Parallel voltage-to-digital power series conversion with auto-calibrating transconductors, error-canceled references, and current-to-power converters

Abstract

The present disclosure relates to parallel voltage-to-digital power series conversion employing an automatically calibrated transconductor, error-canceled reference, and current-to-power converter. An apparatus for converting a detected voltage indicative of a conducted current by a switching circuit into a series of electrical pulses indicative of electrical power dissipated by the switching circuit in response to the conducted current is disclosed. The apparatus includes a transconduction circuit comprising a first circuit for receiving a reference current and a first reference voltage and obtaining a transconductance based on an automatically generated bias current and the reference current and the first reference voltage, wherein a value of the transconductance is determined by the reference current and the first reference voltage. The transconduction circuit further includes a second circuit coupled to the first circuit for receiving a detected voltage and generating a first current based on the detected voltage and the obtained transconductance.

Description

Technical Field

[0001] This document is generally applicable to, but not limited to, electronic circuits, especially battery management systems. Background Technology

[0002] Electric or hybrid electric vehicles typically include one or more battery modules or other portable power sources configured to provide power to vehicle systems. In one example, an electric vehicle may include a group of one or more battery modules connected in series to provide power at a specified voltage (e.g., within the range of 30-600 volts) to drive or power the vehicle's electric drive motor or other drivetrain system. The battery modules may be associated with a battery management system (BMS) configured to protect the battery modules from damage by controlling (e.g., by limiting or regulating) the power drawn from the modules, e.g., during electric vehicle operation. In one example, the BMS may include control circuitry for limiting the amount of current drawn by the electric vehicle's drivetrain system from the battery modules. The control circuitry may interrupt the current drawn from the battery modules when the current or current-related power exceeds the safe operating range of one or more components of the system. Attached Figure Description

[0003] Figure 1 An example of a battery management system is illustrated.

[0004] Figure 2 An example of a conversion circuit is illustrated for converting the current flowing through a switching circuit into a signal indicating the power dissipated as heat in the switching device.

[0005] Figure 3A The illustration shows an example of a circuit configured to obtain transconductance based on a provided reference current and a provided reference voltage.

[0006] Figure 3B The illustration shows an example of a circuit configured to convert voltage into current based on a provided transconductance.

[0007] Figure 4 An example of a circuit configured to generate an output current that is exponentially proportional to the input current is illustrated.

[0008] Figure 5 The illustration shows an example of a circuit configured to generate an error-compensated reference voltage.

[0009] In accompanying drawings that are not necessarily drawn to scale, similar numbers may describe similar parts in different views. Similar numbers with different letter suffixes may represent different instances of similar components. The accompanying drawings illustrate, by way of example and not limitation, the various embodiments discussed in this document. Detailed Implementation

[0010] This disclosure includes techniques for controlling switching devices in a battery management system, such as a BMS used in electric vehicles to supply power from a battery module to a load (e.g., an automotive engine) via the operation of one or more solid-state switching devices (e.g., one or more power gates). These techniques include converting sensed voltages (e.g., voltages generated across shunt resistors in the BMS used to sense current drawn from the battery module) into a series of electrical pulses, where the count of these pulses over time represents the cumulative heat energy or average thermal power dissipated in the BMS switching devices during that period. The cumulative heat energy in the switching devices can indicate the current or transient junction temperature of the switching devices. The resulting series of electrical pulses can be combined with a suitable algorithm and used to disconnect the current path in the BMS by controlling the switching devices when the heat dissipated within the switching devices exceeds the safe operating range of the protected battery module or power source. This can suppress or limit damage to the switching devices due to accumulated heat from over-operation or current consumption and can protect other system components, such as the battery module or motor, from operating at unsafe currents. BMSs using these techniques for high-voltage equipment can be manufactured using solid-state switches as the primary switching devices to control the power delivered to the load. The use of solid-state devices instead of mechanical switches reduces the cost of these systems. Furthermore, reliability and response time can be improved by controlling the operation of switching devices based on the cumulative energy consumed by the devices.

[0011] Figure 1 An example of a battery management system 100 is illustrated. Figure 1 As shown, BMS 100 includes a battery module 105, a load 110, a switching circuit 115, a sensing device 120, and a monitoring circuit 125.

[0012] Battery module 105 may include a group of one or more electrochemical or solid-state battery cells configured to provide power to the system. In one example, battery module 105 includes a group of one or more battery modules arranged to provide power at an indicated output voltage such as 30 to 600 V volts (V).

[0013] Load 110 includes electrical or electromechanical circuitry configured to be driven by power supplied by battery module 105. In this example, load 110 is an electric motor, such as a DC motor used to provide mechanical power in the drivetrain of an electric vehicle.

[0014] Switching circuit 115 includes electronic or electromechanical devices configured to provide controlled or regulated power from a power source, such as battery module 105, to drive or actuate a load, such as load 110. In one example, switching circuit 115 includes one or more semiconductor devices, such as power field-effect transistors (FETs), power diodes, or power bipolar junction transistors arranged to conduct current from battery module 105 to load 110. In another example, switching circuit 115 includes at least one control signal, such as SWITCH_CTRL, driving the switching circuit to control (e.g., limit or regulate) the current flowing from the power source through the switching circuit to the load. Such control may include limiting the amount of current or power drawn from the power source below an indicated current or power. In one example, switching circuit 115 includes a driver circuit (not shown) configured to receive the control signal and, in response to the value or other electrical characteristics of the control signal, drive one or more switching elements in switching circuit 115, such as one or more semiconductor gates or transistors, to turn on or off to control the amount of current flowing through the switching circuit. In one example, the switching circuit 115 includes one or more power FETs and one or more gate drivers arranged to controllably actuate the power FETs.

[0015] The sensing device 120 includes means configured to detect the amount of electrical power conducted by the switching circuit 115. In an example, the sensing device 120 includes a shunt resistor or other circuit coupled in series with the switching circuit 115 and is configured to generate a voltage indicating the amount of current flowing through the sensing device or the switching circuit.

[0016] Monitoring circuit 125 includes circuitry configured to monitor or control the operation of BMS 100. In some examples, monitoring circuit 125 is configured with hardware circuitry or software application to measure and store data indicating the electrical operating characteristics of one or more components of the BMS. In some examples, monitoring circuit 125 measures or calculates the remaining voltage or charge on battery module 105, the current drawn by load 110, or the temperature of switching circuit 115. In some examples, monitoring circuit 125 is configured to control the operation of switching circuit 115 based on a signal, such as a sensed voltage generated by sensing device 120. In one example, monitoring circuit 125 is configured to shut down switching circuit 115 based on a momentary or historical current conducted by switching circuit 115. In another example, monitoring circuit 125 is configured to shut down switching circuit 115 based on momentary or historical heating in switching circuit 115. Monitoring circuit 125 may include conversion circuitry 130, accumulator circuitry 135, and logic circuitry 140. In some examples, monitoring circuit 125 includes a current reference 145 or a voltage reference 150. In other examples, the current reference 145 or the voltage reference 150 is obtained from an external circuit.

[0017] The conversion circuit 130 includes circuitry configured to convert a signal representing the current conducted by the switching circuit 115 into a signal representing or proportional to the amount of electrical power consumed or dissipated by the switching circuit. In one example, the conversion circuit 130 converts an analog signal (e.g., a voltage generated across a shunt resistor) obtained from the sensing device 120 into a digital signal (e.g., a series of electrical pulses) representing the average electrical power consumed or dissipated by the switching circuit 115, or accumulated energy. In another example, the frequency of the electrical pulses generated by the conversion circuit 130 indicates the amount of electrical power consumed or dissipated. In one example, the frequency of the electrical pulses generated by the conversion circuit 130 (e.g., the number of electrical pulses generated over a specified time span or period) increases in response to an increase in the amount of electrical power consumed or dissipated. In another example, the frequency of the electrical pulses generated by the conversion circuit 130 decreases in response to a decrease in the amount of electrical power consumed or dissipated.

[0018] Accumulator circuit 135 includes circuitry configured to accumulate, count, or store data indicating a series of electrical pulses generated by conversion circuit 130. In one example, accumulator circuit 135 includes a counter, such as a binary counter circuit, configured to increment or decrement a stored counter value in response to each electrical pulse generated by conversion circuit 130. In another example, the counter is a Gray code counter configured to increment or decrement the counter value such that only one bit in the binary representation of the counter is changed each time it is incremented or decremented.

[0019] Logic circuit 140 includes analog or digital logic circuitry configured to provide a control signal SWITCH_CTRL to control the operation of switching circuit 115 based on a count of electrical pulses obtained by accumulator circuit 135. In the example, logic circuit 140 checks for changes in these counts at specified time intervals, such as on each positive edge of a timing signal used to drive or actuate the logic circuitry. Logic circuit 140 includes memory or other hardware or software elements configured to implement indicated techniques or algorithms for selectively actuating switching circuit 115 based on the count of electrical pulses obtained by accumulator circuit 135. In the example, logic circuit 140 implements a technique for generating a control signal (e.g., SWITCH_CTRL) based on the count of electrical pulses generated by switching circuit 130 over an indicated time span (e.g., within the indicated number of cycles of timing signal CLK). For example, logic circuitry 140 initiates SWITCH_CTRL in response to determining that the number of electrical pulses generated by switching circuitry 130 within a specified number of cycles of timing signal CLK reaches or exceeds a threshold number of electrical pulses, as described in U.S. Patent Application No. 17 / 219,025, filed March 31, 2021, entitled "Fast Overcurrent Detection in Battery Management System," the contents of which are incorporated herein by reference. In the example, the threshold number of electrical pulses or the indicated time span is selected based on the physical electrical or thermal characteristics of one or more components of BMS 100. Such characteristics may include an electrothermal model of a switching device with or without any heat sink, the results of simulations based on electrical and thermal models, or datasheet parameters such as voltage or current tolerances, or characteristics of switching circuitry 115. In various examples, logic circuitry 140 allows thresholds to be configured for multiple time spans to distinguish one or more cases for controlling or interrupting power drawn from BMS 100. In the example, the first threshold can be used for fast short-circuit situations, such as those requiring a very fast response (e.g., real-time response or response within 1 microsecond) to mitigate damage. In another example, the second threshold can be used for slower overcurrent situations, such as those where failure to take corrective action within an indicated time window (e.g., 1 microsecond to 100 milliseconds) could lead to component damage.

[0020] In operation, BMS 100 is configured to provide current from battery module 105 to load 110, for example, via control switching circuit 115. Over time, or under certain operating conditions, switching circuit 115 may degrade or fail, for example, due to accumulated heat exceeding junction temperature or other operating tolerances of the circuit. This heating and associated damage may be caused by increased or abnormal current drawn by load 110, a fault in battery module 105, current spikes, or another condition that could cause switching circuit 115 to conduct more current or consume more power than specified by the circuit's indicated tolerances. Degraded or damaged switching circuitry will eventually fail, for example, by remaining permanently in a conducting or fully conducting state. Such failures can lead to damage to other components of BMS 100 or system-wide failure, for example, during short-circuit or overcurrent events. In one example, a failure of switching circuit 115 may cause excessive current to be drawn from battery module 105, resulting in damage or destruction of module 105. BMS 100 mitigates these problems by monitoring the current flowing into switching circuit 115 and shutting down the circuit in response to detecting an event or condition that could damage the switching circuit. In an example, BMS 100 monitors the current conducted by switching circuit 115, for example, by monitoring the operation of monitoring circuit 125, such as by the voltage generated across a shunt resistor (e.g., sensing device 120). BMS 100 then determines whether to shut down the switching circuit based on the detected current, the physical characteristics of switching circuit 115 (e.g., power or thermal characteristics), and historical heating in the circuit. In some examples, these techniques can protect switching circuit 115 from damage by shutting it down for a short period after an event that could damage the circuit occurs. In an example, logic circuit 140 can calculate an estimated junction temperature (e.g., junction temperature of the switching device) of switching circuit 115 using historical data generated by sensing device 120, switching circuit 130, or accumulation circuit 135. In an example, the shutdown action is triggered in response to the junction temperature of the switching device or the estimated junction temperature approaching a threshold junction temperature, such as the maximum permissible junction temperature of the switching circuit.

[0021] Figure 2 An example of a conversion circuit 200 for converting current flowing through a switching circuit (e.g., switching circuit 115) into a signal indicating the power dissipated in the switching circuit is shown. Conversion circuit 200 is an example or element of conversion circuit 130. In this example, conversion circuit 130 is an integrated circuit element of the analog front-end circuitry of BMS 100.

[0022] Conversion circuit 200 receives or obtains reference voltage V REF Bias current I REF1 and sensing voltage V s In one example, the reference voltageV REF This is generated within the conversion circuit 200, for example, by circuitry on the integrated circuit die implementing the conversion circuit 200. In another example, V REF Generated by circuitry external to the conversion circuit 200. Bias current. I REF Generated within the conversion circuit 200 and having a nominal or indicated value and associated permissible tolerance variation. Sensing voltage. V s It is a voltage signal obtained from a sensing device such as a shunt resistor or sensing device 120, which is configured to generate a current-sensitive signal. I(t) The voltage response. In one example, V s It is in response to current I(t) The voltage generated on the shunt resistor or sensing device 120.

[0023] In the example, the conversion circuit 130 generates an output signal, such as a pulse train or a series of electrical pulses, the frequency of which is... f p With conduction current I(t) The heat or power in the switching circuit is proportional to the power (e.g., one or more switches or switching devices in switching circuit 115). The frequency is shown in expressions (1) and (2). f p An example of the proportional relationship between heating or power in a switching circuit. The summation in expressions (1) and (20) is performed on the switching device or element of switching circuit 115, such as element E1 to E n ,like Figure 1 As shown.

[0024]

[0025] In expressions (1) and (2), each exponential term Indicates response to current I(t) The components in the switching circuit 115 that generate heat i The current-power relationship, such as that of a FET switch. In the example, the switching circuit 115 includes one or more such elements. i Each can exhibit a linear or nonlinear relationship between current and power. In one example, the linearity of the relationship is determined by an exponential factor. n i Indication. In some examples, each indicated element of the switching circuit 115 is associated with... n iThe value of has values ​​between 1 and 2, where values ​​closer to 1 indicate a linear current-power relationship, and values ​​closer to 2 indicate a more nonlinear current-power relationship. Terminology G i Representation and index n i Or the integral gain associated with each indicating element of the switching circuit 115, where K represents the proportionality constant.

[0026] Expressions (1) and (2) are based on the understanding that the current flowing through sensing device 120 can cause each element of switching circuit 115 to dissipate heat or consume power based on the resistance or impedance presented by each element in response to the current. In one example, if the element i Exhibits constant resistance R oni The current flowing through the component I s (t) With power P(t) i There may be a quadratic relationship between the heat within the component, as shown in expression (3). Current I s (t) It flows through the component i current I(t) One component. In some examples, such as when the components of switching circuit 115... i When connected in series, I(t) and I s (t) It is the same current.

[0027]

[0028] In another example, the element i It can represent the current flowing through the element I s (t) Inversely proportional dynamic resistance R ondyn , making R ondyn Given by expression (4). In this example, the element iThe power within is given by expression (5). An example of such a device is one that produces a constant voltage drop or a voltage drop that is substantially independent of the current flowing through the device, such as a diode. The power consumed in such a device is proportional to the current flowing through the device, since the power is the product of the voltage drop across the device and the current flowing through the device. A dynamic resistance can be associated with such a device such that the value of the dynamic resistance is represented by expression (4). In one example, in a diode or diode-based switching device, the voltage drop across the pn junction of the diode remains substantially constant as the current changes significantly, so the relationship between current and power in a diode is different from that in a power FET or resistor. While the power in a FET operating in the on state can be represented by the relationship shown in expression (3), the power in a diode can be represented or approximated by the relationships shown in expressions (4) and (5).

[0029]

[0030] In some examples, expression (5) can be understood by recognizing the components of switch circuit 115. i dynamic resistance R ondyn It can be more closely approximated as the current flowing through the component. I s (t) It is summarized by non-integer exponents. Therefore, in the constituent elements of the switching circuit 115 i The general expression for the power consumed in one of them can be written as shown in expression (6). In this expression, the dynamic resistance... R ondyn For current I s (t) The dependence of the current is determined by the exponential of the current. n i Explanation, and R oni It is a constant.

[0031]

[0032] Total power in switch circuit 115 P(t) total It is by measuring the power contributed by each component. P(t) i The result obtained by addition is shown in expression (7).

[0033]

[0034] The sensing device 120 is a shunt resistor. R shuntIn the example, the voltage obtained from the sensing device 120 Vs and I s (t) Proportional, and expression (7) can be written as expression (8).

[0035]

[0036] constant C i It is a component of the switching circuit. i The relevant scaling weights, and related to voltage. V s And therefore the input current I s Irrelevant. One or more normalization techniques can be used to normalize each scaling weight. C i Converting to a positive integer, for example, interpreting relation 8.2 as multiplying by the indicated or predetermined number or constant. Such techniques can be used to scale integers to constants. G i Instead of scores C i The current-power relationship is associated with each component of the switching circuit 115. The associated expression can then be converted to a normalized integer scale to obtain the total normalized power in the switching circuit. P N (t) The corresponding expression is (9).

[0037]

[0038] The proportionality constant K can then be incorporated into expression (9) to obtain a pulse sequence frequency that is proportional to the total normalized power in switching circuit 115, as shown in expression (10).

[0039]

[0040] For example, expression 9 can be implemented as the sum of currents. Such a current can be supplied to a current-controlled oscillator to implement equation 10. In the example, to implement equation 9 as the sum of currents and equation 10 as a current-controlled oscillator, conversion circuit 200 includes transconductance circuit 205, current converter circuit 215, and pulse quantizer circuit 225. Conversion circuit 200 may also include gain circuits 210 and 220. The components of conversion circuit 200 are arranged to generate a frequency according to expression (10) and the techniques described herein. f pA series of electrical pulses. In the example, gain circuits 210 and 220 provide scaling or normalization gain. G i In some examples, gain G i It is a programmable integral gain selected based on system or application requirements or parameters of a specific device.

[0041] Transconductance circuit 205 includes transconductance configured as a circuit-based circuit. g m A circuit that converts received voltage into current. In the example, transconductance circuit 205 receives the sensed voltage. V s Reference voltage V REF and bias current I REF1 As input signal. Transconductance g m Based on the input reference voltage V REF and bias current I REF1 Determined according to expression (11). Transconductance circuit 205 is then based on g m Generate current I 1i As shown in expression (12). In the example, I 1 By transconducting circuit 205 or gain circuit 210 G i Scaling to produce scaled or weighted current I 1i-n An array, where each scaled current is I 1i It is associated with element i of the switching circuit 115.

[0042]

[0043] Current converter circuit 215 includes circuitry configured to implement an exponential law current converter that converts input current (e.g., ...) into an input current. I 1 Converted to output current I out or I 2i Output current I out or I 2i With a specified index n iThe magnitude is proportional. In one example, the current converter circuit 215 has the transfer function given in expression (13) and is combined with the gain circuit 220 to produce the output current. I 2i .

[0044]

[0045] The bias current of the current converter circuit 215 is included. I REF2 It is D multiplied by I REF1 D is a natural number specific to the user's application.

[0046] The pulse quantizer circuit 225 includes circuitry configured to generate a series of electrical pulses, the frequency of which is related to the input current. I 2 Or proportional to the total electrical power generated in the switching circuit 115. In the example, I 2 It is electric current I 2i The sum is shown in expression (14). In one example, the pulse quantizer circuit 225 includes an oscillator circuit proportional to the current, which generates a signal with a frequency proportional to the input current. In another example, the pulse quantizer circuit 225 includes a compensation circuit to generate a compensation. I REF1 Varying internal voltage reference V REFQ As described herein, for example, a series of electrical pulses generated by pulse quantizer circuit 225 is provided to accumulator circuit 135.

[0047] In this example, the oscillator circuit is coupled to the current converter circuit 215 and the compensation circuit. The oscillator circuit may include a capacitor to integrate the current. I 2 This generates a sensed voltage. The oscillator circuit may also include a comparator circuit for comparing the sensed voltage with a reference voltage. V REFQ The comparison is performed, and an electrical pulse is generated based on the comparison. In some examples, the oscillator circuit rapidly discharges the capacitor after each electrical pulse to reset the sensed voltage to 0 volts. The oscillator circuit then restarts the current flow analysis on the capacitor. I 2 An integration operation is performed to generate a detection voltage. In this example, the oscillator circuit operates at a voltage much higher than the timing signal. CLK ( Figure 1The capacitor is discharged at a rate that is relatively constant, such that the time taken for the capacitor to discharge is small or negligible compared to the period of the timing signal. In this example, the time taken for the capacitor to discharge is less than 1% of the timing signal period.

[0048] Figure 3A and 3B A transconductance circuit with selectable or programmable transconductance is shown together. Such a transconductance circuit can be an example of transconductance circuit 205. Figure 3A and 3B The circuit shown operates in a primary-secondary or server-client architecture. Primary circuit 300 includes a transconductance indicator generated based on a provided reference current and reference voltage. g m The self-biased circuit generates a transconductance value determined by the ratio of reference current to reference voltage, and is robust or tolerant to process, voltage, and temperature variations. The secondary circuit 360 is configured to replicate or obtain the transconductance from the primary circuit 300 based on the switching voltage generated by the primary circuit 300 during the generation of the bias current. g m The secondary circuit 360 is configured to use the replicated transconductance to generate a voltage similar to the received input voltage (e.g., ...). V s The current is proportional to the current.

[0049] Figure 3A An example of a circuit 300 (e.g., a primary circuit) configured to obtain transconductance based on a provided reference current and a provided reference voltage is illustrated. Circuit 300 includes an input circuit 305 and a bias circuit 320. In one example, the input circuit 305 includes a pair of input transistors 310 and 315 arranged to receive an input signal, such as a differential voltage. V REFM and V REFP In the example, voltage V REFM and V REFP From the input reference voltage V REF The derived constant voltage makes V REF =( V REFP – V REFMIn another example, bias circuit 320 includes a cascaded current mirror formed by transistors 335, 340, 350, and 355. Bias circuit 320 also includes a coupling circuit or coupling stage having transistors 325 and 330. In some examples, transistors 310, 315, 325, and 330 are PFETs, while transistors 335, 340, 350, and 355 are NFETs.

[0050] During operation, the bias circuit 320 generates a voltage V. TUNE This causes the gate-source voltage of transistors 315 and 310 to be... V REF =V REFP –V REFM The differential current generated by the difference is 2 i b =I REF1 The dimensions of transistors 310 and 315 are designed to operate within their linear operating regions, thereby enabling the transistors to... V TUNE The defined drain-source voltage can control the differential current i b The value of the coupled transistors 325 and 330 is greater than the corresponding W / L ratio of transistors 310 and 315. The drain connections of transistors 310 and 315 are source followers; therefore, since transistors 325 and 330 respond to... V TUNE The voltage drops across the source followers are substantially the same (e.g., differing only within an indicated or acceptable error range), and the source-to-drain voltages of transistors 310 and 315 are substantially the same. Furthermore, transistors 310 and 315 are made weaker than transistors 325 and 330, necessitating large voltage drops across them. V DS To generate 2 i b = I REF1 The differential current. The large current across transistors 310 and 315. V DS This reduces the sensitivity of circuit 300 to mismatches (e.g., due to process, temperature, or voltage variations) in the source follower formed by transistors 325 and 330. In the example, for V REF =125mV and I REF1 =1uA, V DS Approximately 1V. For example... Figure 3A As shown, circuit 300 receives a constant current. IREF1 and constant reference voltage (e.g., V REFP – V REFM The cascaded current mirror formed by transistors 335, 340, 350, and 355 will... I REF1 This is converted to the voltage at the drain of transistor 335, because these transistors together form a current mirror amplifier, with its output node located at the drain of 335. The drain of transistor 335 and the gates of transistors 325 and 330 provide negative feedback by generating a voltage. V TUNE To stabilize circuit 300, so that an overcurrent I is intentionally provided on the right-hand side of circuit 300. REF1 The differential current 2 generated by transistors 310 and 315 due to their transconductance i b Compensation. Due to the large gain provided by the current mirror amplifier formed by transistors 335, 350, 340, and 355, negative feedback leads to a differential current of 2. i b Overcurrent compensation I REF1 Due to the negative feedback constraint 2i b = g m ·V REF = I REF1 Voltage V TUNE Modulation leads to transconductance g m = I REF1 / V REF .

[0051] Voltage V TUNE The drain-to-source voltages of the input transistors 310 and 315 are defined by cascaded source follower transistors 325 and 330. V DS Furthermore, due to transconductance and therefore i b When variations may occur due to process, voltage, and temperature (PVT) changes, the operation of bias circuit 320 enables input transistors 310 and 315 to actively regulate voltage V using negative feedback. TUNE Robustly generate transconductance based on the provided reference voltage and the reference current varying across the PVT. g m In the example, circuit 300 does not need to start the circuit because... IREF1 Transistors 340 and 355 are always present and always conducting current due to their diode connections.

[0052] Figure 3B An example of circuit 360 (e.g., a secondary circuit) configured to convert voltage to current based on a provided transconductance is illustrated. In this example, circuit 360 is substantially the same as circuit 300, except that the gate of transistor 380 is not configured to receive any negative feedback, such as the negative feedback received at the gate of transistor 325. Circuit 360 serves as a circuit with a voltage replicated from circuit 300. V TUNE Defined transconductance open-loop circuit operation. Circuit 360 includes input circuitry 365 and bias circuitry 385. In this example, input circuitry 365 includes a pair of input transistors 370 and 375 arranged to receive an input signal, such as a voltage generated by sensing device 120. V s In another example, bias circuit 320 includes a cascaded current mirror formed by transistors 387, 389, 390, and 395. Bias circuit 385 further includes a coupling circuit or coupling stage having transistors 380 and 384. In some examples, transistors 370, 375, 380, and 384 are PFETs, while transistors 387, 389, 390, and 395 are NFETs.

[0053] During operation, the input circuit 365 will... V TUNE Coupled to the gates of transistors 380 and 384. This allows input transistors 370 and 375 to have the same characteristics as input transistors 310 and 315. V DS This determines the value of current IB2 and forces transistors 370 and 375 to have the same transconductance as transistors 310 and 315. I REF1 / ( V REFP - V REFM In linear operation mode, the current generated by the bias circuit 385 i b2 With input voltage V s Proportional, therefore the differential current generated by circuit 360 is proportional to other input voltages. V s ( V INP – V INM ) below have ( I REF1 / ( VREFP - V REFM The transconductance of the input circuit 365 is responsive to the input voltage. V s Generation with current I 1i Proportional output current I out As shown in expression (12). Current I out The parameters contained in expression (12) can be amplified using a conventional current multiplier circuit. G i .

[0054] Figure 4 The diagram illustrates a configuration to generate input current I. IN Example of a circuit 400 with selectable exponentially proportional output current. Figure 4 This is an example of a current converter circuit 215 or an exponential law current converter circuit with a transfer function shown in expression (13). The output current generated by circuit 400... I OUT As shown in expression (15).

[0055]

[0056] The term n can be selected between a value of 1 and 2 by the resistor divider circuit 445. Expression (15) can be obtained from the bipolar junction transistor (BJT) current equation shown in expression (16), or equivalently, expression (16.1).

[0057]

[0058] In expression (16), I It is the collector current. I s It is the reverse saturation current. V be It is the base-to-emitter voltage. V t It is the thermal voltage. In the example where all BJTs in circuit 400 have the same size and matching layout, the voltage can be obtained according to expressions (16.2), (16.3), and (16.4). V 1 , V 2 and V 3Expressions (16.2), (16.3) and (16.4) are approximations of the high emitter-to-base current ratio of these BJTs and the majority or at least most of the base current of each of transistors 410, 415 and 430, compensated by the circuit formed by transistors 405, 425 and 420.

[0059]

[0060] Expressions (16.2) and (16.3) are direct applications of the general expression (16.1) to transistors 440 and 435 for the current flowing through these transistors. I IN Expression (16.4) represents voltage. V 3 By from voltage V 2 The base-emitter voltage of transistor 430 is obtained by subtracting the base-emitter voltage of transistor 430. The base-emitter voltage of transistor 430 is given by the second term in expression (16.4) by directly applying expression (16.1) to transistor 430. Current I REF2 A current mirror formed by transistors 410 and 415 drives transistor 430. In this configuration, transistor 405 provides base current to transistors 415 and 410. The current flowing through transistor 405 is mirrored by transistors 425 and 420 to provide base current compensation to transistor 430. The input of voltage buffer 450 is connected or coupled to a voltage... V 3 In the example, for instance at node N3, the current I generated in or conducted by transistor 455 is given by applying expressions (16) and (16.4). OUT :

[0061] Similarly, if the input of voltage buffer 450 is connected to voltage... V 1 For example, at node N1, the current I generated in or conducted by transistor 455 is given by applying expressions (16) and (16.2). OUT ,like

[0062] In some examples, the input of voltage buffer 450 is connected to the voltage, for example, via a resistor divider circuit 445. V 1 andV Voltage between 3 V 4 For example, at node N4. In this example, the resistor divider circuit 445 has a large resistance value, therefore it does not load nodes N1 and N3. The voltage at the input of the voltage buffer 450. V 4 It can be relative to voltage V 1 and V 3 represents:

[0063] By replacing expression (16.8) with voltage V 4 The value of and replace expressions 16.2 and (16.4) with voltage. V 1 and V 3 The corresponding value, I OUT The value of can be expressed by equation (16.9).

[0064] (16.9)

[0065] Expression (16.9) can be further simplified to I as shown in expression (16.10). OUT value.

[0066]

[0067] Expression (16.10) is solved by substitution. n=1+n' Equivalent to expression (15), where n’ It is a fraction less than 1, and the value of n is between 1 and 2.

[0068] In this example, circuit 400 includes FETs 420 and 425, and BJTs 405, 410, 415, 430, 435, 440, and 455. Circuit 400 also includes a voltage buffer 450 and a switching resistor divider circuit 445.

[0069] In operation, transistors 435 and 440 are diode-connected and conduct the input current I. IN Transistors 415 and 430 conduct the reference current I mirrored from transistor 410. REF2 Transistor 405 provides base current to transistors 410 and 415. This base current is mirrored by transistors 420 and 425 so that transistor 420 can provide base current to transistor 430. The resistor divider circuit 445 is adjustable to select an exponent between 1 and 2. n or n iThis makes the voltage at node N2... V 4 equal to voltage V 1 When n equals 1, and when the voltage V 4 equal to the voltage at node N1 V 3 In some cases, n=2, two or more taps or electrical connections are connected to the resistor divider circuit 445 to obtain two or more output currents, where the different exponents of the input current are in the range of 1 to 2.

[0070] Figure 5 The diagram illustrates a configuration for generating a reference voltage. V REFQ An example of circuit 500 (e.g., a reference circuit). In the example, the reference voltage... V REFQ Used by the pulse quantizer circuit 225, for example by the oscillator in the quantizer circuit, for quantizing the current based on a comparison with a reference voltage. I 2 It is converted into a series of pulses. Aspects of circuit 500 are based on the following implementation.

[0071] In a conventional oscillator, the input current, such as the current I2 provided by expression (14), is stored on a capacitor until the voltage across the capacitor rises to a fixed or constant reference voltage. The voltage across the capacitor is compared with the reference voltage to generate a signal whose frequency is proportional to the input current. As shown in expression (14), the input current and the reference current... I REF1 Proportional or dependent on the reference current I REF1 Therefore, it may have accuracy that is susceptible to or affected by changes in the reference current. This is achieved by adjusting the reference voltage and reference current used by the oscillator. I REF1 Proportional or dependent on the reference current I REF1 This can eliminate or reduce this dependence.

[0072] Furthermore, the oscillator frequency can be inversely proportional to the capacitance value of the capacitor used to store or integrate the input current; therefore, the oscillator frequency can vary with process variations in the capacitance value. This variation can be compensated for by ensuring that the oscillator's reference voltage is inversely proportional to the capacitance value.

[0073] Furthermore, variations in the timing signal used by, for example, accumulator circuit 135 or logic circuit 140 to count the number of pulses generated by conversion circuit 130 within an indicated time span may cause changes or alterations in the number of pulses received within a specified time span. This may be the case even when the current through sensing device 120 or switching circuit 115 remains constant. Such variations can be mitigated or compensated for by varying the oscillator's reference voltage proportionally to the timing or clock signal frequency.

[0074] The above implementations can be used in combination to obtain the reference voltage V according to expression (16). REFQ .

[0075]

[0076] In equation (17), N For a fixed number, t p Where C is the period of the timing signal, and C is the capacitance value of the oscillation capacitor. In the example, N This indicates the number of timing signal periods and can be selected based on the preferred responsiveness or sensitivity of the reference voltage to changes in the timing signal frequency. Oscillator reference voltage V REFQ The definition achieves the reduction of input current I 2 to I REF1 The targets are the dependence of the change, the dependence of the oscillator frequency on the change of the capacitor value, and the effect of the pulse count on the change of the timing signal frequency. The reference voltage represented in expression (17) is obtained by applying a reference current I to the capacitor C. REF Points Time Obtained, for example, through circuit 500.

[0077] In this example, circuit 500 includes transistors 505, 510, 515, and 520. Circuit 500 also includes capacitors 525 and 530, and resistor 535.

[0078] During operation, capacitor 525 is subjected to current I. REF1 A timing signal that sustains charging for N cycles, for example Figure 1 The timing signal CLK is shown. Charging is stopped by deactivating the signal CHARGE and activating the signal CHARGE_B. Capacitor 525 is sampled by providing a short pulse on the signal SAMP to transfer charge from capacitor 525 to capacitor 530. Then capacitor C is discharged by activating or driving the signal RST. The process is then repeated. After some initial startup time, the voltage on capacitor 530 has the value given by expression (17).

[0079] Various examples

[0080] Example 1 is an apparatus for converting a detected voltage indicating current conducted by a switching circuit into a series of electrical pulses indicating electrical power dissipated by the switching circuit in response to the current. The apparatus includes: a transconductance circuit comprising: a first circuit for receiving a reference current and a first reference voltage, and obtaining a transconductance based on an automatically generated bias current, the reference current, and the first reference voltage, the value of which is determined by the reference current and the first reference voltage; and a second circuit coupled to the first circuit for receiving the detected voltage and generating a first current based on the detected voltage and the obtained transconductance.

[0081] In Example 2, the subject of Example 1 includes: wherein the first circuit comprises: a first differential input circuit for receiving the first reference voltage; and a bias circuit for receiving the reference current and generating an automatically generated bias current.

[0082] In Example 3, the main idea of ​​Example 2 includes: wherein the bias circuit is used to automatically adjust the automatically generated bias current in response to process, voltage or temperature changes in the input circuit.

[0083] In Example 4, the main points of Examples 2-3 include: wherein: the first differential input circuit includes a differential field-effect transistor (FET) circuit; and the bias circuit includes a FET current mirror.

[0084] In Example 5, the main points of Examples 2-4 include: a coupling circuit for coupling the automatically generated bias current to a second circuit, the second circuit being configured to generate the obtained transconductance using the coupled automatically generated bias current.

[0085] In Example 6, the essence of Example 5 includes: wherein: the second circuit includes a second differential input circuit for receiving the detected voltage; and a second bias circuit having a bias current determined by the automatically generated bias current of the coupling.

[0086] In Example 7, the subject of Example 6 includes: wherein: the second differential input circuit includes a differential field-effect transistor (FET) circuit; and the second bias circuit includes a FET current mirror.

[0087] In Example 8, the subject of Examples 1–7 includes: a current-to-current converter circuit coupled to the transconductance circuit for receiving the first current and generating a second current proportional to a configurable exponent of the first current.

[0088] In Example 9, the essence of Example 8 includes: an oscillator circuit coupled to the current-to-current converter circuit, the oscillator circuit comprising: a first capacitor for integrating a second current generated by the converter circuit to generate an integrated voltage; a comparator circuit for comparing the integrated voltage with a second reference voltage; and an output circuit for providing the series of electrical pulses based on the comparison; and a reference circuit for generating the second reference voltage based on the reference current and a timing signal for counting electrical pulses in the sequence of electrical pulses, the reference circuit comprising: an integrator circuit having a second capacitor for integrating the reference current; and a control circuit for driving the integrator circuit to generate the second reference voltage based on the integration of the reference current over one or more cycles of the timing signal.

[0089] The main points of Examples 10, 8-9 include: wherein the value of the configurable index of the first current indicates the dynamic resistance of the switching circuit.

[0090] Example 11 is a system for converting a detected voltage indicating a current conducted by a switching circuit into a series of electrical pulses indicating electrical power dissipated by the switching circuit in response to the current conducted by the switching circuit. The system includes: a current-to-current converter circuit coupled to a transconducting circuit for receiving a first current indicating the detected voltage; the current-to-current converter circuit including: a current squaring circuit for amplifying the first current by an arithmetic power; and a scaling circuit for scaling the amplified first current based on the reference current to generate a second current.

[0091] In Example 12, the main idea of ​​Example 11 includes: wherein the current-to-current converter circuit includes an adjustment circuit for selectively adjusting the arithmetic power.

[0092] In Example 13, the main idea of ​​Example 12 includes: wherein the adjustment circuit is configured to selectively adjust the arithmetic power to a value between 1 and 2.

[0093] In Example 14, the main points of Examples 12-13 include: the adjustment circuit said therein includes a resistor divider for selectively adjusting the arithmetic power to a value between 1 and 2.

[0094] In Example 15, the main points of Examples 12-14 include: wherein the system further includes: a transconductance circuit comprising: a first circuit for receiving the reference current and a first reference voltage, and obtaining a transconductance based on an automatically generated bias current and the reference current and the first reference voltage, the value of the transconductance being determined by the reference current and the first reference voltage; and a second circuit coupled to the first circuit for receiving a detected voltage and generating the first current based on the detected voltage and the obtained transconductance.

[0095] In Example 16, the essence of Example 15 includes: an oscillator circuit coupled to the current-to-current converter circuit, the oscillator circuit comprising: a first capacitor for integrating a second current generated by the converter circuit to generate an integrated voltage; a comparator circuit for comparing the integrated voltage with a second reference voltage; and an output circuit for providing the series of electrical pulses based on the comparison; and a reference circuit for generating the second reference voltage based on the reference current and a timing signal for counting electrical pulses in the sequence of electrical pulses, the reference circuit comprising: an integrator circuit having a second capacitor for integrating the reference current; and a control circuit for driving the integrator circuit to generate the second reference voltage based on the integration of the reference current over one or more cycles of the timing signal.

[0096] Example 17 is a method for generating a signal indicating electrical power dissipated by a switching circuit, the method comprising: obtaining a sensed voltage indicating a current conducted by the switching circuit from a sensing circuit; converting the sensed voltage into a first current via a transconductance circuit having an optional transconductance determined by a provided reference voltage and a provided reference current; converting the first current into a second current using a power-law converter circuit based on the dynamic resistance of the switching circuit; generating a series of one or more pulses indicating electrical power consumed by the switching circuit by: integrating the second current onto a first capacitor; comparing a voltage on the first capacitor with a second reference voltage; generating electrical pulses of the pulse sequence based on the comparison; and generating a second reference voltage based on the reference current and a timing signal via a compensation circuit, the reference having an automatically adjusted value to compensate for variations in at least one of a capacitance value, the reference current, or the period of the timing signal.

[0097] In Example 18, the main idea of ​​Example 17 includes: the sensing circuit includes a parallel resistor connected in series with the circuit.

[0098] The gist of Examples 19, 17-18 includes: generating the second reference voltage includes: integrating the reference current on the second capacitor into one or more timing signal periods, the timing signal periods representing time units used to determine the electrical power dissipated by the switching circuit based on the one or more pulses.

[0099] The gist of Examples 20, 17-19 includes that the power-law converter circuit converts the first current into a second current based on the dynamic resistance of the switching circuit by: amplifying the first current to produce an intermediate current having an amplitude that is an optional arithmetic power of the amplitude of the first current; and scaling the intermediate current proportional to the reference current to obtain the second current.

[0100] Example 21 is at least one machine-readable medium, including instructions that, when executed by processing circuitry, cause the processing circuitry to perform the operations of any of the examples 1-20.

[0101] Example 22 is an apparatus that includes the apparatus of any of the embodiments of Examples 1-20.

[0102] Example 23 is a system of any one of Examples 1-20.

[0103] Example 24 is a method of any one of Examples 1-20.

[0104] The above detailed description includes reference to the accompanying drawings, which form a part of the detailed description. The drawings illustrate, by way of illustration, specific embodiments in which the subject matter of the invention can be practiced. These embodiments are also collectively referred to as “examples.” Such examples may include components other than those shown or described. However, the inventors have also contemplated examples that provide only those components shown or described. Furthermore, the inventors have contemplated examples of any combination or arrangement of those components (or one or more aspects thereof) shown or described, or with respect to a particular example (or one or more aspects thereof), or with respect to other examples (or one or more aspects thereof) shown or described herein. In the event of any inconsistency between the usage of this document and any document incorporated by reference, the usage in this document shall prevail.

[0105] In this document, as is common in patent documents, the terms “a” or “an” are used to include one or more, regardless of any other instance or use of “at least one” or “one or more.” In this document, the term “or” is used to indicate a non-exclusive or, therefore “A or B” includes “A but not B,” “B but not A,” and “A and B,” unless otherwise stated. In this document, the terms “comprising” and “wherein” are used as simple equivalents to the corresponding terms “comprising” and “wherein.” Furthermore, in the following claims, the terms “comprising” and “including” are open-ended, meaning that a system, apparatus, article, composition, formulation, or method, including components other than those listed after the term in the claim, is still considered to be within the scope of that claim. Additionally, in the following claims, the terms “first,” “second,” and “third,” etc., are used merely as labels and are not intended to impose numerical requirements on their objects.

[0106] As used herein, the term "connection" refers to a direct electrical connection between connected things without any intermediate devices. The term "coupling" includes a direct electrical connection between connected things, or an indirect connection via one or more passive or active intermediate devices. The term "circuit" corresponds to one or more passive and / or active components arranged to cooperate with each other to provide a desired function. The term "signal" refers to at least one current signal, voltage signal, or data signal, such as an analog signal, a digital signal, or a mixture of analog and digital signals.

[0107] The methods described herein can be implemented, at least in part, by a machine or computer. Some examples may include a computer-readable or machine-readable medium encoded with instructions operable to configure an electronic device to perform the methods described in the examples above. Implementations of these methods may include code, such as microcode, assembly language code, high-level language code, etc. Such code may include computer-readable instructions for performing various methods. This code may form part of a computer program product. Furthermore, in the examples, the code may be tangibly stored on one or more volatile, non-transitory, or non-volatile tangible computer-readable media, for example, during execution or at other times. Examples of such tangible computer-readable media may include, but are not limited to, hard disks, removable disks, removable optical disks (e.g., optical discs and digital video disks), magnetic tapes, memory cards or memory sticks, random access memory (RAM), read-only memory (ROM), etc.

[0108] The above description is intended to be illustrative and not restrictive. For example, the examples above (or one or more aspects thereof) may be used in combination with each other. Other embodiments may be used, for example, after reading the above description by one of ordinary skill in the art. An abstract is provided to conform to 37 CFR §1.72(b) to enable the reader to quickly determine the nature of the technical disclosure. It is understood that this submission is not to be construed as limiting or restricting the scope or meaning of the claims. Furthermore, in the above detailed description, various features may be combined together to simplify this disclosure. This should not be construed as meaning that any unclaimed disclosed feature is essential to any claim. Rather, the inventive subject matter may not be limited to all features of a particular disclosed embodiment. Therefore, the following claims are incorporated herein by way of example or embodiment, each claim existing independently as a separate embodiment, and these embodiments are contemplated to be combined with each other in various combinations or arrangements. The scope of the subject matter of this invention should be determined by reference to the appended claims and the full scope of their equivalents.

Claims

1. An apparatus for converting a detected voltage indicating a current conducted by a switching circuit into a series of electrical pulses indicating electrical power dissipated by the switching circuit in response to the current, the apparatus comprising: Transconductance circuits include: A first circuit is configured to receive a reference current and a first reference voltage, and to obtain a transconductance based on an automatically generated bias current, the reference current, and the first reference voltage, wherein the value of the transconductance is determined by the reference current and the first reference voltage. A second circuit, coupled to the first circuit, is used to receive the detected voltage and to generate a first current based on the detected voltage and the obtained transconductance. A current-to-current converter circuit, coupled to the transconductance circuit, is used to receive the first current and to generate a second current proportional to a configurable exponent of the first current, wherein the configurable exponent of the first current indicates the dynamic resistance of the switching circuit; and A pulse quantizer circuit, coupled to the current-to-current converter circuit, is configured to generate the series of electrical pulses having a frequency proportional to the second current.

2. The apparatus of claim 1, wherein the first circuit comprises: A first differential input circuit is used to receive the first reference voltage; and A bias circuit is used to receive the reference current and to generate the automatically generated bias current.

3. The apparatus of claim 2, wherein the bias circuit is configured to automatically adjust the automatically generated bias current in response to process, voltage, or temperature changes in the first differential input circuit.

4. The apparatus according to claim 2, wherein: The first differential input circuit includes a differential field-effect transistor (FET) circuit; and The bias circuit includes a FET current mirror.

5. The apparatus of claim 2, the apparatus comprising a coupling circuit for coupling the automatically generated bias current to the second circuit, the second circuit being configured to generate the obtained transconductance using the coupled automatically generated bias current.

6. The apparatus according to claim 5, wherein: The second circuit includes: A second differential input circuit is used to receive the detected voltage; and The second bias circuit has a bias current determined by the automatically generated bias current coupled to it.

7. The apparatus according to claim 6, wherein: The second differential input circuit includes a differential field-effect transistor (FET) circuit; and The second bias circuit includes a FET current mirror.

8. The apparatus according to claim 1, further comprising: An oscillator circuit, coupled to the current-to-current converter circuit, the oscillator circuit comprising: A first capacitor is used to integrate the second current generated by the converter circuit to generate an integrated voltage; A comparator circuit is used to compare the integrated voltage with a second reference voltage; and Output circuitry for providing the electrical pulse sequence based on the comparison; and A reference circuit is configured to generate a second reference voltage based on the reference current and a timing signal used to count electrical pulses in the electrical pulse series, the reference circuit comprising: An integrator circuit having a second capacitor to integrate the reference current; and A control circuit is provided to drive the integrator circuit to generate the second reference voltage based on the integration of the reference current over one or more cycles of the timing signal.

9. A system for converting a detected voltage indicating a current conducted by a switching circuit into a series of electrical pulses indicating electrical power dissipated by the switching circuit in response to the current conducted by the switching circuit, the system comprising: A current-to-current converter circuit, coupled to a transconductance circuit, is configured to receive a first current indicating the detected voltage and to generate a second current proportional to a configurable exponent of the first current, wherein the configurable exponent of the first current indicates the dynamic resistance of the switching circuit. The current-to-current converter circuit includes: A current squaring circuit is used to amplify the first current by an arithmetic power of the first current; and A scaling circuit is used to scale the amplified first current based on a reference current to generate the second current; and A pulse quantizer circuit, coupled to the current-to-current converter circuit, is configured to generate the series of electrical pulses having a frequency proportional to the second current.

10. The system of claim 9, wherein the current-to-current converter circuit includes an adjustment circuit for selectively adjusting the arithmetic power.

11. The system of claim 10, wherein the adjustment circuit is configured to selectively adjust the arithmetic power to a value between 1 and 2.

12. The system of claim 10, wherein the adjustment circuit includes a resistor divider for selectively adjusting the arithmetic power to a value between 1 and 2.

13. The system of claim 10, wherein the system further comprises: The transconducting circuit includes: A first circuit is configured to receive the reference current and the first reference voltage, and to obtain the transconductance based on an automatically generated bias current, the reference current, and the first reference voltage, wherein the value of the transconductance is determined by the reference current and the first reference voltage. and A second circuit, coupled to the first circuit, is used to receive the detected voltage and to generate the first current based on the detected voltage and the obtained transconductance.

14. The system of claim 13, further comprising: An oscillator circuit, coupled to the current-to-current converter circuit, the oscillator circuit comprising: A first capacitor is used to integrate the second current generated by the converter circuit to generate an integrated voltage; A comparator circuit is used to compare the integrated voltage with a second reference voltage; and An output circuit is used to provide the series of electrical pulses based on the comparison; and A reference circuit is configured to generate a second reference voltage based on the reference current and a timing signal used to count electrical pulses in the electrical pulse series, the reference circuit comprising: An integrator circuit having a second capacitor to integrate the reference current; and A control circuit is provided to drive the integrator circuit to generate the second reference voltage based on the integration of the reference current over one or more cycles of the timing signal.

15. A method for generating a signal indicating electrical power dissipated by a switching circuit, the method comprising: A sensed voltage indicating the current conducted by the switching circuit is obtained from the sensing circuit; The sensed voltage is converted into a first current via a transconductance circuit, the transconductance circuit having a selectable transconductance determined by a provided reference voltage and a provided reference current; Based on the dynamic resistance of the switching circuit, a power-law converter circuit is used to convert the first current into a second current. A series of one or more pulses indicating the electrical power consumed by the switching circuit are generated in the following manner: Integrate the second current onto the first capacitor; The voltage across the first capacitor is compared with the second reference voltage; The series of electrical pulses is generated based on the comparison of the one or more pulses; and The second reference voltage is generated by a compensation circuit based on the reference current and the timing signal. The second reference voltage has a value that is automatically adjusted to compensate for changes in at least one of the capacitor value, the reference current, or the period of the timing signal.

16. The method of claim 15, wherein the sensing circuit includes a shunt resistor connected in series with the switching circuit.

17. The method of claim 15, wherein generating the second reference voltage comprises: For one or more cycles of the timing signal, the reference current is integrated onto the second capacitor, and the cycle of the timing signal represents a time unit used to determine the electrical power dissipated by the switching circuit based on the one or more pulses.

18. The method of claim 15, wherein the power-law converter circuit converts the first current into the second current based on the dynamic resistance of the switching circuit in such a way that: Amplify the first current to generate an intermediate current having an amplitude that is an optional arithmetic power of the amplitude of the first current; and The intermediate current, which is proportional to the reference current, is scaled to obtain the second current.

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