Battery impedance spectra measurement

1 . An apparatus comprising:

a controller circuit having control inputs and control outputs, the controller circuit configurable to:

receive, via the control inputs, a first signal representing an electrical quantity of a device under test (DUT) within a period;

generate spectral components of the electrical quantity responsive to the first signal, and a matching condition between a first condition when the period starts and a second condition when the period ends;

generate a spectrum of the electrical quantity including the spectral components; and

provide a second signal at the control outputs responsive to generating the spectrum.

2 . The apparatus of claim 1 , wherein the spectral components are first spectral components, and the controller circuit is configurable to:

perform a transform operation determined based on whether the first condition is different from the second condition;

generate second spectral components of the electrical quantity responsive to performing the transform operation on the first signal; and

generate the spectrum including the first and second spectral components.

3 . The apparatus of claim 2 , wherein the electrical quantity is a first electrical quantity, the transform operation is a first transform operation, the spectrum is a first spectrum, and the controller circuit is configurable to:

receive a third signal representing a second electrical quantity of the DUT within the period;

perform a second transform operation determined based on whether a third condition when the period starts is different from a fourth condition when the period ends;

generate a second spectrum of the second electrical quantity responsive to a result of the second transform operation on the third signal;

generate a measurement of a physical property of the DUT responsive to generating the first spectrum and the second spectrum; and

provide the second signal representing the measurement at the control outputs.

4 . The apparatus of claim 3 , wherein the controller circuit is configurable to:

perform Fourier transform operations as part of the first transform operation and the second transform operation responsive to the first and second conditions matching and the third and fourth conditions matching; and

perform Laplace transform operations or Z-transform operations as part of the first transform operation and the second transform operation responsive to the first and second conditions being different and the third and fourth conditions being different.

5 . The apparatus of claim 4 , wherein the controller circuit is configurable to:

receive first parameters of a first Laplace transform expression of a first function that approximates variations of the first electrical quantity within the period;

receive second parameters of a second Laplace transform expression of a second function that approximates variations of the second electrical quantity within the period;

generate the first spectrum responsive to receiving the first signal and the first parameters; and

generate the second spectrum responsive to receiving the third signal and the second parameters.

6 . The apparatus of claim 2 , wherein the controller circuit is configurable to:

responsive to the first condition matching the second condition:

determine a difference between a first value of the electrical quantity of the DUT before the period and a second value of the electrical quantity of the DUT after the period; and

generate the second spectral components responsive to computing a Laplace transform of the difference.

7 . The apparatus of claim 6 , wherein each of the first and second values includes an open circuit voltage (OCV) of the DUT.

8 . The apparatus of claim 2 , wherein the controller circuit is configurable to:

responsive to the first condition not matching the second condition:

determine a first Laplace transform responsive to the first condition;

determine a second Laplace transform responsive to the second condition; and

generate the second spectral components responsive to determining the first Laplace transform and the second Laplace transform.

9 . The apparatus of claim 3 , further comprising an excitation source.

10 . The apparatus of claim 9 , wherein:

the excitation source has an excitation control input, a positive terminal, and a negative terminal, and the excitation source includes a switchable discharge path coupled between the positive and negative terminals;

the controller circuit has an excitation control output coupled to the excitation control input, and the controller circuit is configurable to enable the discharge path; and

the third signal represents a discharge current that flows out of the DUT between the positive and negative terminals.

11 . The apparatus of claim 10 , wherein the excitation source comprises a current source coupled to the positive terminal and configurable to provide a charging current at the positive terminal; and

wherein the third signal represents the charging current.

12 . The apparatus of claim 10 , wherein the excitation source comprises a voltage source;

wherein the excitation source is configurable to apply a voltage across the DUT to generate a current; and

wherein the first electrical quantity is the voltage and the second electrical quantity is the current.

13 . The apparatus of claim 9 , wherein the first electrical quantity is a voltage is provided by the DUT in response to a current supplied by the excitation source, and the current is the second electrical quantity.

14 . The apparatus of claim 3 , wherein the second electrical quantity is periodic at least within the period.

15 . A method comprising:

receiving, from a sense circuit, a first signal representing an electrical quantity of a device under test (DUT) within a period;

generating, by a controller circuit, spectral components of the electrical quantity responsive to the first signal, and a matching condition between a first condition when the period starts and a second condition when the period ends;

generating, by the controller circuit, a spectrum of the electrical quantity including the spectral components; and

providing, by the controller circuit, a second signal responsive to generating the spectrum.

16 . The method of claim 15 , wherein the spectral components are first spectral components, and the method further comprises:

performing, by the controller circuit, a transform operation selected based on whether the first condition is different from the second condition;

generating, by the controller circuit, second spectral components of the electrical quantity responsive to performing the transform operation on the first signal; and

generating, by the controller circuit, the spectrum including the first and second spectral components.

17 . The method of claim 16 , wherein the transformation operation is a first transformation operation, the sense circuit is a first sense circuit, the electrical quantity is a first electrical quantity, the spectrum is a first spectrum, and the method further comprises:

receiving, from a second sense circuit, a third signal representing a second electrical quantity of the DUT within the period;

performing, by the controller circuit, a second transform operation selected based on whether a third condition when the period starts is different from a fourth condition when the period ends;

generating, by the controller circuit, a second spectrum of the second electrical quantity responsive to performing the second transform operation on the third signal;

generating, by the controller circuit, a measurement of a physical property of the DUT responsive generating the first spectrum and the second spectrum; and

providing, by the controller circuit, the second signal representing the measurement.

18 . The method of claim 17 , further comprising:

performing Fourier transform operations as part of the first transform operation and the second transform operation responsive to the first and second conditions matching and the third and fourth conditions matching; and

performing Laplace transform operations or Z-transform operations as part of the first transform operation and the second transform operation responsive to the first and second conditions being different and the third and fourth conditions being different.

19 . A non-transitory computer readable medium storing instructions that, when executed by a processor, cause the processor to:

receive, from a sense circuit, a first signal representing an electrical quantity of a device under test (DUT) within a period;

generate spectral components of the electrical quantity responsive to the first signal, and a matching condition between a first condition when the period starts and a second condition when the period ends;

generate a spectrum of the electrical quantity including the spectral components; and

provide a second signal responsive to generating the spectrum.

20 . The non-transitory computer readable medium of claim 19 , wherein the spectral components are first spectral components, and the non-transitory computer readable medium further stores instructions that, when executed by the processor, cause the processor to:

perform a transform operation selected based on whether the first condition is different from the second condition;

generate second spectral components responsive to performing the transform operation on the first signal; and

generate the spectrum including the first and second spectral components.

21 . The non-transitory computer readable medium of claim 20 , wherein the transform operation is a first transform operation, the sense circuit is a first sense circuit, the electrical quantity is a first electrical quantity, the spectrum is a first spectrum, and the non-transitory computer readable medium further stores instructions that, when executed by the processor, cause the processor to:

receive a third signal representing a second electrical quantity of the DUT within the period;

perform a second transform operation determined based on whether a third condition when the period starts is different from a fourth condition when the period ends;

generate a second spectrum of the second electrical quantity responsive to performing the second transform operation on the third signal; and

generate a measurement of a physical property of the DUT responsive to generating the first spectrum and the second spectrum.

22 . The non-transitory computer readable medium of claim 21 , wherein the non-transitory computer readable medium further stores instructions that, when executed by the processor, cause the processor to:

perform Fourier transform operations as part of the first transform operation and the second transform operation responsive to the first and second conditions matching and the third and fourth conditions matching; and

perform Laplace transform operations or Z-transform operations as part of the first transform operation and the second transform operation responsive to the first and second conditions being different and the third and fourth conditions being different.

23 . The non-transitory computer readable medium of claim 21 , wherein the first electrical quantity is a voltage, the second electrical quantity is a current, the physical property is an impedance, and the measurement is a spectroscopy of the impedance.

24 . The apparatus of claim 3 , wherein the first electrical quantity is a voltage, the second electrical quantity is a current, the physical property is an impedance, and the measurement is a spectroscopy of the impedance.

25 . The method of claim 17 , wherein the first electrical quantity is a voltage, the second electrical quantity is a current, the physical property is an impedance, and the measurement is a spectroscopy of the impedance.

26 . The apparatus of claim 1 , further comprising a sensor circuit coupled to the controller circuit, the sensor circuit configurable to sense the electrical quantity and generate the first signal representing a result of the sensing.

27 . The apparatus of claim 1 , wherein the DUT includes an electrochemical cell.

28 . The apparatus of claim 1 , wherein the first condition is a first condition of the first signal and the second condition is a second condition of the first signal.

29 . The apparatus of claim 28 , wherein the first condition and the second condition of the first signal indicate whether the first signal is periodic within the period.

30 . The apparatus of claim 1 , wherein the first condition is a first condition of the DUT and the second condition is a second condition of the DUT.

31 . The apparatus of claim 30 , wherein the first condition and the second condition of the DUT indicate whether the DUT is in a steady state within the period.

32 . The method of claim 15 , wherein the DUT includes an electrochemical cell.

33 . The method of claim 15 , wherein the first condition is a first condition of the first signal and the second condition is a second condition of the first signal.

34 . The method of claim 33 , wherein the first condition and the second condition of the first signal indicate whether the first signal is periodic within the period.

35 . The method of claim 15 , wherein the first condition is a first condition of the DUT and the second condition is a second condition of the DUT.

36 . The method of claim 35 , wherein the first condition and the second condition of the DUT indicate whether the DUT is in a steady state within the period.

37 . The non-transitory computer readable medium of claim 19 , wherein the DUT includes an electrochemical cell.

38 . The non-transitory computer readable medium of claim 19 , wherein the first condition is a first condition of the first signal and the second condition is a second condition of the first signal.

39 . The non-transitory computer readable medium of claim 38 , wherein the first condition and the second condition of the first signal indicate whether the first signal is periodic within the period.

40 . The non-transitory computer readable medium of claim 19 , wherein the first condition is a first condition of the DUT and the second condition is a second condition of the DUT.

41 . The non-transitory computer readable medium of claim 40 , wherein the first condition and the second condition of the DUT indicate whether the DUT is in a steady state within the period.