be spaced apart along the length of the flow tube. The first and second ultrasonic transducers may be arranged at angles to the flow direction such that the transmission path between the first and second ultrasonic transducers includes at least one reflection from an internal wall of the flow tube. The first and second ultrasonic transducers may be arranged at angles to the flow direction such that the transmission path between the first and second ultrasonic transducers includes at least one reflection from a reflector element which is arranged within the flow tube, embedded in a wall of the flow tube, or integrally formed as part of a wall of the flow tube. The first waveform may be configured to excite a recommended, or designed for, resonance of the first and / or second ultrasonic transducer. The discontinuity may be a discontinuity in one or more of the senses defined with reference to the method. The second duration may be configured to be sufficiently long to allow an oscillation energy of the driven ultrasonic transducer to reduce to a level whereby the voltage across the driven ultrasonic transducer will remain within the predetermined range after the end of the second duration. The predetermined range may be defined in the same way as for the method. The first waveform may have a frequency spectrum in which a majority of the power is within one or more bandwidths corresponding to respective resonances of the driven ultrasonic transducer, and the second waveform may have a frequency spectrum in which a majority of the power is outside the one or more bandwidths corresponding to respective resonances of the driven ultrasonic transducer. The first waveform may have a frequency spectrum in which 50% or more, 60% or more, 70% or more, 80% or more, or 90% or more of the power is within the one or more bandwidths corresponding to respective resonances of the driven ultrasonic transducer. The second waveform may have a frequency spectrum in which 50% or more, 60% or more, 70% or more, 80% or more, or 90% or more of the power is outside the one or more bandwidths corresponding to respective resonances of the driven ultrasonic transducer. The first waveform may have a substantially constant base frequency. The second waveform may have a substantially constant base frequency. Depending upon the application, the term "substantially" may correspond to a tolerance of <com:Math><semantics>±5%<annotation encoding="application / x-tex">\pm 5\%< / annotation>< / semantics>< / com:Math>, or <com:Math><semantics>±10%<annotation encoding="application / x-tex">\pm 10\%< / annotation>< / semantics>< / com:Math>. The frequency of the first waveform may vary as a function of time. The frequency of the first waveform may vary linearly as a function of time. The frequency of the first waveform may vary exponentially as a function of time. The frequency of the first waveform may vary reciprocally as a function of time. The first waveform may take the form of a chirp. The frequency of the second waveform may vary as a function of time. The frequency of the second waveform may vary linearly as a function of time. The frequency of the second waveform may vary exponentially as a function of time. The frequency of the second waveform may vary reciprocally as a function of time. The second waveform may take the form of a chirp. The second waveform may have a phase shift of between and including <com:Math><semantics>π / 2<annotation encoding="application / x-tex">\pi / 2< / annotation>< / semantics>< / com:Math> to <com:Math><semantics>3π / 2<annotation encoding="application / x-tex">3\pi / 2< / annotation>< / semantics>< / com:Math> with respect to the first waveform, and the second duration may be insufficient to cause significant oscillation of the driven ultrasonic transducer in response to the second waveform. The second duration may be configured such that a maximum amplitude of any voltage oscillation induced across the driven ultrasonic transducer following the end of the second waveform is less than or equal to 200 mV. The ultrasonic transducer may be a piezoelectric transducer. The second waveform may be configured to suppress coupling between the first and second ultrasonic transducers. A base frequency of the second waveform may be greater than 1.1 times a primary resonant frequency of the ultrasonic transducer. A base frequency of the second waveform may be greater than 2 times the primary resonant frequency of the driven ultrasonic transducer. A base frequency of the second waveform may be greater than 3 times the primary resonant frequency of the ultrasonic transducer. A base frequency of the second waveform may be greater than 10 times the primary resonant frequency of the ultrasonic transducer. A base frequency of the second waveform may be less than 0.9 times a primary resonant frequency of the ultrasonic transducer. A base frequency of the second waveform may be less than 0.5 times the primary resonant frequency of the ultrasonic transducer. A base frequency of the second waveform may be less than 0.2 times the primary resonant frequency of the ultrasonic transducer. A base frequency of the second waveform may be less than 0.1 times the primary resonant frequency of the ultrasonic transducer. A base frequency of the second waveform may be less than 0.01 times the primary resonant frequency of the ultrasonic transducer. The ultrasonic transducer may be a piezoelectric transducer. The ultrasonic transducer may be a solenoid transducer. A distance separating the first and second ultrasonic transducers along the fluid flow path may be less than 25 mm, less than 50 mm, less than 70 mm, less than 100 mm, less than 200 mm or less than 500 mm. Brief Description of the Drawings Certain embodiments of the present invention will now be described, by way of example, with reference to the accompanying drawings in which: Figure 1 illustrates an ultrasonic time-of-flight flow rate meter; Figure 2 illustrates an alternative configuration for ultrasonic time-of-flight flow rate measurements; Figure 3 illustrates an alternative configuration for ultrasonic time-of-flight flow rate measurements; Figure 4 illustrates ringing of an ultrasonic transducer after the end of a driving signal; Figure 5 illustrates self-oscillation of an ultrasonic transducer after the end of a driving signal; Figure 6 illustrates an example of a driving signal including first and second waveforms; Figure 7 illustrates modified ringing of an ultrasonic transducer after the end of a driving signal; Figure 8 is a schematic illustration of a frequency response of an ultrasonic transducer; Figure 9 illustrates an example of a driving signal including first and second waveforms; Figure 10 illustrates an example of a driving signal including first and second waveforms; Figure 11 illustrates an arrangement for measuring leakage current between transmitting and receiving pathways of an ultrasonic time-of-flight flow rate meter; Figure 12 presents measurements of a current injected to the arrangement of Figure 11 as a function of applied voltage; Figure 13 presents measurements of a leakage current in the arrangement of Figure 11 as a function of applied voltage; Figure 14 presents measurements of a received signal which is not affected by ringing; Figure 15 presents measurements of a received signal which is affected by ringing; Figure 16 presents a comparison of a driving signal which includes only a first waveform with the corresponding a received signal and the voltage across a driven ultrasonic transducer; Figure 17 presents a further comparison of a driving signal which includes only a first waveform with the corresponding received signal and the voltage across a driven ultrasonic transducer; Figure 18 presents a comparison of a driving signal which includes first and second waveforms with the corresponding received signal and the voltage across a driven ultrasonic transducer; Figure 19 presents a portion of the driving signal presented in Figure 18 on a shorter timebase; Figure 20 presents a portion of the voltage across a driven ultrasonic transducer presented in Figure 18 on a shorter timebase; Figure 21 illustrates an example of a frequency variation of first and second waveforms; Figure 22 illustrates a further example of a frequency variation of first and second waveforms; and Figure 22 illustrates a further example of a frequency variation of first and second waveforms; Detailed Description of Certain Embodiments In the following, like parts are denoted by like reference numbers. The specification relates to the use of ultrasonic transducers. Once an ultrasonic transducer has begun oscillating, the ultrasonic transducer stores an oscillation energy which is associated with the motion. This oscillation energy will dissipate with time without continuous energy input. However, when an excitation signal to an ultrasonic transducer is stopped, the oscillation energy causes the ultrasonic transducer to continue oscillating, giving rise to an effect termed "ringing". This ringing, if not properly managed, can cause various problems for ultrasonic time-of-flight based flow measurements. According to previous methods for operating ultrasonic transducers, at the end of a transmit pulse, a transmit driver is set to, for example, either o V or a +ve rail voltage. The resonant oscillation of the ultrasonic transducer continues following the end of the transmit pulse. This oscillation may induce a ringing voltage across the ultrasonic transducer, which is now clamped to, for example, either o V or the +ve rail voltage. In other examples, differential driving may be used. Using differential driving may mean that neither side of the ultrasonic transducer is clamped to ground or o V. The induced ringing voltage may drive other components to which the ultrasonic transducer is connected, for example a multiplexer or an active semiconductor component, beyond the power rail voltage and / or overvoltage tolerance. This may reverse bias such connected components. If an overvoltage tolerance is exceeded, leakage currents may flow from the transmitting ultrasound transducer to other parts of the circuit. In some cases, the leaked current originating from the ringing voltage may be coupled into a receiver amplifier and / or a receiving ultrasound transducer. Such coupling may cause interference with flow rate measurements. A non-exhaustive list of some of the problems which may result from ringing voltages induced in transmitting ultrasonic transducers includes: * Unwanted coupling to connected electronics; ₩ Interference with measurements; Causing cycle slips (this refers to one or more cycles being missed by the receiver, leading to an error of the corresponding number of periods); ⇔ Timing errors in "time of flight" measurements; and • Increasing the minimum required separation distance of transmit and receive ultrasonic transducers. Several approaches for mitigating the effects of induced ringing voltages in transmitting ultrasound transducers have been considered. For example, a clamping diode may be fitted to an ultrasonic transducer, or connected components, to prevent excessive over- voltages. Alternatively, additional discrete components may be added in the form of a clamping circuit connected to the ultrasonic transducer, for example a MOSFET controlled circuit configured to become conductive and drain energy from a transmitting ultrasonic transducer once the transmit pulse is finished. Other options include using a digital to analogue converter (DAC) plus buffer and / or filter to drive a transmitting ultrasonic transducer, or using line drives that can drive middle rail voltages. The problem with these previous approaches is that the number of components and the complexity for an ultrasonic flow meter are increased, with consequences for the size, cost and long term reliability of the flow meter. These approaches may also add capacitance, make matching the ultrasonic transducers more difficult, decrease the coupled energy, and / or decrease efficiency. A consequence of the additional non- matching components is that the zero flow offset of the flow rate meter may be increased. Finally, it is also possible to simply accept the problem of induced ringing voltages, and to increase the separation between paired ultrasonic transducers in an attempt to ensure that ringing voltages in the transmitting ultrasonic transducer have decayed before the transmitted pulse reaches the receiving ultrasonic transducer. This approach is also unsatisfactory because the size of a flow rate meter must be increased to accommodate a larger distance between paired ultrasonic transducers. Increasing the distance also has the effect of increasing the energy needed to make measurements. In general, the greater the distance, the more acoustic attenuation will occur before a transmitted pulse reaches a receiving ultrasonic transducer. In order to maintain a given signal-to-noise ratio over a greater distance, more energy is needed in the drive pulse, for example, a higher drive voltage or an increase in the number of pulses. Flow meters may often be used for long term installations in locations where there is no mains electric connection available, and may need to operate using battery power or energy harvesting, so that the energy required for measurements is a consideration. The present specification is concerned with methods to manage induced ringing voltages of transmitting ultrasonic transducers. The methods of the present specification do not require additional electronic components, and may be implemented within simple, compact and cheap ultrasonic flow rate meters. Consequently, the methods of the present specification may allow a relatively low zero- flow offset to be maintained. Referring to Figure 1, an ultrasonic time-of-flight flow rate meter 1 is shown. The ultrasonic time-of-flight flow rate meter 1 includes a first ultrasonic transducer 2 and a second ultrasonic transducer 3. The first and second ultrasonic transducers 2, 3 are spaced apart along a fluid flow path 6 in the form of a flow tube 4. The first and second transducers 2, 3 are configured such that a transmission path 5 between the first and second ultrasonic transducers 2, 3 has a component in a direction parallel to the fluid flow path 6. In the example shown in Figure 1, the first and second ultrasonic transducers 2, 3 are arranged at opposite ends of the flow tube 4. The ultrasonic transducers 2, 3 are separated by a distance, d, in the direction parallel to the fluid flow path 6. The ultrasonic transducers 2, 3 may be piezoelectric transducers, solenoid transducers, and so forth. The ultrasonic time-of-flight flow rate meter 1 also includes a controller 7, which is configured to drive the first and second ultrasonic transducers 2, 3 alternately. The controller 7 may be a microcontroller, a microprocessor, or any other suitable data processing apparatus. In order to make a measurement of flow rate, the controller 7 may drive the first ultrasonic transducer 2 and measure a first time-of-flight <com:Math><semantics>Δti<annotation encoding="application / x-tex">\Delta t_i< / annotation>< / semantics>< / com:Math> based on reception of the signal at the second ultrasonic transducer 3. The controller 7 then measures a second time of flight <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> by driving the second ultrasonic transducer 3 and receiving the signal at the first ultrasonic transducer 2. If the fluid in the fluid flow tube 4, which may be a gas or a liquid, is moving away from the first ultrasonic transducer 2 and towards the second ultrasonic transducer 3 with a velocity, v, along the fluid flow path 6 then the first and second times-of-flight may be expressed as: [Image disponible dans le document PDF, Image available in the PDF document] (1) In which <com:Math><semantics>tfi<annotation encoding="application / x-tex">t_{fi}< / annotation>< / semantics>< / com:Math> is the time-of-flight from the first ultrasonic transducer 2 to the second ultrasonic transducer 3, <com:Math><semantics>tf2<annotation encoding="application / x-tex">t_{f2}< / annotation>< / semantics>< / com:Math> is the time-of-flight from the second ultrasonic transducer 3 to the first ultrasonic transducer 2, d is the spacing of the ultrasonic transducers 2, 3, v is the fluid velocity and c is the speed of sound in the fluid 17. The equations may be re- arranged to provide an expression for the velocity of the fluid: [Image disponible dans le document PDF, Image available in the PDF document] (2) The controller 7 is configured to drive the respective ultrasonic transducer 2, 3, i.e. the first or second ultrasonic transducer 2, 3 currently acting as transmitter, using a first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> for a first duration <com:Math><semantics>Δti=ti−to<annotation encoding="application / x-tex">\Delta t_i = t_i - t_o< / annotation>< / semantics>< / com:Math>, in which <com:Math><semantics>to<annotation encoding="application / x-tex">t_o< / annotation>< / semantics>< / com:Math> is the time at which excitation of the transmitting ultrasonic transducer 2, 3 is started and <com:Math><semantics>ti<annotation encoding="application / x-tex">t_i< / annotation>< / semantics>< / com:Math> is the time at the end of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math>. The first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> is configured to cause oscillation of the transmitting ultrasonic transducer 2, 3. The first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> may be configured to excite a recommended, or designed for, resonance of the first and / or second ultrasonic transducer 2, 3. For example, if an ultrasonic transducer 2, 3 has a recommended resonance centred at a primary resonance frequency <com:Math><semantics>fi<annotation encoding="application / x-tex">f_i< / annotation>< / semantics>< / com:Math>, then the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math> preferably includes all, or a majority of, the signal power at frequencies lying within a bandwidth <com:Math><semantics>δfi<annotation encoding="application / x-tex">\delta f_i< / annotation>< / semantics>< / com:Math> centred around the primary resonance frequency <com:Math><semantics>fi<annotation encoding="application / x-tex">f_i< / annotation>< / semantics>< / com:Math>. Following the first duration <com:Math><semantics>Δti<annotation encoding="application / x-tex">\Delta t_i< / annotation>< / semantics>< / com:Math>, the controller 7 is configured to drive the transmitting ultrasonic transducer 2, 3 using a second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> for a second duration <com:Math><semantics>Δt2=<annotation encoding="application / x-tex">\Delta t_2 =< / annotation>< / semantics>< / com:Math> <com:Math><semantics>t2−t1<annotation encoding="application / x-tex">t_2 - t_1< / annotation>< / semantics>< / com:Math>, in which <com:Math><semantics>t2<annotation encoding="application / x-tex">t_2< / annotation>< / semantics>< / com:Math> is the time at the end of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>. The second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> and the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math>, are configured to maintain a voltage <com:Math><semantics>VT<annotation encoding="application / x-tex">V_T< / annotation>< / semantics>< / com:Math> across the transmitting ultrasonic transducer 2, 3 within a predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math>. For example, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may include frequencies outside the bandwidth <com:Math><semantics>δfi<annotation encoding="application / x-tex">\delta f_i< / annotation>< / semantics>< / com:Math> centred around the primary resonance frequency <com:Math><semantics>fi<annotation encoding="application / x-tex">f_i< / annotation>< / semantics>< / com:Math>, or preferably outside the bandwidths corresponding to any resonances of the ultrasonic transducers 2, 3. Alternatively, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may be in full or partial anti-phase with the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, so as to oppose and dampen the oscillations of the transmitting ultrasonic transducer 2, 3. In this latter case, the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> should be sufficiently short to avoid re-exciting the transmitting ultrasonic transducer 2, 3 after the initial damping of oscillatory motion. The controller 7 drives the ultrasonic transducer 2, 3 using pulsed or square waveforms having variable frequency, duty cycle and so forth. The controller 7 may output either a high rail voltage, <com:Math><semantics>VRH<annotation encoding="application / x-tex">V_{RH}< / annotation>< / semantics>< / com:Math>, or a low rail voltage <com:Math><semantics>VRL<annotation encoding="application / x-tex">V_{RL}< / annotation>< / semantics>< / com:Math>, and the first and second waveforms <com:Math><semantics>V1(t),V2(t)<annotation encoding="application / x-tex">V_1(t), V_2(t)< / annotation>< / semantics>< / com:Math> alternate between high voltage <com:Math><semantics>VRH<annotation encoding="application / x-tex">V_{RH}< / annotation>< / semantics>< / com:Math> and low voltage <com:Math><semantics>VRL<annotation encoding="application / x-tex">V_{RL}< / annotation>< / semantics>< / com:Math>. This configuration allows the flow rate meter 1 to be simple and compact, with low mismatch of components, permitting relatively low zero-flow offset. According to the methods of the present specification, there should be a discontinuity between the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math> and the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>. The discontinuity may take many forms, for example, the discontinuity may be in the frequencies of the first and second waveforms <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>. For example, the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math> may have a fixed base frequency <com:Math><semantics>fBi<annotation encoding="application / x-tex">f_{Bi}< / annotation>< / semantics>< / com:Math> and the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may have a different fixed base frequency <com:Math><semantics>fB2≠fB1<annotation encoding="application / x-tex">f_{B2} \neq f_{B1}< / annotation>< / semantics>< / com:Math>. The first and second waveforms <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> need not have fixed base frequencies, and in some examples one or both of the base frequencies <com:Math><semantics>fB1<annotation encoding="application / x-tex">f_{B1}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math> may be functions of time, i.e. <com:Math><semantics>fBi(t)<annotation encoding="application / x-tex">f_{Bi}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>fBi(t)<annotation encoding="application / x-tex">f_{Bi}(t)< / annotation>< / semantics>< / com:Math>. In such examples, the discontinuity may occur in the values of base frequency, i.e. <com:Math><semantics>fBi(ti)≠fBi(ti)<annotation encoding="application / x-tex">f_{Bi}(t_i) \neq f_{Bi}(t_i)< / annotation>< / semantics>< / com:Math>. Waveforms in which the base frequency changes over time are sometimes referred to as "chirps". Typical types of chirp include a linear chirp having a frequency varying according to: [Image disponible dans le document PDF, Image available in the PDF document] (3) In which <com:Math><semantics>fB(t)<annotation encoding="application / x-tex">f_B(t)< / annotation>< / semantics>< / com:Math> is the base frequency of either the first waveform <com:Math><semantics>fBi(t)<annotation encoding="application / x-tex">f_{Bi}(t)< / annotation>< / semantics>< / com:Math> or the second waveform <com:Math><semantics>fB2(t)<annotation encoding="application / x-tex">f_{B2}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>α<annotation encoding="application / x-tex">\alpha< / annotation>< / semantics>< / com:Math> is a gradient and <com:Math><semantics>β<annotation encoding="application / x-tex">\beta< / annotation>< / semantics>< / com:Math> is a constant. Another type of chirp is an exponential chirp having a frequency varying according to: [Image disponible dans le document PDF, Image available in the PDF document] (4) In which <com:Math><semantics>γ<annotation encoding="application / x-tex">\gamma< / annotation>< / semantics>< / com:Math> and <com:Math><semantics>ε<annotation encoding="application / x-tex">\varepsilon< / annotation>< / semantics>< / com:Math> are constants. A further type of chirp is a reciprocal chirp having a frequency varying according to: [Image disponible dans le document PDF, Image available in the PDF document] (5) In which <com:Math><semantics>ρ<annotation encoding="application / x-tex">\rho< / annotation>< / semantics>< / com:Math> is a scaling constant and <com:Math><semantics>τ<annotation encoding="application / x-tex">\tau< / annotation>< / semantics>< / com:Math> is an optional constant included to avert divergence for <com:Math><semantics>t→0<annotation encoding="application / x-tex">t \rightarrow 0< / annotation>< / semantics>< / com:Math>. The first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> may be any one of a fixed frequency signal, a linear chirp, an exponential chirp, a reciprocal chirp, and so forth. Independently of the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may be any one of a fixed frequency signal, a linear chirp, an exponential chirp, a reciprocal chirp, and so forth. Additionally or alternatively, the discontinuity may occur in the gradients of base frequency <com:Math><semantics>fBt(t)<annotation encoding="application / x-tex">f_{B_t}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>fB2(t)<annotation encoding="application / x-tex">f_{B_2}(t)< / annotation>< / semantics>< / com:Math> with respect to time: [Image disponible dans le document PDF, Image available in the PDF document] (6) Other forms which the discontinuity may take include a discontinuity in phase between the first and second waveforms <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>. For example: [Image disponible dans le document PDF, Image available in the PDF document] (7) In which <com:Math><semantics>V0<annotation encoding="application / x-tex">V_0< / annotation>< / semantics>< / com:Math> is an amplitude and in which the phase <com:Math><semantics>φ1≠φ2<annotation encoding="application / x-tex">\varphi_1 \neq \varphi_2< / annotation>< / semantics>< / com:Math>. In some examples according to the present specification, the discontinuity may take the form of a deviation between the last cycle or half-cycle of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> and the first cycle or half cycle of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>, the deviation being one or more of 10% of frequency, 10% of period, 10% of pulse width, 10% of duty cycle and / or more than <com:Math><semantics>π / 8<annotation encoding="application / x-tex">\pi / 8< / annotation>< / semantics>< / com:Math> of phase. In practical circumstances, it may be useful to define a discontinuity factor, <com:Math><semantics>Dt<annotation encoding="application / x-tex">D_t< / annotation>< / semantics>< / com:Math>, as <com:Math><semantics>Df=(fB2(t1+δt)−fB1(t1−δt)) / fB1(t1−δt)<annotation encoding="application / x-tex">D_f = (f_{B2}(t_1 + \delta t) - f_{B1}(t_1 - \delta t)) / f_{B1}(t_1 - \delta t)< / annotation>< / semantics>< / com:Math>, in which <com:Math><semantics>δt<annotation encoding="application / x-tex">\delta t< / annotation>< / semantics>< / com:Math> is a small increment of time, which may take values within the range 10 ns <com:Math><semantics>≤δt≤<annotation encoding="application / x-tex">\leq \delta t \leq< / annotation>< / semantics>< / com:Math> 10 µs. The small increment of time <com:Math><semantics>δt<annotation encoding="application / x-tex">\delta t< / annotation>< / semantics>< / com:Math> may preferably be about 100 ns. Alternatively, the discontinuity factor may be defined as <com:Math><semantics>Df=(f(tt+T(tt))−f(tt)) / f(tt)<annotation encoding="application / x-tex">D_f = (f(t_t + T(t_t)) - f(t_t)) / f(t_t)< / annotation>< / semantics>< / com:Math>, in which <com:Math><semantics>f(tt)<annotation encoding="application / x-tex">f(t_t)< / annotation>< / semantics>< / com:Math> is the end frequency of the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math> and <com:Math><semantics>T(t1)=1 / f(t1)<annotation encoding="application / x-tex">T(t_1) = 1 / f(t_1)< / annotation>< / semantics>< / com:Math> is the length of the final period of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math>. Whichever definition is used, in some examples the discontinuity factor <com:Math><semantics>Df<annotation encoding="application / x-tex">D_f< / annotation>< / semantics>< / com:Math> is preferably greater than or equal to 2. In other examples the discontinuity factor <com:Math><semantics>Df<annotation encoding="application / x-tex">D_f< / annotation>< / semantics>< / com:Math> may be greater than or equal to 1. In further examples the discontinuity factor <com:Math><semantics>Df<annotation encoding="application / x-tex">D_f< / annotation>< / semantics>< / com:Math> may be greater than or equal to 0.5. For example, if the base frequency <com:Math><semantics>fBi<annotation encoding="application / x-tex">f_{Bi}< / annotation>< / semantics>< / com:Math> of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> is 440 kHz just before the end <com:Math><semantics>ti<annotation encoding="application / x-tex">t_i< / annotation>< / semantics>< / com:Math> of the first duration <com:Math><semantics>Δti<annotation encoding="application / x-tex">\Delta t_i< / annotation>< / semantics>< / com:Math>, then in an example of the method using a discontinuity factor of <com:Math><semantics>Df=3.55<annotation encoding="application / x-tex">D_f = 3.55< / annotation>< / semantics>< / com:Math>, the base frequency <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math> of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> would be 2 MHz just after the start of the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math>. Alternatively, if the method was implemented using a discontinuity factor of <com:Math><semantics>Df=1<annotation encoding="application / x-tex">D_f = 1< / annotation>< / semantics>< / com:Math>, then the base frequency <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math> of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> would be 880 kHz just after the start of the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math>. In a further example, if the method was implemented using a discontinuity factor of <com:Math><semantics>Df=0.5<annotation encoding="application / x-tex">D_f = 0.5< / annotation>< / semantics>< / com:Math>, then the base frequency <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math> of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> would be 660 kHz just after the start of the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math>. Further examples of the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> and the discontinuity are described hereinafter. The hereinbefore described types of discontinuity are not mutually exclusive. In examples according to the present specification, multiple types of the hereinbefore described discontinuities may exist simultaneously between the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math> and the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>. The second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> is preferably configured to be sufficiently long to allow an energy associated with the oscillation of the first or second ultrasonic transducer 2, 3 to reduce to a level whereby the voltage <com:Math><semantics>VT<annotation encoding="application / x-tex">V_T< / annotation>< / semantics>< / com:Math> across the first or second ultrasonic transducer 2, 3 will remain within the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math> after the end of the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math>. An appropriate second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> may be determined from calibration experiments, by varying the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> and measuring the amplitude of any induced ringing voltage which occurs at the end of the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math>. Individual calibration of each ultrasonic time-of-flight flow rate meter 1 is not necessary. Provided that calibration experiments are performed using a sampling of ultrasonic time-of- flight flow rate meters 1 which is large enough to capture the variance in performance, a single value of the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> may be determined for use with subsequently constructed ultrasonic time-of-flight flow rate meters 1. The key components of an ultrasonic time-of-flight flow rate meter 1 for implementing methods of the present specification are the first and second ultrasonic transducers 2, 3, the flow tube 4 and the controller 7, as described hereinbefore. For context Figure 1 shows further components of one example of an ultrasonic time-of-flight flow rate meter 1. The controller 7 outputs a drive signal 8 to the transmitting ultrasonic transducer 2, 3 via a first impedance matching resistor R1 and a first switch or multiplexer 9. The first switch 9 may be controlled to supply the drive signal 8 to either the first ultrasonic transducer 2 or the second ultrasonic transducer 3. Whichever ultrasonic transducer 2, 3 receives the drive signal 8 is the transmitting ultrasonic transducer for a measurement. The drive signal 8 includes or consists of the hereinbefore described first and second waveforms <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>. The first impedance matching resistor R1 may have a value of 820 <com:Math><semantics>Ω<annotation encoding="application / x-tex">\Omega< / annotation>< / semantics>< / com:Math>. Whichever ultrasonic transducer 2, 3 does not receive the drive signal 8 is the receiving ultrasonic transducer for a measurement. The receiving ultrasonic transducer 2, 3 detects an ultrasound signal from the transmitting ultrasonic transducer 2, 3, and converts it into a received electrical signal 10. The received signal 10 is returned to the controller 7 via a second switch or multiplexer 11 and a signal conditioning circuit 12. The first and second switches 9, 11 are configured so that when, for example, the first switch 9 connects to the first ultrasonic transducer 2, the second switch 11 will connect to the second ultrasonic transducer 3, and vice-versa. The signal conditioning circuit 12 may perform amplification and or filtering of the received signal 10 to generate a conditioned signal 13. The controller determines a time-of-flight by comparing the drive signal 8 with the conditioned signal 13. A second matching resistor R2 may have a value of 820 <com:Math><semantics>Ω<annotation encoding="application / x-tex">\Omega< / annotation>< / semantics>< / com:Math>. The flow tube 4 is contained within an enclosure 14 having a fluid inlet 15 and a fluid outlet 16. The enclosure 14 is arranged so that fluid 17 entering the fluid inlet 15 can only pass to the fluid outlet 16 by passing along the fluid flow path 6 through the flow tube 4. The fluid 17 may be a liquid or a gas. For example, the fluid 17 may be water or natural gas. The methods of the present specification will be principally explained with reference to the ultrasonic time-of-flight flow rate meter 1 shown in Figure 1. However, as noted hereinbefore, the methods of the present specification are not limited to this configuration of an ultrasonic time-of-flight flow rate meter 1. Alternative time-of-flight measurement configurations Referring also to Figure 2, a first alternative configuration for time-of-flight measurements using first and second ultrasonic transducers 2, 3 is shown. Instead of being arranged at opposed ends of the flow tube 4, the first and second ultrasonic transducers 2, 3 may be offset from the fluid flow path 6 formed by the flow tube 4, and oriented at angles <com:Math><semantics>±θ<annotation encoding="application / x-tex">\pm \theta< / annotation>< / semantics>< / com:Math> to the fluid flow path 6. Both ultrasonic transducers 2, 3 are arranged on a first side 18 of the flow tube 4. The transmission path 5 includes a reflection from a second side 19 of the flow tube 4, opposed to the first side 18. The flow tube 4 may include a separate reflector (not shown), or the second side 19 of the flow tube 4 may be integrally formed to function as a suitable reflector for the transmission path 5. The component of the length of the transmission path 5 that is within the flow tube 4 and parallel to the fluid flow path 6 has length d, such that if the width of the flow tube 4 is w, then <com:Math><semantics>tan(θ)=2w / d<annotation encoding="application / x-tex">tan(\theta) = 2w / d< / annotation>< / semantics>< / com:Math>. Provided that the geometry is known or may be calibrated, Equations (1) and (2) may be adapted for time-of-flight based flow rate measurements using the configuration shown in Figure 2. In practice, a flow- rate meter may be calibrated using at least one flow rate of fluid passing through the meter, which compensates for various parameters including the physical geometry of the meter. The first and second ultrasonic transducers 2, 3 may be external to the flow tube 4, as shown in Figure 2. In such a configuration, first and second ultrasonic transducers 2, 3 may be connected to the flow tube 4 using impedance matching materials 20 to enhance transmission of ultrasound in and / or out of the flow tube 4. Alternatively, the first and / or second ultrasonic transducers 2, 3 may be embedded within, or integrally formed as part of, a wall providing the first side 18. Referring also to Figure 3, a second alternative configuration for time-of-flight measurements using first and second ultrasonic transducers 2, 3 is shown. The second alternative configuration of first and second ultrasonic transducers 2, 3 is similar to the first alternative configuration shown in Figure 2, except that the second ultrasonic transducer 3 is arranged on the second side 19 of the flow tube 4, such that the transmission path 5 does not include a reflection, and such that <com:Math><semantics>tan(θ2)=w / d<annotation encoding="application / x-tex">tan(\theta_2) = w / d< / annotation>< / semantics>< / com:Math>. Ringing in an ultrasonic time-of-flight flow rate meter Referring also to Figures 4 and 5, the induced ringing voltages which the presently described methods may reduce or prevent will be further explained. In the example shown in relation to Figures 4 and 5, the drive signal 8 only includes the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>. Referring in particular to Figure 4, the voltage <com:Math><semantics>VT(t)<annotation encoding="application / x-tex">V_T(t)< / annotation>< / semantics>< / com:Math> across the transmitting ultrasonic transducer 2, 3 is illustrated. It should be noted that the voltage <com:Math><semantics>VT(t)<annotation encoding="application / x-tex">V_T(t)< / annotation>< / semantics>< / com:Math> across the transmitting ultrasonic transducer 2, 3 may not be identical to the drive signal 8 as a result of the finite capacitance and inductance of the circuit. In particular, the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> of the drive signal 8 in the illustrated example takes the form of a square or pulsed waveform which varies between an upper rail voltage <com:Math><semantics>VRU<annotation encoding="application / x-tex">V_{RU}< / annotation>< / semantics>< / com:Math> and a lower rail voltage <com:Math><semantics>VRL<annotation encoding="application / x-tex">V_{RL}< / annotation>< / semantics>< / com:Math>. When the drive signal 8 supplied to a transmitting ultrasonic transducer finishes, the ideal situation would be that the ultrasonic transducer 2, 3 stops vibrating immediately. For example, ideally the oscillation 21 of the ultrasonic transducer 2, 3 should stop when the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math> ends at time <com:Math><semantics>t1<annotation encoding="application / x-tex">t_1< / annotation>< / semantics>< / com:Math>. However, in reality the ultrasonic transducers 2, 3 will not stop immediately because of the remaining oscillation energy, and the ultrasonic transducer will undergo a self- oscillation 22 which decays over time. As a consequence of the nature of the ultrasonic transducer 2, 3 as a device for converting between voltage and displacement, the self- oscillation 22 of the ultrasonic transducer 2, 3 will induce a ringing voltage 23, across the ultrasonic transducer 2, 3. When the output which supplies the drive signal 8 is clamped to, for example, <com:Math><semantics>VRL=0<annotation encoding="application / x-tex">V_{RL} = 0< / annotation>< / semantics>< / com:Math> V at the end of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math>, the superposition of the induced ringing voltage 23 may cause the voltage across the ultrasonic transducer <com:Math><semantics>VT(t)<annotation encoding="application / x-tex">V_T(t)< / annotation>< / semantics>< / com:Math> to drop below the lower bound <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math> of the predetermined range, for example the lower rail voltage <com:Math><semantics>VRL<annotation encoding="application / x-tex">V_{RL}< / annotation>< / semantics>< / com:Math> plus an overvoltage tolerance. Similar behaviour may occur with respect to the upper bound <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math> of the predetermined range, for example the upper rail voltage <com:Math><semantics>VRU<annotation encoding="application / x-tex">V_{RU}< / annotation>< / semantics>< / com:Math> plus an overvoltage tolerance, if the output which supplies the drive signal 8 is clamped to the upper rail voltage <com:Math><semantics>VRU<annotation encoding="application / x-tex">V_{RU}< / annotation>< / semantics>< / com:Math> at the end of the first waveform <com:Math><semantics>VI(t)<annotation encoding="application / x-tex">V_I(t)< / annotation>< / semantics>< / com:Math>. In the example shown in Figure 4, the bounds <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math> of the predetermined range are respectively slightly above and below the upper and lower rail voltages <com:Math><semantics>VRU<annotation encoding="application / x-tex">V_{RU}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VRL<annotation encoding="application / x-tex">V_{RL}< / annotation>< / semantics>< / com:Math>, reflecting an over-voltage tolerance of the circuitry before significant current leakage occurs. Depending on the application, an over-voltage tolerance may correspond to, for example, <com:Math><semantics>±5%<annotation encoding="application / x-tex">\pm 5\%< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>±10%<annotation encoding="application / x-tex">\pm 10\%< / annotation>< / semantics>< / com:Math> or <com:Math><semantics>±15%<annotation encoding="application / x-tex">\pm 15\%< / annotation>< / semantics>< / com:Math> of the range <com:Math><semantics>VRU−VRL<annotation encoding="application / x-tex">V_{RU} - V_{RL}< / annotation>< / semantics>< / com:Math> between the upper and lower rail voltages <com:Math><semantics>VRU<annotation encoding="application / x-tex">V_{RU}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VRL<annotation encoding="application / x-tex">V_{RL}< / annotation>< / semantics>< / com:Math>. Depending on the application, an over-voltage may correspond to, for example below -0.2 V and above 3.5 V. The induced ringing voltage 23 may be detrimental to the operation of an ultrasonic time-of-flight flow rate meter 1. For example, the induced ringing voltage 23 may cause interference to connected or coupled electronics if the voltage <com:Math><semantics>V7(t)<annotation encoding="application / x-tex">V_7(t)< / annotation>< / semantics>< / com:Math> across the ultrasonic transducer 2, 3 exceeds the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math>. For example, if the first ultrasonic transducer 2 is driven and the subsequent induced ringing voltage 23 exceeds the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math>, then the induced ringing voltage may couple to the second ultrasonic transducer 3. Such coupling may be misinterpreted as a received signal 10. For example, such coupling may occur as a result of current leakage to the conditioning circuit 12 via the second switch 11, in response to the induced ringing voltage 23 exceeding an overvoltage tolerance of the second switch 11. Such interference may be detrimental because it makes the effective drive signal 8 longer and prohibits the use of short and / or compact flow tubes 4, because there needs to be some "quiet" time to separate the transmitted and received pulses to avoid coupled interference due to the induced ringing voltage from overlapping in time with the real received signal 10. Furthermore, the induced ringing voltage 23 and associated interference injected to other parts of the ultrasonic time-of-flight flow rate meter 1 may distort a correlation or timing algorithm executed by the controller 7. The hereinbefore described problems are not an exhaustive description of the problems which may be caused by induced ringing voltages 23 in an ultrasonic time-of-flight flow rate meter 1. The problem of induced ringing voltages 23 may arise in measurements of any fluid, including natural gas and water. In general, the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math> may be a designed for driving voltage range of the first or second ultrasonic transducers 2, 3. The predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math> may extend beyond the designed for driving voltage range of the first or second ultrasonic transducers 2, 3 by an overvoltage tolerance margin. Alternatively, the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math> may be a designed for rail-to-rail voltage <com:Math><semantics>VRU<annotation encoding="application / x-tex">V_{RU}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VRL<annotation encoding="application / x-tex">V_{RL}< / annotation>< / semantics>< / com:Math> of a further component which is connected to the first or second ultrasonic transducers 2, 3. For example, the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math> may be a designed for rail-to-rail voltage <com:Math><semantics>VRU<annotation encoding="application / x-tex">V_{RU}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VRL<annotation encoding="application / x-tex">V_{RL}< / annotation>< / semantics>< / com:Math> of first and / or second switches 9, 11. The predetermined range V<com:Sub>H< / com:Sub>, V<com:Sub>L< / com:Sub> may extend beyond the designed for rail-to-rail voltage <com:Math><semantics>VRU<annotation encoding="application / x-tex">V_{RU}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VRL<annotation encoding="application / x-tex">V_{RL}< / annotation>< / semantics>< / com:Math> of a further component which is connected to the first or second ultrasonic transducers 2, 3 by an overvoltage tolerance margin. For example, in a circuit designed to use a 3.3 V supply, the predetermined range may be between and including -0.2 V to 3.5 V. In a further example of a circuit designed to use a 5 V supply, the predetermined range may be between and including -0.2 V to 5.2 V. By maintaining the voltage <com:Math><semantics>VT(t)<annotation encoding="application / x-tex">V_T(t)< / annotation>< / semantics>< / com:Math> across an ultrasonic transducer 2, 3 within a predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math>, the methods of the present specification may prevent or reduce coupling between a transmitting ultrasonic transducer 2, 3 and one or more receiving ultrasonic transducers 2, 3. For example, the methods of the present specification may prevent or reduce coupling between the first ultrasonic transducer 2 and the second ultrasonic transducer 3 via the first and / or second switches 9, 11, and vice versa. First method of maintaining a voltage across an ultrasonic transducer within a predetermined range Referring also to Figures 6 and 7, a first example of the method is illustrated. The transmitting ultrasonic transducer 2, 3 is driven using a drive signal 8 which includes a first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math> followed by a second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>. The first and second waveforms <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> are both square or pulsed waveforms between a lower rail voltage <com:Math><semantics>VRL<annotation encoding="application / x-tex">V_{RL}< / annotation>< / semantics>< / com:Math> and an upper rail voltage <com:Math><semantics>VRU<annotation encoding="application / x-tex">V_{RU}< / annotation>< / semantics>< / com:Math>. The first waveform <com:Math><semantics>VI(t)<annotation encoding="application / x-tex">V_I(t)< / annotation>< / semantics>< / com:Math> is used to drive the transmitting ultrasonic transducer 2, 3 for the first duration <com:Math><semantics>Δti<annotation encoding="application / x-tex">\Delta t_i< / annotation>< / semantics>< / com:Math> between time <com:Math><semantics>to<annotation encoding="application / x-tex">t_o< / annotation>< / semantics>< / com:Math> (not shown in Figure 6 and 7) and time <com:Math><semantics>t1<annotation encoding="application / x-tex">t_1< / annotation>< / semantics>< / com:Math>. During the first period <com:Math><semantics>Δt1<annotation encoding="application / x-tex">\Delta t_1< / annotation>< / semantics>< / com:Math>, the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> excites oscillation 21 of the ultrasonic transducer 2, 3. The first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> has a base frequency <com:Math><semantics>fBi<annotation encoding="application / x-tex">f_{Bi}< / annotation>< / semantics>< / com:Math> which is within the bandwidth <com:Math><semantics>δfi<annotation encoding="application / x-tex">\delta f_i< / annotation>< / semantics>< / com:Math> of a primary resonance frequency <com:Math><semantics>ft<annotation encoding="application / x-tex">f_t< / annotation>< / semantics>< / com:Math> of the ultrasonic transducer 2, 3. After time <com:Math><semantics>t1<annotation encoding="application / x-tex">t_1< / annotation>< / semantics>< / com:Math>, the drive signal 8 switches to the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> for the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> for <com:Math><semantics>t1<t≤t2<annotation encoding="application / x-tex">t_1 < t \le t_2< / annotation>< / semantics>< / com:Math>. The second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> and the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> are configured to maintain the voltage <com:Math><semantics>VT(t)<annotation encoding="application / x-tex">V_T(t)< / annotation>< / semantics>< / com:Math> across the ultrasonic transducer 2, 3 within the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math>. The second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> has a base frequency <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math> which is outside the bandwidth <com:Math><semantics>δfi<annotation encoding="application / x-tex">\delta f_i< / annotation>< / semantics>< / com:Math> of a primary resonance frequency <com:Math><semantics>fi<annotation encoding="application / x-tex">f_i< / annotation>< / semantics>< / com:Math> of the ultrasonic transducer 2, 3 (or any other resonances <com:Math><semantics>f2<annotation encoding="application / x-tex">f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f3<annotation encoding="application / x-tex">f_3< / annotation>< / semantics>< / com:Math> of the ultrasonic transducer 2, 3). Thus, in this example the discontinuity is a discontinuity in the base frequencies <com:Math><semantics>fB1<annotation encoding="application / x-tex">f_{B1}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math>. Consequently, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> does not excite further oscillation 21 of the ultrasonic transducer 2, 3. The self-oscillation 22 of the ultrasonic transducer 2, 3 is not significantly modified by the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>, i.e. the self-oscillation 22 is not damped. However, the rapid cycling of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> maintains an average voltage output from the controller 7 close to the centre of the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math>. As a result, a modified ringing voltage 24 resulting from the self- oscillation 22 of the ultrasonic transducer 2, 3 is relatively more centred within the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math>, about the average value of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>, thereby reducing the probability of the voltage <com:Math><semantics>VT(t)<annotation encoding="application / x-tex">V_T(t)< / annotation>< / semantics>< / com:Math> across the ultrasonic transducer 2, 3 exceeding the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math>. The second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> is preferably configured to be sufficiently long to allow the self- oscillation 22 of the ultrasonic transducer 2, 3 to reduce to a level whereby the voltage <com:Math><semantics>VT(t)<annotation encoding="application / x-tex">V_T(t)< / annotation>< / semantics>< / com:Math> across the ultrasonic transducer 2, 3 will remain within the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math> after the end of the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math>. For example, as shown in Figure 7, when the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> ends at time <com:Math><semantics>t2<annotation encoding="application / x-tex">t_2< / annotation>< / semantics>< / com:Math>, the amplitude of the self-oscillation 22 has reduced sufficiently that the residual ringing is small enough to that it does not drop below the lower bound <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math> of the predetermined range. In summary, the first example of the method concerns appending a discontinuous, out- of-band second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> at the end of the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>. Because the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> has a base frequency <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math> outside of the bandwidth <com:Math><semantics>δf1<annotation encoding="application / x-tex">\delta f_1< / annotation>< / semantics>< / com:Math> of the primary resonance <com:Math><semantics>f1<annotation encoding="application / x-tex">f_1< / annotation>< / semantics>< / com:Math> (or any other resonances <com:Math><semantics>f2,f3<annotation encoding="application / x-tex">f_2, f_3< / annotation>< / semantics>< / com:Math>), the ultrasonic transducer 2, 3 effectively filters the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> by itself. The second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> also has the effect of holding the ultrasonic transducer 2, 3 in, or at least closer to, the middle of its operating range, thereby allowing the self-oscillation 22 to decay in a controlled manner and avoiding the ringing voltage 23 behaviour observed when only the first waveform <com:Math><semantics>VI(t)<annotation encoding="application / x-tex">V_I(t)< / annotation>< / semantics>< / com:Math> is used. Referring also to Figure 8, a schematic frequency response of an ultrasonic transducer 2, 3 is shown. In addition to a primary resonance frequency <com:Math><semantics>f1<annotation encoding="application / x-tex">f_1< / annotation>< / semantics>< / com:Math> having an associated bandwidth <com:Math><semantics>δf1<annotation encoding="application / x-tex">\delta f_1< / annotation>< / semantics>< / com:Math>, an ultrasonic transducer may include further resonance frequencies <com:Math><semantics>f2<annotation encoding="application / x-tex">f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f3<annotation encoding="application / x-tex">f_3< / annotation>< / semantics>< / com:Math> and so forth, each of which is associated with a corresponding bandwidth <com:Math><semantics>δf2<annotation encoding="application / x-tex">\delta f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf3<annotation encoding="application / x-tex">\delta f_3< / annotation>< / semantics>< / com:Math> and so forth. Although three resonances <com:Math><semantics>f1<annotation encoding="application / x-tex">f_1< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f2<annotation encoding="application / x-tex">f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f3<annotation encoding="application / x-tex">f_3< / annotation>< / semantics>< / com:Math> are shown in Figure 8, there is no upper limit on the number of resonances frequencies <com:Math><semantics>f1,f2,f3<annotation encoding="application / x-tex">f_1, f_2, f_3< / annotation>< / semantics>< / com:Math>. Between the resonant bandwidths <com:Math><semantics>δf1,δf2<annotation encoding="application / x-tex">\delta f_1, \delta f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf3<annotation encoding="application / x-tex">\delta f_3< / annotation>< / semantics>< / com:Math>, there are inert bandwidths <com:Math><semantics>Δf01<annotation encoding="application / x-tex">\Delta f_{01}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>Δf12<annotation encoding="application / x-tex">\Delta f_{12}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>Δf23<annotation encoding="application / x-tex">\Delta f_{23}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>Δf34<annotation encoding="application / x-tex">\Delta f_{34}< / annotation>< / semantics>< / com:Math>, and so forth. Frequencies within the inert bandwidths <com:Math><semantics>Δf01<annotation encoding="application / x-tex">\Delta f_{01}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>Δf12<annotation encoding="application / x-tex">\Delta f_{12}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>Δf23<annotation encoding="application / x-tex">\Delta f_{23}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>Δf34<annotation encoding="application / x-tex">\Delta f_{34}< / annotation>< / semantics>< / com:Math> cause very little, or no, response in the ultrasonic transducer 2, 3. In some examples the higher resonant frequencies <com:Math><semantics>f2<annotation encoding="application / x-tex">f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f3<annotation encoding="application / x-tex">f_3< / annotation>< / semantics>< / com:Math> and so forth may represent harmonics of the primary resonance frequency <com:Math><semantics>fi<annotation encoding="application / x-tex">f_i< / annotation>< / semantics>< / com:Math>. However, in general the behaviour of the ultrasonic transducer 2, 3 may be more complex, and the higher resonant frequencies <com:Math><semantics>f2<annotation encoding="application / x-tex">f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f3<annotation encoding="application / x-tex">f_3< / annotation>< / semantics>< / com:Math> need not be harmonics of the primary resonance frequency <com:Math><semantics>f1<annotation encoding="application / x-tex">f_1< / annotation>< / semantics>< / com:Math>. According to the first example of the method, the first waveform <com:Math><semantics>VI(t)<annotation encoding="application / x-tex">V_I(t)< / annotation>< / semantics>< / com:Math> should have a frequency spectrum in which a majority of the signal power is within one or more bandwidths <com:Math><semantics>δf1<annotation encoding="application / x-tex">\delta f_1< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf2<annotation encoding="application / x-tex">\delta f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf3<annotation encoding="application / x-tex">\delta f_3< / annotation>< / semantics>< / com:Math> corresponding to respective resonances <com:Math><semantics>f1<annotation encoding="application / x-tex">f_1< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f2<annotation encoding="application / x-tex">f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f3<annotation encoding="application / x-tex">f_3< / annotation>< / semantics>< / com:Math> of the ultrasonic transducer 2, 3. Additionally, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> should have a frequency spectrum in which a majority of the signal power is outside the one or more bandwidths <com:Math><semantics>δf1<annotation encoding="application / x-tex">\delta f_1< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf2<annotation encoding="application / x-tex">\delta f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf3<annotation encoding="application / x-tex">\delta f_3< / annotation>< / semantics>< / com:Math> corresponding to respective resonances <com:Math><semantics>f1<annotation encoding="application / x-tex">f_1< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f2<annotation encoding="application / x-tex">f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f3<annotation encoding="application / x-tex">f_3< / annotation>< / semantics>< / com:Math> of the ultrasonic transducer. In other words, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> should have a frequency spectrum in which a majority of the signal power is within one or more inert bandwidths <com:Math><semantics>Δf01<annotation encoding="application / x-tex">\Delta f_{01}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>Δf12<annotation encoding="application / x-tex">\Delta f_{12}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>Δf23<annotation encoding="application / x-tex">\Delta f_{23}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>Δf34<annotation encoding="application / x-tex">\Delta f_{34}< / annotation>< / semantics>< / com:Math> of the ultrasonic transducer 2, 3. For example, the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math> may have a frequency spectrum in which 50% or more, 60% or more, 70% or more, 80% or more, or 90% or more of the power is within the one or more bandwidths <com:Math><semantics>δf1<annotation encoding="application / x-tex">\delta f_1< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf2<annotation encoding="application / x-tex">\delta f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf3<annotation encoding="application / x-tex">\delta f_3< / annotation>< / semantics>< / com:Math> corresponding to respective resonances <com:Math><semantics>f1<annotation encoding="application / x-tex">f_1< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f2<annotation encoding="application / x-tex">f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f3<annotation encoding="application / x-tex">f_3< / annotation>< / semantics>< / com:Math> of the ultrasonic transducer 2, 3. The second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may have a frequency spectrum in which 50% or more, 60% or more, 70% or more, 80% or more, or 90% or more of the power is outside the one or more bandwidths <com:Math><semantics>δf1<annotation encoding="application / x-tex">\delta f_1< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf2<annotation encoding="application / x-tex">\delta f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf3<annotation encoding="application / x-tex">\delta f_3< / annotation>< / semantics>< / com:Math> corresponding to respective resonances <com:Math><semantics>f1,f2,f3<annotation encoding="application / x-tex">f_1, f_2, f_3< / annotation>< / semantics>< / com:Math> of the ultrasonic transducer2, 3. Referring also to Figure 9, a complete drive signal 8 including the first and second waveforms <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> is illustrated. The first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> includes a number of pulses having a base frequency <com:Math><semantics>fBi<annotation encoding="application / x-tex">f_{Bi}< / annotation>< / semantics>< / com:Math> within the bandwidth <com:Math><semantics>δf1<annotation encoding="application / x-tex">\delta f_1< / annotation>< / semantics>< / com:Math> of a primary resonance <com:Math><semantics>f2<annotation encoding="application / x-tex">f_2< / annotation>< / semantics>< / com:Math> of an ultrasonic transducer 2, 3. After the end of the first duration <com:Math><semantics>Δti<annotation encoding="application / x-tex">\Delta t_i< / annotation>< / semantics>< / com:Math>, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> is also a pulsed waveform. However, the base frequency <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math> of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> is outside the bandwidth <com:Math><semantics>δf1<annotation encoding="application / x-tex">\delta f_1< / annotation>< / semantics>< / com:Math> of a primary resonance <com:Math><semantics>f1<annotation encoding="application / x-tex">f_1< / annotation>< / semantics>< / com:Math> of an ultrasonic transducer 2, 3. In the example shown, <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math> is within the inert bandwidth <com:Math><semantics>Δf12<annotation encoding="application / x-tex">\Delta f_{12}< / annotation>< / semantics>< / com:Math> between the primary resonance frequency <com:Math><semantics>f1<annotation encoding="application / x-tex">f_1< / annotation>< / semantics>< / com:Math> and a secondary resonance frequency <com:Math><semantics>f2<annotation encoding="application / x-tex">f_2< / annotation>< / semantics>< / com:Math>. Second method of maintaining a voltage across an ultrasonic transducer within a predetermined range A second example of the method is similar to the first example, except that the form of the discontinuity between the first and second waveforms <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> is different. Referring also to Figure 10, schematic waveforms <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> according to the second example are shown. Unlike the first example, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> is configured to apply frequencies within the bandwidth <com:Math><semantics>δf1<annotation encoding="application / x-tex">\delta f_1< / annotation>< / semantics>< / com:Math> of the primary resonance <com:Math><semantics>f1<annotation encoding="application / x-tex">f_1< / annotation>< / semantics>< / com:Math>, or the bandwidths <com:Math><semantics>δf2<annotation encoding="application / x-tex">\delta f_2< / annotation>< / semantics>< / com:Math> of further resonant frequencies <com:Math><semantics>f2<annotation encoding="application / x-tex">f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f3<annotation encoding="application / x-tex">f_3< / annotation>< / semantics>< / com:Math>. In some examples, the frequencies of the first and second waveforms may be continuous, i.e. <com:Math><semantics>fBi(t1)=fBi(t2)<annotation encoding="application / x-tex">f_{Bi}(t_1)=f_{Bi}(t_2)< / annotation>< / semantics>< / com:Math>. Instead, in the second example of the method, the phase is discontinuous between the first and second waveforms <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>. For example, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> shown in Figure 10 has the same constant base frequency <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math> as the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, i.e. <com:Math><semantics>fB2=fB1<annotation encoding="application / x-tex">f_{B2} = f_{B1}< / annotation>< / semantics>< / com:Math>. However, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> has a phase shift of <com:Math><semantics>π<annotation encoding="application / x-tex">\pi< / annotation>< / semantics>< / com:Math> with respect to the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>. Consequently, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> will actively dampen the self-oscillation 22 of the ultrasonic transducer 2, 3. If the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> goes on for long enough, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> would start to drive oscillations 21 of the ultrasonic transducer 2 in the opposite sense to the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math>. However, the length of the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> is configured to be just sufficient to dampen, or arrest, the self-oscillation 22 of the ultrasonic transducer 2, and not significantly longer. An appropriate length of the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> may be determined from calibration experiments using a number of representative ultrasonic transducers 2, 3. Provided that the sampling of ultrasonic transducers 2, 3 used for such calibration experiments captures the typical variance between ultrasonic transducers 2, 3, there will be no need to calibrate each ultrasonic transducer 2, 3 individually. Although a phase discontinuity of <com:Math><semantics>π<annotation encoding="application / x-tex">\pi< / annotation>< / semantics>< / com:Math> will be most effective, any phase discontinuity in the range between and including <com:Math><semantics>π / 2<annotation encoding="application / x-tex">\pi / 2< / annotation>< / semantics>< / com:Math> to <com:Math><semantics>3π / 2<annotation encoding="application / x-tex">3\pi / 2< / annotation>< / semantics>< / com:Math> may be used in the second method. Measurements of coupling between transmission and reception channels Referring also to Figure 11, an arrangement 25 for measuring the extent of coupling between transmission and reception channels of an ultrasonic time-of-flight flow rate meter 1 is shown. The arrangement 25 is similar to the ultrasonic time-of-flight flow rate meter 1, except that the ultrasonic transducers 2, 3 are disconnected and the controller 7 and signal conditioning circuit 12 are omitted. A voltage <com:Math><semantics>VA<annotation encoding="application / x-tex">V_A< / annotation>< / semantics>< / com:Math> was applied to a first node 26 which connects the outputs of the first and second switches 9, 11 which would normally be connected to the first ultrasonic transducer 2. A total current <com:Math><semantics>IA<annotation encoding="application / x-tex">I_A< / annotation>< / semantics>< / com:Math> injected to the first node 26 was measured. The input to the first switch 9 was connected to the supply voltage <com:Math><semantics>VRU=VCC=3.3<annotation encoding="application / x-tex">V_{RU} = V_{CC} = 3.3< / annotation>< / semantics>< / com:Math>V via a first impedance matching resistor R1 = 820 <com:Math><semantics>Ω<annotation encoding="application / x-tex">\Omega< / annotation>< / semantics>< / com:Math>. The input to the second switch 11 was connected to ground (GND) via a second matching resistor <com:Math><semantics>R2=820Ω<annotation encoding="application / x-tex">R_2 = 820 \Omega< / annotation>< / semantics>< / com:Math>. The voltage <com:Math><semantics>VA<annotation encoding="application / x-tex">V_A< / annotation>< / semantics>< / com:Math> was greater than <com:Math><semantics>VCC<annotation encoding="application / x-tex">V_{CC}< / annotation>< / semantics>< / com:Math> in these experiments. At the same time, a voltage <com:Math><semantics>VB<annotation encoding="application / x-tex">V_B< / annotation>< / semantics>< / com:Math> was also measured on a second node 27 which connects the ports of the first and second switches 9, 11 which would normally be connected to the second ultrasonic transducer 3. A current <com:Math><semantics>IB<annotation encoding="application / x-tex">I_B< / annotation>< / semantics>< / com:Math> from the second node 27 to ground via the second matching resistor R2 was calculated. In an ideal case, and when <com:Math><semantics>VA<annotation encoding="application / x-tex">V_A< / annotation>< / semantics>< / com:Math> remains within the supply rail voltages, <com:Math><semantics>VRL=GND<annotation encoding="application / x-tex">V_{RL} = GND< / annotation>< / semantics>< / com:Math> to <com:Math><semantics>VRU=VCC<annotation encoding="application / x-tex">V_{RU} = V_{CC}< / annotation>< / semantics>< / com:Math>, or alternatively when <com:Math><semantics>VA<annotation encoding="application / x-tex">V_A< / annotation>< / semantics>< / com:Math> remains within a predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math>, the voltage <com:Math><semantics>VB<annotation encoding="application / x-tex">V_B< / annotation>< / semantics>< / com:Math> on the second node 27 and the current <com:Math><semantics>IB<annotation encoding="application / x-tex">I_B< / annotation>< / semantics>< / com:Math> to ground via the second matching resistor R2 should be zero. When <com:Math><semantics>VA<annotation encoding="application / x-tex">V_A< / annotation>< / semantics>< / com:Math> is outside the supply rail voltages <com:Math><semantics>VRU=VCC<annotation encoding="application / x-tex">V_{RU} = V_{CC}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VRL=GND<annotation encoding="application / x-tex">V_{RL} = GND< / annotation>< / semantics>< / com:Math>, the switches 9, 11 may become reverse biased or electrostatic discharge (ESD) protection may be triggered. This may cause current coupling between the first and second nodes 26, 27 through the first and / or second switches 9, 11, so that <com:Math><semantics>IB<annotation encoding="application / x-tex">I_B< / annotation>< / semantics>< / com:Math> and <com:Math><semantics>VB<annotation encoding="application / x-tex">V_B< / annotation>< / semantics>< / com:Math> are no longer zero. Referring also to Figure 12, the injected current <com:Math><semantics>IA<annotation encoding="application / x-tex">I_A< / annotation>< / semantics>< / com:Math> is plotted as a function of the voltage <com:Math><semantics>VA<annotation encoding="application / x-tex">V_A< / annotation>< / semantics>< / com:Math> applied to the first node 29. Referring also to Figure 13, the leakage current <com:Math><semantics>IB<annotation encoding="application / x-tex">I_B< / annotation>< / semantics>< / com:Math> is plotted as a function of the voltage <com:Math><semantics>VA<annotation encoding="application / x-tex">V_A< / annotation>< / semantics>< / com:Math> applied to the first node 26. It may be observed from Figure 13 that as the voltage <com:Math><semantics>VA<annotation encoding="application / x-tex">V_A< / annotation>< / semantics>< / com:Math> applied to the first node 26 increases to above around 200 mV greater than the rail voltage <com:Math><semantics>VRU=Vcc<annotation encoding="application / x-tex">V_{RU}=V_{cc}< / annotation>< / semantics>< / com:Math>, the leakage current <com:Math><semantics>IB<annotation encoding="application / x-tex">I_B< / annotation>< / semantics>< / com:Math> begins to increase significantly. This suggests an overvoltage tolerance of approximately 200 mV. When the first and second ultrasonic transducers 2, 3 are attached, overvoltages caused by induced ringing voltages 23 may also leak to the received signal 10 path in a similar way. Experimental observations of ringing Referring also to Figures 14 and 15, measurements of interference caused by ringing voltages 23 are presented. Figure 14 presents a measurement of the received signal 10 when the self-oscillation 22 of the transmitting ultrasonic transducer 2, 3 is within the designed for voltage range of the switches 9, 11 (the predetermined range V<com:Sub>H< / com:Sub>, V<com:Sub>L< / com:Sub>), so that an induced ringing voltage 23 is not coupled to the received signal 10 side. Figure 15 presents a measurement of the received signal 10 when self-oscillation 22 of the transmitting ultrasonic transducer 2, 3 induces a ringing voltage 23 which exceeds the designed for voltage range of the switches 9, 11 (the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math>). Each of Figures 14 and 15 shows a portion of the conditioned signal 13 after digitisation by the controller 7. The vertical axes in Figure 14 and 15 represent signal amplitude in analog-to-digital converter (ADC) counts, and are proportional to the voltage of the conditioned signal 13. The horizontal axes represent time in microseconds, µs. The received signal 10 from gas (in this case air) which is used for time-of-flight measurements starts at around 150 <com:Math><semantics>μ<annotation encoding="application / x-tex">\mu< / annotation>< / semantics>< / com:Math>s. Before <com:Math><semantics>t1≈50μ<annotation encoding="application / x-tex">t_1 \approx 50 \mu< / annotation>< / semantics>< / com:Math>s, the observed oscillation in Figures 14 and 15 is due to capacitive coupling of the drive signal 8 into the electronics which process the received signal 10. At <com:Math><semantics>t1≈50<annotation encoding="application / x-tex">t_1 \approx 50< / annotation>< / semantics>< / com:Math> µs, the drive signal 8 stops, and the output of the controller 7 providing the drive signal is set to <com:Math><semantics>VRU=VCC<annotation encoding="application / x-tex">V_{RU}=V_{CC}< / annotation>< / semantics>< / com:Math>. As explained hereinbefore, the transmitting ultrasonic transducer 2, 3 continues to self-oscillate 22, and if the induced ringing voltage 23 exceeds the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math> of electronics connected between the transmitting ultrasonic transducer 2, 3 and the electronics which process the received signal 10, then a leakage current <com:Math><semantics>IB<annotation encoding="application / x-tex">I_B< / annotation>< / semantics>< / com:Math> may be coupled into the path of the received signal 10. As may be observed from Figure 15, when interference occurs, this may cause a significant spike 28 which then decays as the self-oscillation 22 decays. If the actual received signal 10 arrives before any interference has fully decayed, then this may cause errors in the time-of-flight measurements. One option would be to simply increase the length d of the flow tube 4 to ensure that there is time for any interference to die down. However, this will prevent a flow rate meter 1 from being compact. The methods of the present specification address the problem in a different way, by reducing or preventing such interference by maintaining the voltage <com:Math><semantics>VT(t)<annotation encoding="application / x-tex">V_T(t)< / annotation>< / semantics>< / com:Math> across a transmitting ultrasonic transducer 2, 3 within the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math>. Using the methods of the present specification, the length d separating the first and second ultrasonic transducers 2, 3 may be relatively shorter, whilst retaining a simple design of ultrasonic time-of-flight flow rate meter. Referring also to Figure 16, further measurements relating to the measurements of Figure 15 are plotted. The top panel of Figure 16 shows a measured drive signal 8 which includes only a first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>. In the example measured, the drive signal 8 was clamped to the supply voltage <com:Math><semantics>VRU=VCC=3.3<annotation encoding="application / x-tex">V_{RU} = V_{CC} = 3.3< / annotation>< / semantics>< / com:Math> V when the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> finished at time <com:Math><semantics>ti<annotation encoding="application / x-tex">t_i< / annotation>< / semantics>< / com:Math>. The middle panel of Figure 16 shows the conditioned signal 13 shown in Figure 15 across a longer period of time. The bottom panel of Figure 16 shows the voltage <com:Math><semantics>VT(t)<annotation encoding="application / x-tex">V_T(t)< / annotation>< / semantics>< / com:Math> across the transmitting ultrasonic transducer 2, 3. It may be observed that an induced ringing voltage 23 occurs which significantly exceeds the supply voltage <com:Math><semantics>VRU=VCC=3.3 V<annotation encoding="application / x-tex">V_{RU} = V_{CC} = 3.3 \text{ V}< / annotation>< / semantics>< / com:Math>. This induced ringing voltage 23 is the cause of the voltage spike 28 observed in the corresponding conditioned signal 13 (middle panel). To obtain the data plotted in Figure 16, the transmitting ultrasonic transducer 2, 3 was driven using a first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> in the form of a linear chirp having an end frequency of <com:Math><semantics>f(t1)=437 kHz<annotation encoding="application / x-tex">f(t_1) = 437 \text{ kHz}< / annotation>< / semantics>< / com:Math>. Referring also to Figure 17, the driving signal 8, received signal 10 and voltage <com:Math><semantics>VT(t)<annotation encoding="application / x-tex">V_T(t)< / annotation>< / semantics>< / com:Math> across the transmitting ultrasonic transducer 2, 3 are shown for an experiment which was the same as for Figure 16, except that the drive signal 8 was clamped to the ground voltage <com:Math><semantics>VRL=GND=0<annotation encoding="application / x-tex">V_{RL} = GND = 0< / annotation>< / semantics>< / com:Math> V when the first waveform <com:Math><semantics>VI(t)<annotation encoding="application / x-tex">V_I(t)< / annotation>< / semantics>< / com:Math> finished at time <com:Math><semantics>tI<annotation encoding="application / x-tex">t_I< / annotation>< / semantics>< / com:Math>. Similar to Figure 16, in Figure 17 an induced ringing voltage 23 which dips significantly below the GND voltage of o V may be observed, leading to interference in the form of a spike 28 in the corresponding conditioned signal 13. Experimental verification of the method Referring also to Figure 18, experimental measurements are presented which correspond to an application of the first method of the present specification. The top panel of Figure 18 shows a measured drive signal 8 which includes a first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math> followed by a second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> having a significantly higher base frequency <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math>. In the example measured, the drive signal 8 was clamped to the supply voltage <com:Math><semantics>VRU=VCC=3.3<annotation encoding="application / x-tex">V_{RU} = V_{CC} = 3.3< / annotation>< / semantics>< / com:Math> V when the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> finished at time <com:Math><semantics>t2<annotation encoding="application / x-tex">t_2< / annotation>< / semantics>< / com:Math>. The middle panel of Figure 18 shows the conditioned signal 13. The bottom panel of Figure 18 shows the voltage <com:Math><semantics>VT(t)<annotation encoding="application / x-tex">V_T(t)< / annotation>< / semantics>< / com:Math> across the transmitting ultrasonic transducer 2, 3. Referring also to Figure 19, the data shown in the top subplot of Figure 18 is shown on a shorter timebase focused around the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math>. Referring also to Figure 20, the data shown in the bottom subplot of Figure 18 is shown on the same timebase as Figure 19. It may be observed that the modified ringing voltage 24 observed during the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> remains bounded between <com:Math><semantics>VRL=GND=0<annotation encoding="application / x-tex">V_{RL} = GND = 0< / annotation>< / semantics>< / com:Math> and <com:Math><semantics>VRU=VCC=3.3<annotation encoding="application / x-tex">V_{RU} = V_{CC} = 3.3< / annotation>< / semantics>< / com:Math> V. Although a small amount of ringing is still observed at the end of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>, the amplitude is greatly reduced as the self-oscillation 22 has had time to decay. Modifications It will be appreciated that many modifications may be made to the embodiments hereinbefore described. Such modifications may involve equivalent and other features which are already known in the design and use of ultrasonic time-of-flight flow meters, and which may be used instead of, or in addition to, features already described herein. Features of one embodiment may be replaced or supplemented by features of another embodiment. Referring also to Figure 21, an example according to the method is illustrated. The first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math> may have a base frequency <com:Math><semantics>fB1(t)<annotation encoding="application / x-tex">f_{B_1}(t)< / annotation>< / semantics>< / com:Math> which varies with time to provide a linear chirp spanning the bandwidth <com:Math><semantics>δfi<annotation encoding="application / x-tex">\delta f_i< / annotation>< / semantics>< / com:Math> of a primary resonance <com:Math><semantics>fi<annotation encoding="application / x-tex">f_i< / annotation>< / semantics>< / com:Math>. The second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> has a fixed base frequency <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math> which is significantly higher than the final base frequency <com:Math><semantics>fBi(ti)<annotation encoding="application / x-tex">f_{Bi}(t_i)< / annotation>< / semantics>< / com:Math> of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math>, and outside the bandwidth <com:Math><semantics>δfi<annotation encoding="application / x-tex">\delta f_i< / annotation>< / semantics>< / com:Math> of a primary resonance <com:Math><semantics>f1<annotation encoding="application / x-tex">f_1< / annotation>< / semantics>< / com:Math>, or indeed any other resonance <com:Math><semantics>f2<annotation encoding="application / x-tex">f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f3<annotation encoding="application / x-tex">f_3< / annotation>< / semantics>< / com:Math> and so forth. Referring also to Figure 22, an example according to the method is illustrated. The first waveform <com:Math><semantics>VI(t)<annotation encoding="application / x-tex">V_I(t)< / annotation>< / semantics>< / com:Math> may have a base frequency <com:Math><semantics>fBI(t)<annotation encoding="application / x-tex">f_{BI}(t)< / annotation>< / semantics>< / com:Math> which varies with time to provide an exponential chirp spanning the bandwidth <com:Math><semantics>δf1<annotation encoding="application / x-tex">\delta f_1< / annotation>< / semantics>< / com:Math> of a primary resonance <com:Math><semantics>f1<annotation encoding="application / x-tex">f_1< / annotation>< / semantics>< / com:Math>. The second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may have a base frequency <com:Math><semantics>fB2(t)<annotation encoding="application / x-tex">f_{B2}(t)< / annotation>< / semantics>< / com:Math> which varies with time to provide a linear or exponential chirp, which moves outside of the bandwidth <com:Math><semantics>δft<annotation encoding="application / x-tex">\delta f_t< / annotation>< / semantics>< / com:Math> of the primary resonance <com:Math><semantics>f1<annotation encoding="application / x-tex">f_1< / annotation>< / semantics>< / com:Math> with a greatly increased gradient. For example, the base frequencies <com:Math><semantics>fB1<annotation encoding="application / x-tex">f_{B1}< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math> may satisfy: [Image disponible dans le document PDF, Image available in the PDF document] (8) Referring also to Figure 23, an example according to the method is illustrated. The first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math> may have a base frequency <com:Math><semantics>fB1(t)<annotation encoding="application / x-tex">f_{B_1}(t)< / annotation>< / semantics>< / com:Math> which varies with time to provide an exponential chirp spanning the bandwidth <com:Math><semantics>δfi<annotation encoding="application / x-tex">\delta f_i< / annotation>< / semantics>< / com:Math> of a primary resonance <com:Math><semantics>fi<annotation encoding="application / x-tex">f_i< / annotation>< / semantics>< / com:Math>. The second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> has a fixed base frequency <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math> which is significantly lower than the final base frequency <com:Math><semantics>fBi(ti)<annotation encoding="application / x-tex">f_{Bi}(t_i)< / annotation>< / semantics>< / com:Math> of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math>, and outside the bandwidth <com:Math><semantics>δfi<annotation encoding="application / x-tex">\delta f_i< / annotation>< / semantics>< / com:Math> of a primary resonance <com:Math><semantics>fi<annotation encoding="application / x-tex">f_i< / annotation>< / semantics>< / com:Math>, or indeed any other resonance <com:Math><semantics>f2<annotation encoding="application / x-tex">f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>f3<annotation encoding="application / x-tex">f_3< / annotation>< / semantics>< / com:Math> and so forth. Although specific examples of the first and second waveforms <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> have been described and illustrated, the methods of the present specification are not limited thereto. Any combination of first and second waveforms <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may be used, provided that there is a discontinuity between the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, and that the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>, and the second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> are configured to maintain a voltage <com:Math><semantics>VT(t)<annotation encoding="application / x-tex">V_T(t)< / annotation>< / semantics>< / com:Math> across the ultrasonic transducer 2, 3 within the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL•<annotation encoding="application / x-tex">V_{L_{\bullet}}< / annotation>< / semantics>< / com:Math> For example, the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> may have a substantially constant base frequency <com:Math><semantics>fB1<annotation encoding="application / x-tex">f_{B_1}< / annotation>< / semantics>< / com:Math>. Equally, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may have a substantially constant base frequency <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math>. Depending upon the application, the term "substantially" may correspond to a tolerance of <com:Math><semantics>±<annotation encoding="application / x-tex">\pm< / annotation>< / semantics>< / com:Math> 5%, or <com:Math><semantics>±<annotation encoding="application / x-tex">\pm< / annotation>< / semantics>< / com:Math> 10%. The base frequency <com:Math><semantics>fBi(t)<annotation encoding="application / x-tex">f_{Bi}(t)< / annotation>< / semantics>< / com:Math> of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_{i}(t)< / annotation>< / semantics>< / com:Math> may vary as a function of time, for example according to a linear, exponential or reciprocal chirp. The base frequency <com:Math><semantics>fB2(t)<annotation encoding="application / x-tex">f_{B2}(t)< / annotation>< / semantics>< / com:Math> of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may vary as a function of time, for example according to a linear, exponential or reciprocal chirp. The frequency variation of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> with time may be a continuous extension of the frequency variation of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> with time, and the discontinuity may occur in other properties such as phase, duty cycle, and so forth. The methods of the present specification may be applied to measure flow rates of any fluids, including liquids or gasses. The methods may be used to measure the flow rate of natural gas. The methods may be used to measure the flow rate of water. The methods may be used to measure a flow rate of a fluid, and the measured flow rate may be used for fiscal metering purposes. Although the ultrasonic time-of-flight flow rate meter 1 has been described with reference to ultrasonic transducers, for example piezoelectric transducers, which are connected between ground and a driving potential, this need not be the case. In some implementations of the methods of the present specification, the ultrasonic transducers 2, 3 may be driven using a differential driving circuit. For example, instead of connecting one end of an ultrasonic transducer 2, 3 to ground and the other to drive signal 8 or upper / lower rail voltage, an ultrasonic transducer 2, 3 used to transmit may be connected across the outputs of a differential drive circuit. Similarly, an ultrasonic transducer 2, 3 used to receive a signal may be connected across the inputs of a differential amplifier. An ultrasonic time-of-flight flow meter 1 according to the present specification may be a gas meter for measuring flow rates of natural gas. The first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math> may comprise a linear chirp composed of square wave or top-hat pulses. The linear chirp may span a range of frequencies between and including 360 kHZ and 440 kHz, i.e. <com:Math><semantics>fBi(t0)=360 kHz<annotation encoding="application / x-tex">f_{Bi}(t_0) = 360 \text{ kHz}< / annotation>< / semantics>< / com:Math> and <com:Math><semantics>fBi(ti)=440 kHz<annotation encoding="application / x-tex">f_{Bi}(t_i) = 440 \text{ kHz}< / annotation>< / semantics>< / com:Math>. A bandwidth <com:Math><semantics>δfi<annotation encoding="application / x-tex">\delta f_i< / annotation>< / semantics>< / com:Math> of a primary resonance <com:Math><semantics>fi<annotation encoding="application / x-tex">f_i< / annotation>< / semantics>< / com:Math> of the ultrasonic transducer may be within the range of frequencies between and including 360 kHZ and 440 kHz. Each individual pulse making up the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> may have a duration of approximately 2.5 microseconds. The first duration <com:Math><semantics>Δt1<annotation encoding="application / x-tex">\Delta t_1< / annotation>< / semantics>< / com:Math> may be approximately 100 <com:Math><semantics>μ<annotation encoding="application / x-tex">\mu< / annotation>< / semantics>< / com:Math>s. The first duration <com:Math><semantics>Δt1<annotation encoding="application / x-tex">\Delta t_1< / annotation>< / semantics>< / com:Math> may encompass about 40 individual pulses. The second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may comprise a pulsed waveform having a base frequency <com:Math><semantics>fB2=2<annotation encoding="application / x-tex">f_{B2} = 2< / annotation>< / semantics>< / com:Math> MHz. The base frequency <com:Math><semantics>fB2=2<annotation encoding="application / x-tex">f_{B2} = 2< / annotation>< / semantics>< / com:Math> MHz may be outside any bandwidth <com:Math><semantics>δf1,δf2,δf3<annotation encoding="application / x-tex">\delta f_1, \delta f_2, \delta f_3< / annotation>< / semantics>< / com:Math> which corresponds to a resonance of the ultrasonic transducer 2, 3. The second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> may be approximately 8 µs. The second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> may be between 2 to 5 times a duration of an average period of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math>. The distance d separating the ultrasonic transducers 2, 3 may be between and including 50 mm and 100 mm. The distance <com:Math><semantics>d<annotation encoding="application / x-tex">d< / annotation>< / semantics>< / com:Math> separating the ultrasonic transducers 2, 3 may be approximately 70 mm. An ultrasonic time-of-flight flow meter 1 according to the present specification may be a water meter for measuring flow rates of water. The first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> may comprise a pulsed waveform having a substantially constant base frequency <com:Math><semantics>fBI<annotation encoding="application / x-tex">f_{B_I}< / annotation>< / semantics>< / com:Math>. The base frequency <com:Math><semantics>fBi<annotation encoding="application / x-tex">f_{Bi}< / annotation>< / semantics>< / com:Math> of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> may be between and including the range of 0.8 MHz to 1.2 MHz. The base frequency <com:Math><semantics>fBi<annotation encoding="application / x-tex">f_{Bi}< / annotation>< / semantics>< / com:Math> of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> may be approximately 1 MHz. The base frequency <com:Math><semantics>fBi<annotation encoding="application / x-tex">f_{Bi}< / annotation>< / semantics>< / com:Math> of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> may be tuned to a primary resonance frequency <com:Math><semantics>f1<annotation encoding="application / x-tex">f_1< / annotation>< / semantics>< / com:Math> of the ultrasonic transducer 2, 3. The first duration <com:Math><semantics>Δt1<annotation encoding="application / x-tex">\Delta t_1< / annotation>< / semantics>< / com:Math> may be approximately 17 microseconds. The first duration <com:Math><semantics>Δt1<annotation encoding="application / x-tex">\Delta t_1< / annotation>< / semantics>< / com:Math> may encompass about 17 cycles of the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>. The second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may comprise a pulsed waveform having a base frequency <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math> of 5 MHz. The base frequency <com:Math><semantics>fB2<annotation encoding="application / x-tex">f_{B2}< / annotation>< / semantics>< / com:Math> of 5 MHz may be outside any bandwidth <com:Math><semantics>δf1<annotation encoding="application / x-tex">\delta f_1< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf2<annotation encoding="application / x-tex">\delta f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf3<annotation encoding="application / x-tex">\delta f_3< / annotation>< / semantics>< / com:Math> which corresponds to a resonance of the ultrasonic transducer 2, 3. The second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math> may be approximately 2 microseconds. The distance d separating the ultrasonic transducers 2, 3 may be between and including 90 mm and 135 mm. The distance d separating the ultrasonic transducers 2, 3 may be approximately 115 mm. Methods have been described in which an ultrasonic transducer 2, 3 is driven using a first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> for a first duration <com:Math><semantics>Δti<annotation encoding="application / x-tex">\Delta t_i< / annotation>< / semantics>< / com:Math>, followed by driving using a second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> for a second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math>. However, in other examples, the drive signal 6 may include a third waveform <com:Math><semantics>V3(t)<annotation encoding="application / x-tex">V_3(t)< / annotation>< / semantics>< / com:Math>, a fourth waveform <com:Math><semantics>V4(t)<annotation encoding="application / x-tex">V_4(t)< / annotation>< / semantics>< / com:Math>, and so forth. For example, immediately following the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, the drive signal 6 may include a second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> in the form of a linear or exponential chirp which rapidly shifts to a frequency outside any bandwidth <com:Math><semantics>δf1<annotation encoding="application / x-tex">\delta f_1< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf2<annotation encoding="application / x-tex">\delta f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf3<annotation encoding="application / x-tex">\delta f_3< / annotation>< / semantics>< / com:Math> which corresponds to a respective resonance of the ultrasonic transducer 2, 3. The third waveform <com:Math><semantics>V3(t)<annotation encoding="application / x-tex">V_3(t)< / annotation>< / semantics>< / com:Math> may be selected from a third group consisting of a third fixed frequency waveform, a third exponential chirp, a third linear chirp or a third reciprocal chirp. The third waveform <com:Math><semantics>V3(t)<annotation encoding="application / x-tex">V_3(t)< / annotation>< / semantics>< / com:Math> may be continuous or discontinuous with the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>. Similarly a fourth waveform <com:Math><semantics>V4(t)<annotation encoding="application / x-tex">V_4(t)< / annotation>< / semantics>< / com:Math> and / or further waveforms may be inserted into the oscillation exciting segment, <com:Math><semantics>t0<annotation encoding="application / x-tex">t_0< / annotation>< / semantics>< / com:Math> to <com:Math><semantics>t1<annotation encoding="application / x-tex">t_1< / annotation>< / semantics>< / com:Math>, of the drive signal, or into the non-exciting segments <com:Math><semantics>t1<annotation encoding="application / x-tex">t_1< / annotation>< / semantics>< / com:Math> to <com:Math><semantics>t2<annotation encoding="application / x-tex">t_2< / annotation>< / semantics>< / com:Math>. Such fourth <com:Math><semantics>V4(t)<annotation encoding="application / x-tex">V_4(t)< / annotation>< / semantics>< / com:Math> and / or further waveforms may be selected from corresponding groups consisting of fixed frequency waveforms, exponential chirps, linear chirps or reciprocal chirps. In a further example, the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> may include two or more distinct sub- waveforms <com:Math><semantics>VIA(t)<annotation encoding="application / x-tex">V_{IA}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VIB(t)<annotation encoding="application / x-tex">V_{IB}(t)< / annotation>< / semantics>< / com:Math> and so forth. Each sub-waveform <com:Math><semantics>VIA(t)<annotation encoding="application / x-tex">V_{IA}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VIB(t)<annotation encoding="application / x-tex">V_{IB}(t)< / annotation>< / semantics>< / com:Math> of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> may be configured to cause oscillation of the ultrasonic transducer 2, 3. The two or more sub-waveforms <com:Math><semantics>V1A(t)<annotation encoding="application / x-tex">V_{1A}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V1B(t)<annotation encoding="application / x-tex">V_{1B}(t)< / annotation>< / semantics>< / com:Math> may be continuous or discontinuous with preceding or following sub-waveforms <com:Math><semantics>ViA(t)<annotation encoding="application / x-tex">V_{iA}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>ViB(t)<annotation encoding="application / x-tex">V_{iB}(t)< / annotation>< / semantics>< / com:Math>. When the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> includes two or more sub-waveforms <com:Math><semantics>VLA(t)<annotation encoding="application / x-tex">V_{LA}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VIB(t)<annotation encoding="application / x-tex">V_{IB}(t)< / annotation>< / semantics>< / com:Math> and so forth, there is a discontinuity between the final sub-waveform of the first waveform <com:Math><semantics>Vi(t)<annotation encoding="application / x-tex">V_i(t)< / annotation>< / semantics>< / com:Math> and the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>. Similarly, the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may include two or more distinct sub-waveforms <com:Math><semantics>V2A(t)<annotation encoding="application / x-tex">V_{2A}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2B(t)<annotation encoding="application / x-tex">V_{2B}(t)< / annotation>< / semantics>< / com:Math> and so forth. Each sub-waveform <com:Math><semantics>V2A(t)<annotation encoding="application / x-tex">V_{2A}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2B(t)<annotation encoding="application / x-tex">V_{2B}(t)< / annotation>< / semantics>< / com:Math> of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may be configured, in combination with the overall second duration <com:Math><semantics>Δt2<annotation encoding="application / x-tex">\Delta t_2< / annotation>< / semantics>< / com:Math>, to maintain the voltage across the ultrasonic transducer <com:Math><semantics>VT(t)<annotation encoding="application / x-tex">V_T(t)< / annotation>< / semantics>< / com:Math> within the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math>. The two or more sub-waveforms <com:Math><semantics>V2A(t)<annotation encoding="application / x-tex">V_{2A}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2B(t)<annotation encoding="application / x-tex">V_{2B}(t)< / annotation>< / semantics>< / com:Math> may be continuous or discontinuous with preceding or following sub-waveforms <com:Math><semantics>V2A(t)<annotation encoding="application / x-tex">V_{2A}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2B(t)<annotation encoding="application / x-tex">V_{2B}(t)< / annotation>< / semantics>< / com:Math>. When the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> includes two or more sub-waveforms <com:Math><semantics>V2A(t)<annotation encoding="application / x-tex">V_{2A}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2B(t)<annotation encoding="application / x-tex">V_{2B}(t)< / annotation>< / semantics>< / com:Math> and so forth, there is a discontinuity between the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math> and the first sub-waveform <com:Math><semantics>V2A(t)<annotation encoding="application / x-tex">V_{2A}(t)< / annotation>< / semantics>< / com:Math> of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math>. In one example of a drive signal 8 including sub-waveforms, a first waveform <com:Math><semantics>VI(t)<annotation encoding="application / x-tex">V_I(t)< / annotation>< / semantics>< / com:Math> may excite the transmitting ultrasonic transducer 2, 3. A second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may include first and second sub-waveforms <com:Math><semantics>V2A(t)<annotation encoding="application / x-tex">V_{2A}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2B(t)<annotation encoding="application / x-tex">V_{2B}(t)< / annotation>< / semantics>< / com:Math>. The first sub-waveform <com:Math><semantics>V2A(t)<annotation encoding="application / x-tex">V_{2A}(t)< / annotation>< / semantics>< / com:Math> of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may be the same as the first waveform <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, except for a phase shift of between <com:Math><semantics>π / 2<annotation encoding="application / x-tex">\pi / 2< / annotation>< / semantics>< / com:Math> to <com:Math><semantics>3π / 2<annotation encoding="application / x-tex">3\pi / 2< / annotation>< / semantics>< / com:Math>, so that the first sub-waveform <com:Math><semantics>V2A(t)<annotation encoding="application / x-tex">V_{2A}(t)< / annotation>< / semantics>< / com:Math> of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may dampen or substantially dampen the self-oscillation 22 of a transmitting ultrasonic transducer 2, 3. Finally, the second sub-waveform <com:Math><semantics>V2B(t)<annotation encoding="application / x-tex">V_{2B}(t)< / annotation>< / semantics>< / com:Math> of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may have a base frequency <com:Math><semantics>fB<annotation encoding="application / x-tex">f_B< / annotation>< / semantics>< / com:Math> which is outside any bandwidth <com:Math><semantics>δf1<annotation encoding="application / x-tex">\delta f_1< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf2<annotation encoding="application / x-tex">\delta f_2< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>δf3<annotation encoding="application / x-tex">\delta f_3< / annotation>< / semantics>< / com:Math> that corresponds to a respective resonance of the ultrasonic transducer 2, 3. The first sub-waveform <com:Math><semantics>V2A(t)<annotation encoding="application / x-tex">V_{2A}(t)< / annotation>< / semantics>< / com:Math> of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> may dampen the self- oscillation 22, whilst the second sub-waveform <com:Math><semantics>V2B(t)<annotation encoding="application / x-tex">V_{2B}(t)< / annotation>< / semantics>< / com:Math> of the second waveform <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> maintains the induced voltage 24 resulting from any residual self-oscillation safely within the predetermined range <com:Math><semantics>VH<annotation encoding="application / x-tex">V_H< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>VL<annotation encoding="application / x-tex">V_L< / annotation>< / semantics>< / com:Math>. In this way, the total length of self-oscillation 22 may be reduced, and the distance <com:Math><semantics>d<annotation encoding="application / x-tex">d< / annotation>< / semantics>< / com:Math> separating a pair of ultrasonic transducers 2, 3 may be further reduced. An ultrasonic time-of-flight flow rate meter 1 has been described in which a single pair of first and second ultrasonic transducers 2, 3 is used for time-of-flight measurements. However, in other examples, more than one pair of ultrasonic transducers 2, 3 may be used. In such examples, any ultrasonic transducer 2, 3 which is used to generate an ultrasound pulse may be driven using a drive signal 8 comprising first and second waveforms <com:Math><semantics>V1(t)<annotation encoding="application / x-tex">V_1(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2(t)<annotation encoding="application / x-tex">V_2(t)< / annotation>< / semantics>< / com:Math> as described (each optionally including two or more sub- waveforms <com:Math><semantics>V1A(t)<annotation encoding="application / x-tex">V_{1A}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V1B(t)<annotation encoding="application / x-tex">V_{1B}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2A(t)<annotation encoding="application / x-tex">V_{2A}(t)< / annotation>< / semantics>< / com:Math>, <com:Math><semantics>V2B(t)<annotation encoding="application / x-tex">V_{2B}(t)< / annotation>< / semantics>< / com:Math>). Although claims have been formulated in this application to particular combinations of features, it should be understood that the scope of the disclosure of the present invention also includes any novel features or any novel combination of features disclosed herein either explicitly or implicitly or any generalization thereof, whether or not it relates to the same invention as presently claimed in any claim and whether or not it mitigates any or all of the same technical problems as does the present invention. The applicant hereby gives notice that new claims may be formulated to such features and / or combinations of such features during the prosecution of the present application or of any further application derived therefrom.

Claims

1. A method for an ultrasonic time-of-flight flow meter, comprising: driving an ultrasonic transducer using a first waveform for a first duration, the first waveform configured to cause oscillation of the ultrasonic transducer; driving the ultrasonic transducer using a second waveform for a second duration, wherein the second waveform does not excite further oscillation of the ultrasonic transducer, wherein there is a discontinuity between the first waveform and the second waveform, and wherein the second waveform and the second duration are configured to maintain a voltage across the ultrasonic transducer within a predetermined range.

2. A method according to claim 1, wherein the second duration is configured to allow an oscillation energy of the transducer to reduce to a level whereby the voltage across the ultrasonic transducer will remain within the predetermined range after the end of the second duration.

3. A method according to claim 1 or claim 2, wherein the predetermined range is a designed for driving voltage range of the ultrasonic transducer, or the designed for driving voltage range of the ultrasonic transducer plus an overvoltage tolerance.

4. A method according to claim 1 or claim 2, wherein the predetermined range is a rail-to-rail voltage of a further component which is connected to the ultrasonic transducer, or the rail-to-rail voltage of the further component plus an overvoltage tolerance.

5. A method according to any one of claims 1 to 4, wherein the first waveform has a frequency spectrum in which a majority of the power is within one or more bandwidths corresponding to respective resonances of the ultrasonic transducer; and wherein the second waveform has a frequency spectrum in which a majority of the power is outside the one or more bandwidths corresponding to respective resonances of the ultrasonic transducer.

6. A method according to any one of claims 1 to 5, wherein the first waveform has a constant base frequency to a tolerance of ± 10 % \pm 10\% .

7. A method according to any one of claims 1 to 6, wherein the second waveform has a constant base frequency to a tolerance of ± 10 % \pm 10\% .

8. A method according to any one of claims 1 to 5, wherein the frequency of the first waveform varies as a function of time.

9. A method according to any one of claims 1 to 5 or 8, wherein the frequency of the second waveform varies as a function of time.

10. A method according to any one of claims 1 to 9, wherein the method is used to measure a flow rate of a liquid.

11. A method according to any one of claims 1 to 9, wherein the method is used to measure a flow rate of a gas.

12. A method according to any one of claims 1 to 10, wherein the method is used to measure a flow rate of water.

13. A method according to any one of claims 1 to 9 or 11, wherein the method is used to measure a flow rate of natural gas.

14. A method according to any one of claims 1 to 13, wherein the method is used to measure a flow rate used for fiscal metering purposes.

15. An ultrasonic time-of-flight flow meter comprising: a first ultrasonic transducer and a second ultrasonic transducer spaced apart along a fluid flow path and configured such that a transmission path between the first and second ultrasonic transducers has a component in a direction parallel to the fluid flow path; a controller configured to drive the first and second ultrasonic transducers alternately, wherein the controller is configured to: drive the driven ultrasonic transducer using a first waveform for a first duration, the first waveform configured to cause oscillation of the driven ultrasonic transducer; drive the driven ultrasonic transducer using a second waveform for a second duration, wherein the second waveform is configured not to excite further oscillation of the ultrasonic transducer; wherein there is a discontinuity between the first waveform and the second waveform, and wherein the second waveform and the second duration are configured to maintain a voltage across the driven ultrasonic transducer within a predetermined range.

16. An ultrasonic time-of-flight flow meter according to claim 15, wherein the second duration is configured to allow an oscillation energy of the driven ultrasonic transducer to reduce to a level whereby the voltage across the driven ultrasonic transducer will remain within the predetermined range after the end of the second duration.

17. An ultrasonic time-of-flight flow meter according to claims 15 or 16, wherein the first waveform has a frequency spectrum in which a majority of the power is within one or more bandwidths corresponding to respective resonances of the driven ultrasonic transducer; and wherein the second waveform has a frequency spectrum in which a majority of the power is outside the one or more bandwidths corresponding to respective resonances of the driven ultrasonic transducer.

18. An ultrasonic time-of-flight flow meter according to any one of claims 15 to 17, wherein the second waveform is configured to suppress coupling between the first and second ultrasonic transducers.