Exponential signal measurement device

Abstract

Non-uniform sampling devices and techniques and anti-offset luminescence lifetime estimation enable sensing of gas presence and amplitude, such as the level or concentration of O2. The partial pressure of O2 is closely related to the service life of light quenched by O2. Since the lifetime measurement is robust to factors such as optical path changes, lifetime measurement is superior to intensity measurement. The disclosed method implemented in 180 nm CMOS features a dedicated AFE (Analog Front End) that 1) obtains luminescence lifetime information with low noise and 2) utilizes time-gated excitation without the need for optical filters to extract luminescence responses from the excitation light. The lifetime ([tau]) is calculated using the time difference between the equal voltage steps, and 4) the accuracy of the average error measured reaches 0.3%.

Description

Background Art

[0001] Among the vital signs of human health, respiratory parameters are key indicators of the body's physiological status. Quantifying the real-time dynamics and physiological distribution of blood gas measurements of oxygen (O2) and carbon dioxide (CO2) is crucial for clinicians to understand the mechanisms associated with pathological and normal physiological conditions.

[0002] Respiratory health is measured through five main parameters: respiratory rate and quality, arterial oxygen partial pressure (PaO2), arterial oxygen saturation (SaO2), and arterial carbon dioxide partial pressure (PaCO2). Respiratory rate refers to the number of times an individual inhales and exhales during a given period of time. Respiratory quality describes the effectiveness of each breath, which is quantified as vital capacity, maximum respiratory pressure, and expiratory minute volume, all of which determine how easily an individual can inhale and exhale air from their lungs. Summary of the Invention

[0003] Non-uniform sampling equipment and techniques and offset-resistant luminescence lifetime estimation enable sensing of gas presence and amplitude (such as the level or concentration of O2). The partial pressure of O2 is closely related to the lifetime of the luminescence quenched by O2. Lifetime measurements are superior to intensity measurements because they are robust to factors such as optical path changes. The disclosed method is characterized by a dedicated AFE (analog front end) that obtains luminescence lifetime information with 1) low noise and 2) utilizes time-gated excitation without the need for optical filters to extract the luminescence response from the excitation light. The lifetime (τ) is calculated using the time difference between equal voltage steps, and the accuracy of the average error of the measurement reaches 0.3%.

[0004] The luminescent film emits light in response to a light stimulus of a specific wavelength, and the sensed voltage value provides an exponential response indicative of the gaseous stimulus. The disclosed method for measuring a timing constant in a measurement circuit for voltage pulses receives a set of points or values based on voltage values from a sensor device; and evaluates a timing exhibited by the set of points derived from the exponential response. An evaluation circuit calculates a timing constant based on the evaluated timing, and determines the presence and magnitude of a substance sensed by the sensor device based on the timing constant.

[0005] An example configuration demonstrates a non-uniform sampling device and technique for measuring the luminescence lifetime and decay of a photosensitive material for oxygen sensing. The system features a switched-capacitor circuit that implements a fixed voltage step for quantization, enabling long integration times without saturating the front-end amplifier. Control circuitry automatically tunes the light-emitting diode (LED) excitation pulse to avoid overloading or underloading the front-end as the photodiode current varies with oxygen partial pressure (PO2). Time-gating of the front-end integrator eliminates the need for optical filtering. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] The above and other objects, features and advantages of the present invention will become apparent from the following description of particular embodiments of the present invention as illustrated in the accompanying drawings, in which like reference numerals refer to the same parts throughout the different views. The drawings are not necessarily drawn to scale, emphasis instead being placed upon illustrating the principles of the invention.

[0007] Figure 1 is a contextual diagram of luminescence emission and decay for oxygen sensing as disclosed herein;

[0008] Figures 2A to 2C Shown based on Figure 1 The excitation intensity of the luminescent emission;

[0009] Figures 3A to 3C is a graph and circuit for detecting voltage thresholds at which intensity measurements are made;

[0010] Figure 4 The figure shows the image which has been shifted for analysis. Figure 3A and Figure 3B Voltage level in

[0011] Figure 5 Shown for processing Figures 2A to 4 Circuit diagram of the voltage threshold;

[0012] Figures 6A to 6C Shown Figure 5 Example circuit segments in the circuit of ;

[0013] 7A to 7C Shown by Figures 5 to 6C circuitry for receiving and / or processing the measured response signal;

[0014] Figure 8 Shown Figures 5 to 7C Error detection and resolution in circuits; and

[0015] Figures 9A to 8 B shows the use of Figures 5 to 8 A graph of the oxygen sensed by the circuit. DETAILED DESCRIPTION

[0016] Luminescent gas measurement allows small, localized devices to directly sense blood gas levels based on partial pressures from epidermal exposure. In particular, oxygen and carbon dioxide can be detected and concentrations sensed by a skin-mounted device with pulsed LED light emission, coupled to a light-sensitive device (typically a photodiode) that measures the emission decay following the LED pulse, which varies with the presence of gas.

[0017] In an example arrangement as disclosed herein, the sensor device is a photodetector, and the external stimulus is light emitted from a photoluminescent film (luminescent film). The external stimulus is based on the photoluminescent film in a gaseous environment, and the calculated timing constant indicates the sensed gas. An evaluation circuit determines the gas concentration based on the voltage value generated by the external stimulus detected by the sensor device. The set of points need only include at least three points on an exponential decay driven by the external stimulus (e.g., emitted light from the luminescent film excited by an external light pulse). The luminescent film is sensitive to a certain type of gas and emits light of a predetermined wavelength in response to the wavelength of the external light pulse. These three points lie on a curve defined by the emitted light and indicate the presence and magnitude of the sensed gas.

[0018] To achieve tuning and accuracy, the evaluation circuit may generate several correction factors. The circuit evaluates multiple voltage values from the sensor device when the external stimulus is dormant in the absence of an external light pulse, and adjusts the calculated timing constant for the correction factors based on the evaluated multiple voltage values.

[0019] Alternatively, the evaluation circuit identifies a correction factor based on a voltage value response slope between voltage values exhibited by the set of points, and adjusts the calculated timing constant for the correction factor based on a sensing delay between adjacent points in the set of points.

[0020] Any suitable stimulus response can provide three points for calculating the timing constant. Since only three points are required and extensive iteration of high-precision values is not required, the timing constant can be calculated using lower-cost circuit components. The correction factor mentioned above further mitigates any loss of accuracy.

[0021] Therefore, it is clear that the ability to monitor the breathing of high-risk patients in real time at home is critical to preventing respiratory failure. Care providers can assess the effectiveness of breathing by measuring blood gases, namely oxygen (O2) and carbon dioxide (CO2). Recently, luminescent gas sensing has re-emerged as an attractive approach for creating miniaturized, non-invasive transcutaneous blood gas monitors. Conventional medical devices measure the partial pressures of O2 and CO2 molecules that diffuse through the skin, which are directly related to arterial O2 and CO2. This conventional approach often has substantial power and / or size requirements that are not commensurate with wearable devices. In contrast, the configuration described in this article uses a dedicated analog front end (AFE) with lightweight estimation methods and computation to obtain accurate sensor readings.

[0022] The configuration herein presents a non-uniform sampling technique and an offset-resistant luminescence lifetime estimation algorithm for O2 sensing. The partial pressure of O2 (PO2) is closely related to the lifetime of the luminescence quenched by O2. Lifetime measurements are superior to intensity measurements because they are robust to factors such as optical path changes, thereby reducing susceptibility to motion artifacts and skin color differences. Luminescence responses as affected by partial O2 pressure are disclosed in U.S. application No. 17 / 066,570, entitled "WEARABLE BLOOD GAS MONITOR," previously filed by the applicant on October 9, 2020, which is incorporated herein by reference in its entirety. The present disclosure provides a circuit for efficiently and compactly measuring sampled values using as few as three data points or readings of optical emissions at a predetermined wavelength, including but not limited to luminescent film-based oxygen sensing.

[0023] A specific configuration of the disclosed system features a dedicated AFE that collects luminescence lifetime information and utilizes time-gated excitation, eliminating the need for optical filters to extract the luminescence response from the excitation light. The lifetime (τ) is calculated using the time difference between equal voltage steps using a proposed anti-drift calculation. The average error of the measurement is expected to be 1.9% accurate without post-processing. The specific configuration demonstrates PO2 measurement using a gas container, however other usage contexts and stimuli can also be employed. The specific configuration can be attached to the patient's epidermal surface or adjacent to other physiological sources to measure blood and / or respiratory gases.

[0024] Figure 1 is a context diagram of luminescence emission and decay for oxygen sensing as disclosed herein. Figure 1 , showing the elements of a luminescent O2 sensing mechanism. In the example arrangement, the external stimulus is based on a luminescent film 100 in a gaseous environment, and the calculated timing constant indicates the sensed gas. The O2 sensitive dye or film is composed of functional groups (including luminescent molecules) called luminophores. When illuminated with an LED having a wavelength of approximately 450nm (blue or violet light), in step 1, the excited photons interact with the luminescent molecules in the film. In step 2, this excites the electrons to a higher state. When the luminophore is exposed to higher energy photons (450nm light), the electrons in the luminophore jump to a higher energy level. After a period of time, the electrons attempt to return to the ground state. As depicted in step 3, the electrons slowly return to the ground state, emitting lower energy photons. For luminescent materials, excited electrons can enter a triplet state, which prevents the electrons from returning directly to the ground state. When the electrons return to the ground state from this triplet state, photons with a longer wavelength (650nm) are emitted. However, O2 limits or "quenches" the emission, as shown in step 4, so this emission is "quenched" or suppressed by the presence of O2 in the sensing region. Figure 2CThe Stern-Volmer equation shown inside describes the kinetics of this interaction. The intensity (I) and τ (timing constant) are determined by the rate constant K SV and the intensity / lifetime (I0 / τ0) under anaerobic conditions is related to PO2.

[0025] Figures 2A to 2C Shown based on Figure 1 The excitation intensity of the luminescent emission. Figures 1 to 2C , luminescent molecules are stored or embedded in the sensing film 100. Photoluminescence is one of the possible events caused by the interaction between light and matter. Molecules capable of luminescence contain functional groups called luminophores. Luminophores are responsible for the photoluminescence properties of a material. When a luminophore absorbs a photon 1', the luminophore is excited to a higher energy state. When the luminophore relaxes from the excited state, the luminophore can emit photons in the form of emission 4'. Typically, when a higher energy (shorter) wavelength enters the material, a lower (longer) energy wavelength is emitted. The difference between these two spectra is called the Stokes shift.

[0026] The two main processes that describe photon emission during deexcitation are fluorescence and phosphorescence. Fluorescence occurs in a wide range of materials but is difficult to observe due to its lifetime being on the order of tens of nanoseconds. The second process, phosphorescence, is generally less likely to occur but is more easily observed due to its lifetime being on the order of microseconds to seconds. The use of heavy atoms in the luminophore increases the probability of phosphorescence and improves the efficiency of the process, thereby reducing the lifetime.

[0027] This photophysical quenching effect can be broadly described as energy transfer. The luminescent material A is excited by some external energy and is thus raised to a higher energy state A. * Then, A * is exposed to a quenching substance Q, and a portion of the energy is transferred to the quenching substance Q by a quenching rate constant k. sv Transfer to Q. The intensity of the excitation 1' has a peak 102 driven by the LED driver. The resulting emission forms a peak 104, and the intensity of this peak varies with the presence of O2, where the intensity 104 is greater the lower the presence of oxygen, since oxygen has a tendency to quench the emission 4'. Figure 2C The variation of intensity 110 over time 120 is shown, wherein the decay of intensity 110 over time 120 gives the oxygen concentration.

[0028] Figures 3A to 3C Shows a graph and circuit for detecting voltage thresholds at which intensity measurements are taken. Figures 1 to 3C , showing the intensity signal aggregation. The inhomogeneous luminescence lifetime estimation calculation is started using a decay exponent with an offset:

[0029]

[0030] Using an integrating circuit or similar computing element gives the voltage at time t:

[0031]

[0032] The integration operation scales and inverts the exponent but does not affect the timing constant. We now have a voltage signal that can be quantized:

[0033]

[0034] Let the integration be performed over time 130, recording the time it takes for the voltage 132 to increase by a fixed amount ΔV. The disclosed circuit only needs to measure three samples, one at any point in time t0, and the remaining samples at subsequent voltage steps 134-1..134-2 of equal magnitude, as Figure 3A As shown in Figure 2. The sample defines the set of points based on voltage values, and only three points are needed to calculate the corresponding timing constants. The set of points is taken at t0, t1, and t2 and is based on equal voltage intervals ΔV.

[0035] Now there are three voltages separated by a fixed ΔVs. To simplify notation, the negative sign can be removed from the amplitude component.

[0036]

[0037] The difference between adjacent voltages can be taken to minimize the DC offset component. If the DC current component is small, the time steps are relatively close, or the feedback capacitor is relatively large, the DC component decreases.

[0038]

[0039] Next, these two voltage differences can be divided to cancel out the amplitude of the exponential, leaving only the time information:

[0040]

[0041] Multiply both sides by:

[0042]

[0043] Simplifying to get:

[0044]

[0045] The measured time difference can be used to solve for the timing constant τ. The three time values that define the luminescence decay interval based on equal sense voltage values can be mapped / calculated to the oxygen level.

[0046] In order to implement the non-uniform luminescence lifetime estimation calculation in hardware, a component is needed to reliably create repeatable voltage steps to calculate the level crossing at each voltage step. The level crossing detector can be implemented as a resistor string 162-1..162-3 (collectively referred to as 162) across several comparators, such as Figure 3B As shown, as the integrated voltage rises, each of the three comparators 160-1 to 160-3 (collectively, 160) is switched to a set voltage level corresponding to the voltage step 134-1 or 134-2, and at recorded times t0–t2. This technique captures the concept of non-uniform sampling but presents several issues. It requires three comparators, which can present challenges in terms of power, component cost, and size. The three comparators and resistors are matched to ensure that the voltage steps 134 are equal.

[0047] Matching and power issues in the comparator can be addressed by having some additional logic that changes the point on the resistor string 162 that the comparator 160 references. Figure 3C The technique shown requires only a single comparator 160. It may still be sensitive to resistor matching and noise, but these can be mitigated by shuffling and averaging. Because the integrated voltage swings between ground and a reference voltage, this technique is suitable for a specific dynamic range. The resistor string allows voltage values to be received from a set of interconnected comparators and / or from a single comparator adapted to sense current levels based on three sensing voltage levels. Additional voltage levels / thresholds can be employed with corresponding comparators and voltage thresholds.

[0048] In the call Figure 3B and Figure 3C In the case of a level crossing detector (as applied to the example configuration), an intensity sensor defined by a photodiode measures an intensity signal having an amplitude that varies with the intensity of the emission 4'. In the example configuration, where a photodiode is used to sense the emission 4', the current flowing through the photodiode varies with the intensity of the emission. The photodiode may have an integrated red pass filter. The disclosed method for measuring a timing constant in a measurement circuit for a voltage pulse comprises: receiving a set of points based on voltage values from a sensor device; and evaluating the timing exhibited by the set of points. The AFE calculates the timing constant based on the evaluated timing and determines the presence and amplitude of the substance (here O2) sensed by the sensor device based on the timing constant. The calculated gas concentration is based on the voltage value and / or current level generated by an external stimulus presented by the intensity of the emission 4' and detected by the sensor device. It will be appreciated that level crossing exhibited as a voltage level may also be implemented using current sensing by manipulating the dependencies of current, voltage and resistance accordingly.

[0049] Figure 4Shown as Figure 3A and Figure 3B The voltage levels in the proposed luminescence lifetime estimation method are shifted on the same calculation timing thresholds t0 to t2 for analysis. The AFE uses the time difference (Δt) between the fixed voltage steps (ΔV) 460-1..460-3) (collectively referred to as 460) to extract the timing constant (τ) of the decay exponential. This calculation, which can be implemented in hardware, is a modification of the fast lifetime determination. The non-uniform sampling circuit can include a level crossing circuit that is used to calculate the time based on the duration that the decay detection signal reaches a predetermined voltage defined by equal voltage thresholds. The level shifting circuit is used to separate the duration of each of the threshold crossings based on the received voltage value corresponding to the decay detection signal.

[0050] Each voltage step 460 corresponds to the resistor value set by the resistor string 162 for activating the corresponding comparator 160. The integration of the exponential does not change the timing constant (τ), which is a key parameter to be measured. The current generated by the photodiode is integrated to capture the exponential signal. When the integrated signal voltage reaches a preset threshold, the system records the time of the level crossing (e.g., t0, t1), and the integration is performed continuously. The difference between the two level crossings is taken to eliminate the integration constant. Determining the level crossing at t0 to t2 effectively shifts the voltage step 460 to a single voltage range 460'. This operation eliminates any offset error in the system. The quotient of the two differences eliminates the amplitude component of the exponential. The result is a transcendental equation that depends only on the sampling times t0, t1, and t2 of the level crossing and the unknown light timing constant τ. τ is calculated within a few iterations using a basic root-finding algorithm. This lightweight anti-offset algorithm only requires three samples, thereby relaxing the data rate requirements.

[0051] Figure 5 Shown for processing Figures 2A to 4 The voltage threshold circuit diagram. Figure 5 A circuit for evaluating exponential decay is presented in

[15] , comprising: a sensor device (e.g., a photodiode) for transmitting a detection signal indicative of an exponentially decaying stimulus; and a stimulation circuit for generating a trigger signal (excitation signal 1') for triggering the exponentially decaying stimulus (emission 4'). A non-uniform sampling circuit calculates a timing constant defining the decay rate of the exponentially decaying stimulus, and a resulting estimator maps the timing constant to a concentration level of a measurand, wherein the exponentially decaying stimulus is indicative of the measurand (e.g., O2). Similar circuitry can be used for other stimuli using the evaluation of exponentially decaying stimuli / responses for any suitable medium.

[0052] refer to Figure 5 , and continue to refer to Figures 1 to 4The operation is divided into an excitation phase and a readout phase. During the excitation phase, the light emitting diode (LED) driver generates pulses with a set intensity and duration to excite the O2 sensitive film with blue light (λ = 450 nm). Integrators A1 and C F By switch Set to unity gain to avoid saturation of the AFE due to high intensity LED bursts. F 169 is reset only during the excitation phase, thus minimizing the impact of reset noise. The performed temporal signal gating extracts relatively weak luminescence signals from strong excitation signals without optical filtering.

[0053] In the readout phase, the photodiode D1 captures the emitted red photons (λ=650 nm), generating a current (I PD ),as follows Figure 7C Depicted. A1 167 and C F 169 integrates this current to generate a voltage. The integrator uses non-uniform switched capacitor technology to increase its output V AFE Comparator A2 (160) detects the level crossing and sends a signal (V COMP ). The SCU sends four non-overlapping signals in sequence ( arrive ) to drive the switched capacitor C SW This action injects a fixed amount of charge into the summing node Σ166 of the integrator. The charge injection causes V AFE Subtracting ΔV from the fixed voltage at , allows A1 to continue integrating the photocurrent.

[0054] In certain configurations, there may be a voltage that is proportional to the overdrive voltage (V ov ) is related to the comparator 160 delay (how much the input signal exceeds the comparator threshold). The more the input exceeds the threshold, the easier it is for the comparator to make a decision. An exponentially earlier, steeper rise time will cross the threshold more quickly, resulting in a larger overdrive voltage during the comparator's decision time. An exponentially later, flatter rise time will take longer to cross the threshold, and therefore the comparator will take longer to make a decision.

[0055] The device and circuitry may evaluate a plurality of voltage values from the sensor device while the external stimulus is dormant and adjust the calculated timing constant for a correction factor based on the evaluated plurality of voltage values.

[0056] The digital logic can be implemented on a suitable FPGA (field programmable gate array) or other processing controller that controls the power-up sequence, the timing of the excitation and readout phases, the front-end bias, and the LED driver power. An important function of the FPGA 170 is automatic "gain control" of the LED driver. The FPGA 170 counts the number of comparator 160 (A2) pulses and adjusts the LED driver 172 to ensure that the same number of pulses is present for each measurement. For low PO2, the luminescence sensor emits many red photons for a given amount of excitation blue photons, so the LED drive current is set weaker. Conversely, for high PO2, the LED drive is increased to excite more photons. If the number of pulses from the AFE is less than the set threshold, the LED bias is increased by one bit, and vice versa. If the pulses match the threshold, no change is made. Automatic LED driver tuning extends the dynamic range of O2 measurement.

[0057] Figures 6A to 6C Shown Figure 5 Example circuit segment from the circuit in . Figure 6A and Figure 6B Contains a simplified schematic diagram of the AFE 168. Reference Figures 1 to 6B Front-end amplifier A1 167 is a telescopic cascode with PMOS inputs and a common-source output stage. The timing constant of the front end should be at least an order of magnitude smaller than the luminous decay time, thereby reducing the error introduced by the front end to less than 1%. Comparator A2 performs the level-crossing detection function of the sampler. This circuit detects when the integrator output reaches the threshold and triggers the switched capacitor circuit to inject a fixed amount of charge into the summing node of the operational amplifier, generating a voltage step 460° (ΔV), as shown in FIG. Figure 4 Depicted.

[0058] To achieve narrow LED pulses, a current steering technique inspired by emitter-coupled logic is employed. A regulated current source controls the tail current, which sets the LED drive, based on a bias voltage provided by the controller. When the main control loop issues a command to activate the O2 sensing membrane, the controller turns on a replica current path. This action awakens the tail current source and establishes the LED drive current. Once the replica path establishes the LED driver current, the controller quickly switches to the active channel to activate the emitter. The driver can set LED pulse intensity up to 1A with 10-bit resolution and pulse widths as narrow as a few hundred nanoseconds. Figure 6C Example circuitry for the SCU 164 is shown.

[0059] Further described below and in 7A to 9BThe graphs shown in Figure 3 illustrate a series of tests, including bandwidth and input-referred noise to evaluate key front-end performance; transient tests to evaluate the hardware implementation of the τ estimation algorithm; and gas tests to demonstrate the O2 measurement performance of the example configuration.

[0060] 7A to 7C Shown by Figures 5 to 6C The circuit receives and / or processes the measured response signal. During the 40μs excitation phase (30μs replica and 10μs active), the auxiliary LED driver uses a maximum of 15μJ at high PO2 to excite the sensor. During the excitation and readout phases (100μs), the AFE uses 130nJ to collect three samples for the τ calculation. The input-referred noise 180 and the bandwidth of A1 are respectively Figure 7A and Figure 7B The integrated noise is 124uV rms , which is measured over a bandwidth of 200 Hz to 100 kHz, and the 1 / f corner is ~10 kHz. The measured gain bandwidth product GBWP of the front-end amplifier is 10 MHz.

[0061] τ is the lifetime estimation algorithm proposed, using the comparator pulse V COMP To evaluate the accuracy and precision of this technique, an exponentially decaying current ( Figure 7C i test ). The lifetime was also calculated by fitting an exponential model to the same stimulation current waveform for comparison.

[0062] Figure 8 The error between the proposed algorithm and the exponential model is shown. Figure 8 For timing constants ranging from 1 to 20 μs (a relevant range for human transcutaneous O2 estimation), the average error is ~-1.9%, with error bounds of +1% / -4%. The error increases for t < 1 μs due to comparator response delays. F In the case of 2pF, the sampler requires a minimum of 3pC to perform the calculation.

[0063] Figures 9A to 9B Shows the use Figures 5 to 8 A graph of oxygen sensed by the circuit. In vitro gas testing is a ratiometric mass flow rate use case. Figure 5The O2 sensor in the circuit is deployed over a range of PO2. To control PO2, O2 and nitrogen (N2) are mixed in a controlled ratio at 760 mmHg (1 atm). An MKS1179A mass flow controller (MFC) sets the gas mixture ratio. For fixed volume, temperature, and pressure, the partial pressure of the gas is directly related to the mass of the gas in the mixture. PO2 is swept from 0 to 228 mmHg in steps of 14.25 mmHg. PC software controls the mass flow setpoint and data readout.

[0064] exist Figure 9A The calculated timing constant is plotted against PO2, and Figure 9B This is a Stern-Volmer plot of the same data. Deviations from a linear relationship at relatively high PO2 are due to the inability of some luminophores to be quenched by O2. The non-uniform sampler can measure PO2 from 0 to 150 mmHg (covering the human-relevant range) with a mean error of 2.2 mmHg, which is below the FDA standard of 5 mmHg.

[0065] Those skilled in the art will readily appreciate that the procedures and methods defined herein can be delivered to a user processing and rendering device in many forms, including but not limited to: a) information permanently stored on a non-writable storage medium (such as a ROM device); b) information changeably stored on a writable non-temporary storage medium (such as a solid-state drive (SSD) and media, flash drives, floppy disks, tapes, CDs, RAM devices, and other magnetic and optical media); or c) information transmitted to a computer via a communication medium (in an electronic network such as the Internet or a telephone modem line). The operations and methods can be implemented in a software executable object or as a set of coded instructions executed by a processor that executes in response to these instructions, including a virtual machine and a hypervisor-controlled execution environment. Alternatively, the operations and methods disclosed herein can be embodied in whole or in part using hardware components or a combination of hardware, software, and firmware components, such as an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a state machine, a controller, or other hardware component or device.

[0066] While the systems and methods defined herein have been particularly shown and described with reference to embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention as encompassed by the appended claims.

Claims

1. A method for measuring a time constant in a measurement circuit for a voltage pulse, the method comprising: receiving a set of points based on voltage values from a sensor device; Evaluate the time series exhibited by the set of points; calculating a timing constant based on the evaluated timing; as well as The presence and magnitude of a substance sensed by the sensor device is determined based on the timing constant. 2 . The method of claim 1 , further comprising determining the gas concentration based on a voltage value generated by the external stimulus detected by the sensor device.

3. The method according to claim 1, wherein The set of points includes at least 3 points on an exponential decay driven by the external stimulus.

4. The method of claim 2, further comprising: evaluating a plurality of voltage values from the sensor device when the external stimulus is dormant; as well as The calculated timing constant is adjusted for a correction factor based on the evaluated plurality of voltage values.

5. The method of claim 2, further comprising: identifying a correction factor based on a slope of a voltage value response between the voltage values exhibited by the set of points; as well as The calculated timing constant is adjusted for the correction factor based on a sensing delay between adjacent points in the set of points.

6. The method of claim 2, wherein: The sensor device is a photodetector and the external stimulus is emitted light.

7. The method according to claim 6, wherein: The external stimulus is based on a luminescent film in a gaseous environment, and the calculated timing constant is indicative of the sensed gas.

8. The method of claim 1, further comprising receiving the voltage values from a set of interconnected comparators.

9. The method of claim 1, further comprising receiving the voltage values from a single comparator adapted to sense the current level based on three sensing voltage levels.

10. The method of claim 9, wherein: The received set of points is based on corresponding current values of a constant voltage difference between the set of points.

11. A circuit for evaluating exponential decay, the circuit comprising: a sensor device for transmitting a detection signal indicative of an exponentially decaying stimulus; a stimulation circuit, the stimulation circuit being configured to generate a trigger signal, the trigger signal being configured to trigger the exponential decay stimulation; a non-uniform sampling circuit for calculating a timing constant defining a decay rate of the exponentially decaying stimulus; as well as A result estimator is configured to map the time series constant to a concentration level of a substance being measured, the exponentially decaying stimulus being indicative of the substance being measured.

12. The circuit of claim 11, wherein The non-uniform sampling circuit includes a level crossing circuit for calculating a time based on a duration for which a decaying detection signal reaches a predetermined voltage defined by an equal voltage threshold.

13. The apparatus of claim 12, further comprising a level shift circuit for separating a duration of each of the threshold crossings based on a received voltage value corresponding to the decay detection signal. 14 . The apparatus of claim 12 , further comprising a resistor string configured to transmit a timing signal based on the voltage of the detection signal reaching the voltage threshold.

15. The apparatus of claim 11, wherein: The stimulation circuit is operable to generate the trigger signal at predetermined timing intervals, and the calculated time is based on the predetermined timing intervals.

16. The apparatus of claim 15, wherein: The trigger signal is an optical signal of a predetermined wavelength, and the decay stimulus is based on luminescence decay of an emission wavelength quenched by the presence of the substance being measured.

17. The apparatus of claim 13, wherein: The level shift circuit is further configured to correct for DC leakage current in the following manner: evaluating a plurality of voltage values from the sensor device while the exponentially decaying stimulus is dormant; and The calculated timing constant is adjusted for a correction factor based on the evaluated plurality of voltage values.

18. The apparatus of claim 13, wherein: The level shift circuit is further configured to: identifying a correction factor based on a voltage value response slope between the voltage values exhibited by the received voltage values; and The calculated timing constant is adjusted for the correction factor based on a sensing delay between received voltage values.

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