Apparatuses and methods for testing electrochemical cells by measuring frequency response

1. A method of estimating an impedance of a device to be measured, comprising:

generating a sum-of-sines (SOS) signal comprising a summation of two or more sinusoidal signals at different frequencies with a frequency step factor therebetween;

mitigating a zero-order hold delay by advancing the SOS signal by a time step to create a stimulus signal, wherein the time step comprises a time period between successive elements of a digital representation of one of the two or more sinusoidal signals;

applying the stimulus signal to the device to be measured with an impedance measurement device;

detecting a response signal with the impedance measurement device, the response signal comprising a response of the device to be measured to the stimulus signal; and

estimating the impedance of the device to be measured using a sum-of-sines analysis of the response signal.

2. The method of claim 1 , further comprising, prior to applying the stimulus signal to the device to be measured:

pre-emphasizing a magnitude of each of the two or more sinusoidal signals such that a magnitude of the response signal is substantially flat over a frequency range encompassing all of the two or more sinusoidal signals when the stimulus signal is applied to a shunt impedance; and

pre-emphasizing a phase of each of the two or more sinusoidal signals such that a phase shift of the response signal is substantially near zero when the stimulus signal is applied to the shunt impedance.

3. The method of claim 1 , further comprising calibrating a magnitude of each of the two or more sinusoidal signals before applying the stimulus signal to the device to be measured by;

applying the stimulus signal to a first shunt impedance and detecting a first response signal of the impedance measurement device with the first shunt impedance;

applying the stimulus signal to a second shunt impedance and detecting a second response signal of the impedance measurement device with the second shunt impedance;

applying the stimulus signal to a third shunt impedance and detecting a third response signal of the impedance measurement device with the third shunt impedance;

at each frequency of the two or more sinusoidal signals, combining the first response signal, the second response signal and the third response signal to determine a magnitude calibration; and

applying the magnitude calibration to each of the two or more sinusoidal signals of the stimulus signal.

4. The method of claim 3 , further comprising converting each of the first response signal, the second response signal, and the third response signal from a time domain to a frequency domain prior to the combining and wherein the combining is performed in the frequency domain using a least squares linear regression to determine the magnitude calibration.

5. The method of claim 1 , further comprising calibrating a phase of each of the two or more sinusoidal signals before applying the stimulus signal to the device to be measured by;

applying the stimulus signal including an added first phase shift to a shunt impedance and detecting a first response signal of the impedance measurement device with the shunt impedance;

applying the stimulus signal including an added second phase shift to the shunt impedance and detecting a second response signal of the impedance measurement device with the shunt impedance;

applying the stimulus signal including an added third phase shift to the shunt impedance and detecting a third response signal of the impedance measurement device with the shunt impedance;

at each frequency of the two or more sinusoidal signals, combining the first response signal, the second response signal and the third response signal to determine a phase calibration; and

applying the phase calibration to each of the two or more sinusoidal signals of the stimulus signal.

6. The method of claim 5 , further comprising converting each of the first response signal, the second response signal, and the third response signal from a time domain to a frequency domain prior to the combining and wherein the combining is performed in the frequency domain using a least squares linear regression to determine the phase calibration.

7. The method of claim 1 , further comprising calibrating the impedance measurement device before applying the stimulus signal to the device to be measured by:

determining a gain correction for each frequency of the two or more sinusoidal signals using three or more shunt impedances encompassing an expected magnitude of the impedance of the device to be measured by:

pre-emphasizing a magnitude of each of the two or more sinusoidal signals in the stimulus signal;

applying the stimulus signal to each of the three or more shunt impedances and detecting a magnitude-calibration response signal for each of the three or more shunt impedances; and

combining the magnitude-calibration response signals to develop the gain corrections for each frequency of the two or more sinusoidal signals;

determining a phase correction for each frequency of the two or more sinusoidal signals using three or more phase shifts by:

pre-emphasizing a phase of each of the two or more sinusoidal signals in the stimulus signal using the three or more phase shifts;

applying the stimulus signal to at least one of the three or more shunt impedances;

detecting a phase-calibration response signal for each of the three or more phase shifts; and

combining the phase-calibration response signals to develop the phase corrections for each frequency of the two or more sinusoidal signals; and

applying the corresponding gain corrections and the corresponding phase corrections to each frequency of the two or more sinusoidal signals of the stimulus signal.

8. The method of claim 1 , further comprising calibrating the impedance measurement device before applying the stimulus signal to the device to be measured by:

pre-emphasizing a magnitude and phase of each of the two or more sinusoidal signals;

applying the stimulus signal to one or more shunt impedances at a known Root Mean Square (RMS) current;

detecting a current calibration response signal of the one or more shunt impedances with the impedance measurement device;

determining calibration coefficients from the current calibration response signal; and

using the calibration coefficients to scale a magnitude of each of the two or more sinusoidal signals to an RMS value less than or equal to the known RMS current.

9. The method of claim 8 , wherein the known RMS current is substantially 500 mA or less.

10. The method of claim 8 , wherein:

the two or more sinusoidal signals at different frequencies have some overlap and a longest frequency range is used for an act of applying the stimulus signal to the one or more shunt impedances at the known Root Mean Square (RMS) current; and

the method further includes scaling the two or more sinusoidal signals to a number of frequencies that is a subset of the frequencies in the longest frequency range.

11. An impedance measurement device comprising:

a processor;

a data acquisition system; and

a sum-of-sines-generator for generating a sum-of-sines (SOS) signal comprising a summation of two or more sinusoidal signals at different frequencies with a frequency step factor therebetween; and

wherein one or more of the processor and the data acquisition system are configured to:

perform a function of the sum-of-sines-generator;

advance the SOS signal by a time step to create a stimulus signal, wherein the time step comprises a time period between successive elements of a digital representation of one of the two or more sinusoidal signals;

apply the stimulus signal to a device to be measured;

while the stimulus signal is being applied, sample a response signal, the response signal comprising a response of the device to be measured to the stimulus signal; and

analyze the response signal with a sum-of-sines analysis to estimate the impedance of the device to be measured.

12. The impedance measurement device of claim 11 , further comprising:

two or more shunt impedances configured to be selectively coupled to the stimulus signal; and

wherein one or more of the processor and the data acquisition system are further configured to modify the stimulus signal prior to applying the stimulus signal to the device to be measured by:

pre-emphasizing a magnitude of each of the two or more sinusoidal signals such that a magnitude of the response signal is substantially flat over a frequency range encompassing all of the two or more sinusoidal signals when the stimulus signal is applied to at least one of the two or more shunt impedances; and

pre-emphasizing a phase of each of the two or more sinusoidal signals such that a phase shift of the response signal is substantially near zero when the stimulus signal is applied to at least one of the two or more shunt impedances.

13. The impedance measurement device of claim 11 , further comprising:

two or more shunt impedances configured to be selectively coupled to the stimulus signal; and

wherein one or more of the processor and the data acquisition system are further configured to perform a plurality of magnitude calibration processes prior to applying the stimulus signal to the device to be measured, wherein each magnitude calibration process of the plurality is performed while coupled to a different shunt impedance and comprises:

forming the shunt impedance by selectively enabling at least one of the two or more shunts;

applying the stimulus signal to the shunt impedance;

detecting a calibration response signal of the impedance measurement device with the shunt impedance; and

at each frequency of the two or more sinusoidal signals:

combining the calibration response signals from each magnitude calibration process of the plurality to determine a magnitude calibration; and

applying the magnitude calibration to each of the two or more sinusoidal signals.

14. The impedance measurement device of claim 11 , further comprising:

two or more shunt impedances configured to be selectively coupled to the stimulus signal; and

wherein one or more of the processor and the data acquisition system are further configured to perform a plurality of phase calibration processes prior to applying the stimulus signal to the device to be measured, wherein each phase calibration process of the plurality is performed with a different calibration phase shift on the stimulus signal and comprises:

forming a shunt impedance by selectively enabling at least one of the two or more shunts;

applying the stimulus signal with the calibration phase shift to the shunt impedance;

detecting a calibration response signal of the impedance measurement device with the shunt impedance; and

at each frequency of the two or more sinusoidal signals:

combining the calibration response signals from each phase calibration process of the plurality to determine a phase calibration; and

applying the phase calibration to each of the two or more sinusoidal signals.

15. The impedance measurement device of claim 11 , further comprising:

two or more shunt impedances configured to be selectively coupled to the stimulus signal; and

wherein one or more of the processor and the data acquisition system are further configured to:

perform a plurality of magnitude calibration processes prior to applying the stimulus signal to the device to be measured, wherein each magnitude calibration process of the plurality is performed while coupled to a different shunt impedance and comprises:

forming the shunt impedance by selectively enabling at least one of the two or more shunts;

applying the stimulus signal to the shunt impedance; and

detecting a magnitude calibration response signal of the impedance measurement device with the shunt impedance;

perform a plurality of phase calibration processes prior to applying the stimulus signal to the device to be measured; wherein each phase calibration process of the plurality is performed with a different calibration phase shift on the stimulus signal and comprises:

forming a shunt impedance for phase measurement by selectively enabling at least one of the two or more shunts;

applying the stimulus signal with the calibration phase shift to the shunt impedance for phase measurement; and

detecting a phase calibration response signal of the impedance measurement device with the shunt impedance for phase measurement; and

at each frequency of the two or more sinusoidal signals:

combining the magnitude calibration response signals from each magnitude calibration process of the plurality to determine a magnitude calibration;

combining the phase calibration response signals from each phase calibration process to determine a phase calibration; and

applying the magnitude calibration and the phase calibration to each of the two or more sinusoidal signals.

16. The impedance measurement device of claim 15 , further comprising converting each magnitude calibration response signal and each phase calibration response signal from a time domain to a frequency domain prior to the combining and wherein the combining is performed in the frequency domain using a least squares linear regression to determine the magnitude calibration and the phase calibration.

17. The impedance measurement device of claim 11 , wherein one or more of the processor and the data acquisition system are further configured to calibrate the impedance measurement device before applying the stimulus signal to the device to be measured by:

pre-emphasizing a magnitude and phase of each of the two or more sinusoidal signals;

applying the stimulus signal to one or more shunt impedances at a known Root Mean Square (RMS) current;

detecting a current calibration response signal of the one or more shunt impedances with the impedance measurement device;

determining calibration coefficients from the current calibration response signal; and

using the calibration coefficients to scale a magnitude of each of the two or more sinusoidal signals to an RMS value less than or equal to the known RMS current.

18. The impedance measurement device of claim 12 , wherein the two or more shunt impedances are non-inductive.

19. An impedance measurement device, comprising:

a processor;

a data acquisition system;

a sum-of-sines generator for generating a stimulus signal to be applied to a device to be measured, the stimulus signal including a summation of two or more sinusoidal signals at different frequencies with a frequency step factor therebetween; and

an amplifier circuit configured to generate an output signal proportional to a difference between a first input and a second input, wherein the first input is operably coupled to the device to be measured and the second input is operably coupled to a buck signal from the data acquisition system; and

wherein one or more of the processor and the data acquisition system are configured to:

set a voltage of the buck signal to an initial value;

sample the output signal;

modify the voltage of the buck signal responsive to the sampled output signal;

repeat the sampling of the output signal and the modifying of the voltage on the buck signal until the output signal is within an error tolerance;

once within the error tolerance, maintain the voltage on the buck signal as a final buck voltage;

apply the stimulus signal to the device to be measured to generate a response signal including a bias voltage of the device to be measured;

sample the output of the amplifier circuit while the stimulus signal is being applied to generate a bias-removed response signal comprising the response signal with an approximation of the bias voltage removed; and

estimate the impedance of the device to be measured using a sum-of-sines analysis of the bias-removed response signal.

20. The impedance measurement device of claim 19 , wherein:

the buck signal is a coarse buck signal;

the amplifier circuit includes a third input operably coupled to a fine buck signal from the data acquisition system and the amplifier circuit is configured to generate the output signal proportional to a difference between the device to be measured and the fine buck signal when the coarse buck signal is held constant; and

after the final buck voltage is determined and is being applied to the amplifier circuit, one or more of the processor and the data acquisition system are further configured to:

set a voltage of the fine buck signal to a fine initial value;

sample the output signal;

modify the voltage of the fine buck signal responsive to the sampled output signal;

repeat the sampling of the output signal and the modifying of the voltage of the fine buck signal until the output signal is within a fine error tolerance; and

once within the fine error tolerance, maintain the voltage on the fine buck signal as a final fine buck voltage.

21. The impedance measurement device of claim 20 , wherein the amplifier circuit comprises:

a first differential amplifier comprising:

a first input operably coupled to the device to be measured;

a second input operably coupled to the coarse buck signal; and

an output; and

a second differential amplifier comprising:

a first input operably coupled to the output of the first differential amplifier;

a second input operably coupled to the fine buck signal; and

an output operably coupled to the data acquisition system.

22. The impedance measurement device of claim 20 , wherein a final coarse buck voltage and a final fine buck voltage are determined using a digital feedback system with total ground isolation.

23. The impedance measurement device of claim 19 , wherein the amplifier circuit is configured for and capable of comparing mid-range voltages.

24. The impedance measurement device of claim 23 , wherein the mid-range voltages are substantially equal to 50 volts.

25. The impedance measurement device of claim 19 , wherein the amplifier circuit is configured for and capable of comparing high-range voltages.

26. The impedance measurement device of claim 25 , wherein the high-range voltages are substantially equal to 300 volts.

27. The impedance measurement device of claim 19 , further comprising a circuit combination operably coupled between the data acquisition system and the device to be measured, the circuit combination including a coupling capacitor, and two or more relays configured for interfacing to the high-range voltages such that:

one or more first relays close to charge the coupling capacitor to the high-range voltage of the device to be measured while a second relay isolates the impedance measurement device from the coupling capacitor;

after the coupling capacitor is charged, the second relay closes to couple the impedance measurement device to the coupling capacitor to apply the stimulus signal; and

after the sampling of the response signal, the one or more first relays open to decouple the device to be measured from the coupling capacitor.