Recently, Picotest has had several questions from customers working to measure battery impedance. There are numerous publications and articles about testing battery impedance, even from vector network analyzer (VNA) manufacturers such as OMICRON Lab, including a useful 2017 application note guide from Florian Hämmerle.¹

This article will discuss some of the reasons for measuring battery impedance. It will investigate some of the reasons for the challenges in addition to presenting several methods of measuring battery impedance. This article will not include the analysis of results, given that this is its own topic; however, it will briefly touch upon why analysis can also cause confusion. 

Why Measure Batteries

There are two common reasons for measuring battery impedance. One reason is to understand how the voltage rail, powered by the battery, will respond to dynamic currents presented by the operation of the powered circuit. The second reason is that battery impedance is an indicator of the battery’s state of health (SOH). There are many articles published relating battery SOH to impedance and so this article doesn’t need to go into detail about the spectrography. The measurement also provides the inductance of the cable harness, defining the capacitor required on the circuit board the battery is powering. This cable can generally be removed using time domain reflectometry measurement and de-embedding, even using the math expressions in a VNA.

The battery used to demonstrate the test methods is shown in Figure 1.

Figure 1. 7.4 V 500 mA-hr lithium ion drone battery.

A 7.4V 500mA-hr lithium ion battery was chosen for convenience. This type of battery is readily available and inexpensive. They are commonly used in remote controlled airplanes and drones. The connectors for this battery also provide convenient probe access for impedance measurements. This access is shown in the black connector of Figure 1.

Connecting the Instrument

In general, it is important to pay careful attention to the voltage ratings of the instrument you use to measure the battery. Both an oscilloscope and the OMICRON Lab Bode 100 VNA will be used to perform the measurements for this article. 50 Ω inputs will be used on both instruments for the purpose of fidelity and because the source signal is generated from a 50 Ω  source. The voltage ratings for the signal generator and receiver ports are different for each instrument, but for the Bode 100 the MAXIMUM DC input voltage on the OUTPUT port is 5 Vrms (3.3 V recommended, which is below the battery voltage). The Tektronix MSO6B oscilloscope used here has a voltage rating of 2.3 Vrms for input sensitivity settings below 100 mV/div and 5.5 Vrms for sensitivity settings greater than 100 mV/div. All these ratings are below the voltage of the battery being measured, requiring caution to avoid damaging the instrument. A DC Block, such as the P2131A, is useful in protecting the instrument’s input ports.²

Impedance Methods

There are a variety of methods of measuring the battery impedance. This article will consider four methods. These methods are all acceptable, but each method provides a different result, making the assessment complicated. The methods are shown in Table 1. To keep the battery connectivity consistent, a P2102A 2-port probe is used for every measurement method.

Table 1. A breakdown of methods considered in this article.

Notes

1. Some oscilloscopes offer options for FRA/VNA measurements. If so, they can be used in place of the VNA.
2. The voltage at the instrument can be reduced by using an attenuating 2-port probe. For example, a 2X probe would reduce the battery voltage to 3.7 V at the instrument, or a 5X probe would result in 1.48 V at the instrument. The Bode 100/500 VNAs include support for these probes; most instruments do not. 

DC ∆V/∆I Method

This is the simplest of the methods and so it is performed first. The P2102A 2-port probe is connected to a J2111B current injector using one of the probe’s ports while the second port is connected to the digital multimeter (DMM). The J2111B bias switch is used to change the battery current from 0 mA to 25 mA. The DMM measures the voltage in both states; these can be externally subtracted, or the DMM delta mode can be used to directly measure the voltage change in response to the 25 mA current change.

Figure 2. The DC battery voltage at 0 mA, at 25 mA, and the difference voltage.

This method is quite simple, though it does not offer the same resolution or calibration of some of the other methods.

2-Port Shunt-Through Method

At the other extreme, the 2-port shunt-through method is a very precise frequency-dependent measurement. There is a great deal published about this measurement, including on the Picotest Solution page. The simple setup for the OMICRON Lab Bode 100/500 VNA is shown in Figure 3.

Figure 3. The basic connections for the 2-port shunt-through method. Note the voltage warnings provided to protect the equipment from damage.

One port of the probe connects to the VNA output while the other port connects to CH2. The battery voltage exceeds the rating of the Bode 100/500 ports, so a P2131A Port Saver® DC Block is connected to each port. The measurement also includes a ground loop. A J2115A ground loop isolator is used on CH2. A J2102B or other ground loop isolator could also be used. This setup is shown in Figure 4.

Figure 4. A visual of the 2-port probe connection to the battery. In the background, the DC block and J2115A ground isolator are seen connected on the Bode 100 CH 2.

The 2-port shunt-through is very accurate and well supported with calibration. The probe calibration substrate is shown in the foreground, just to the left of the battery in Figure 4.

The results using the Bode 500 are shown in Figure 5. Note that while one generally does not measure batteries to 100 MHz, this is shown to illustrate the capability of accurately measuring low impedance to high frequencies using this method. The OPEN, SHORT, and LOAD calibration traces are also shown to illustrate the measurement impedance ceiling and floor.

Figure 5. The post-calibration impedance floor (red), ceiling (green), and the 50 Ω measurement (blue) along with the battery measurement (violet), which is well between the floor and the ceiling. Measurement is from 100 Hz to 100 MHz.

While this measurement is very good at showing the practical dynamic range and frequency response, it does not provide decent resolution of the battery impedance.

Recalibrating the instrument for a reduced frequency range provides greatly improved measurement resolution, shown in Figure 6.

Figure 6. A higher resolution plot showing the frequency dependent battery impedance from 1 Hz to 100 kHz. At 100 kHz, the battery cable inductance is clearly visible.

Now the frequency dependency is clearly shown and the impedance extracted at 1kHz is 142mΩ, far below the measurement seen with the DMM. At 1 Hz, the impedance is much higher and climbing towards the DC value of 240 mΩ. This measurement also provides the battery and cable inductance at 420 nH.

AC dV/dl and Step Load Methods

The AC dV/dI measurement is a Frequency Response Analyzer (FRA) or Gain-Phase measurement. This measurement is supported by the Bode 100/500 and most other FRAs as well, as in some oscilloscopes that include FRA support. The major difference between the AC dV/dI method and the step load method is the signal provided to the current modulator. In the case of the step load the signal is a pulse, while in the AC dV/dI method the signal is a swept sine. The latter requires gain-phase support in whichever instrument is used. The identical setups are shown in Figure 7.

Figure 7. The current injector setup for the step load and the 3-port impedance are identical. The software and signal generator are different, with one using a pulse and the time domain while the other uses a swept sine wave and the frequency domain.

Determining the Capacitor

One of the reasons for measuring the battery impedance was to determine the capacitor required to reduce the impact of the cable inductance at the circuit board where it is used. Two equations are used to determine a suitable capacitor value. The first uses the battery resistance, close to where it becomes inductive to determine the capacitance, and the second equation determines the ideal capacitor ESR.

The ideal capacitor for this battery is a 29 uF capacitor with 120 mΩ  ESR. Since this is between standard values, 22 uF 100 mΩ and 33 uF 100 mΩ, capacitors were soldered to a header to mate with the battery connector, as shown in Figure 8.

Figure 8. The 22 uF and 33 uF 100 mΩ tantalum capacitors (circled black squares) are soldered to the pins of a 2.54 mm pitch header for connection to the battery connector. The probe is still located at the battery connector, so the resulting inductance includes the header pins to the capacitors.

The impedance without the capacitor and with each of the capacitors is shown in a single plot in Figure 9. The impedance with the 22 uF capacitor added is shown in blue and with the 33 uF capacitor added is shown in green.

Figure 9. The battery impedance and the battery impedance with the 22 uF (blue) and 33 uF (green) capacitors attached. The inductance is greatly reduced and the capacitor ESR is a bit lower than ideal. 

It is noted here that while these capacitors are described as 100 mΩ ESR, these are usually the MAXIMUM ESR. The actual ESR is typically much lower. It is preferred to have this impedance be very flat, which would indicate a higher ESR capacitor or a resistor added in series with the capacitor to improve the flatness. The inductance is reduced from 420 nH to 6 nH, with the 6 nH mostly being due to the inductance of the connector pins. This reduced inductance does greatly improve the step load response. 

The step load response, with and without the 33 uF capacitor, is also shown in the step load response in Figure 10.

Figure 10. The step load response of the battery with and without the capacitor attached. This demonstrates the very significant improvement the capacitor provides; the voltage excursion is reduced by more than 90% with the addition of the capacitor.

Replacing the DC Block with a power rail probe allows accurate DC voltage measurement with the voltage offset. The setup is shown in Figure 11.

Figure 11. Replacing the voltage probe with a power rail probe allows a more accurate measurement of the voltage change in response to a change in current. This probe doesn’t support the 2-port shunt-through impedance, but does show a more accurate DC voltage assessment to the step load. 

The 3.1 mV voltage change in response to a 25 mA step load results in 124 mΩ  at 1 ms after the onset of the current, very close to the 2-port shunt-through impedance result at 1 kHz.

Figure 12. The voltage change in response to a 25 mA step is 3.1 mV 1 ms after the onset of the pulse. The 1 ms time is consistent with a 1kHz period and this results in 124 mΩ, very close to the 2-port shunt-through measurement at 1 kHz.

Conclusion

Four different methods of measuring battery impedance were shown. Interestingly, each method provided different, but correct results. At low frequency, the AC impedance does converge with the DC measurement, but at higher frequency, the results are frequency dependent. The step load, using a power rail probe for accurate DC measurement, also converges with the 2-port shunt-through impedance at 1 kHz.

While many specifications provide 1 kHz impedance, there is not a special reason for this frequency, and the 2-port and 3-port methodologies can provide data over a wide frequency range. The assessment of the battery SOH from the impedance data is quite complex and dependent on the actual battery. This information is generally determined from the measurement of many battery samples as they degrade through their life cycle.

An added benefit of the frequency domain measurement was the determination of the ideal capacitor, used at the circuit board, to negate the impact of the interconnecting cable inductance and greatly improving the dynamic step load response of the circuit on the printed circuit board.

REFERENCES

1.  "Battery Impedance Measurement," Bode 100 Application Note, Omicron Lab. 
2. "Application Note – Port Saver – The Smart DC Block," Picotest.