## Using the MFIA Impedance Analyzer to characterize the ESR of a Super-capacitor

*Introduction*

Super-capacitors are very useful devices providing power for applications ranging from SRAM to high-speed trains. The energy density is 10 – 100 times higher than that of standard (electrolytic) capacitors. And although they have a lower energy density than lithium-ion batteries, they have a much higher power density, which is useful when bursts of power are required, see figure 1. Furthermore, they can be charged and recharged over a million times.

*Figure 1: Ragone plot of energy density vs power density of various energy storage devices including Super-capacitors. Adapted from Wikipedia.*

When characterizing any capacitor, three critical parameters are capacitance, leakage current and equivalent series resistance (ESR). In this blog, we focus on the ESR of a 3000 F Super-capacitor.

Reliable knowledge of a capacitor’s ESR is key to designing efficient circuits, such as for RF power applications. Standard measurement procedures, such as the Maxwell 6-Step process, give values of ESR as a static value. In contrast to this technique, we present a frequency dependent technique which characterizes the ESR from mHz to kHz.

Optimization of components based on their ESR can significantly reduce internal heating, and the ESR can also be used as a parameter to judge the “health” of a super-capacitor; increasing ESR indicates end of life ageing.

Super-capacitors offer a unique challenge for impedance analyzers as they have low-impedance, and need to be measured at low frequency. This is a strength of the MFIA impedance analyzer as we show in this blog post. In contrast to other impedance analyzers, the MFIA infers the voltage and the current signals directly without needing a feedback loop such as a bridge circuit. This means the MFIA can measure down to frequencies of mHz.

*Experimental Setup*

The device under test (DUT) is a 3000 F, 2.7 V (3.0 W/h) PowerStor Super-capacitor from Eaton. It was soldered to a through-hole 4-terminal carrier with an eight-pin plug (Sullins PPPC081LFBN-RC). The carrier was connected to the MFIA impedance test fixture (MF-ITF) as shown in figure 2. The 4-terminal cables are length matched to ensure proper zero phase between voltage and current which is essential when measuring ESR at higher frequencies.

*Figure 2. Super-capacitor connected to the MFIA via the impedance test fixture (MF-ITF). *

*Using lock-in technology to measure impedance*

The MFIA is based on the proven lock-in technology of the MFLI. A key strength of lock-in technology is employed to measure the impedance; simultaneous phase-sensitive voltage and current measured at the DUT. The impedance value is given by the measured voltage divided by the measured current while taking the phase into account. The MFIA employs one of two basic measurement circuits for this task: a two-terminal setup advantageous for high impedances, and a four-terminal circuit which is suitable for most situations and advantageous for low impedances. As super-capacitor will result in low impedance values in the ESR dominant region the four-terminal measurement method is the proper choice. The schematic of the measurement setup is shown in Figure 3.

Figure 3 illustrates the schematic setup; the DUT is driven by a sinusoidal signal voltage on the right, and the voltage drop across the DUT is measured, while the current is monitored on the left. Two additional leads are connected to either side of the DUT for measuring the voltage drop across. All the current flows through the LCUR and HCUR connectors, whereas LPOT and HPOT are current-free and serve as non-invasive probes for the electrical potential. This four-terminal setup is advantageous for measuring small impedances, since it is insensitive to the effect of series impedances in the cables, connectors, soldering points, etc.

*Figure 3 Schematic diagram of a 4-Terminal setup to measure impedance. The impedance is the measured voltage divided by the measured current taking the phase into account. *

However, these lock-in measurements alone are not enough, as the internal components of the MFIA themselves contribute to the impedance measurement in the form of parasitics. To circumnavigate this, the MFIA is factory calibrated to compensate for its internal parasitics and to match the different input ranges. Furthermore, any additional parasitics due to a user test fixture or cables linking to the DUT can be eliminated by using the Compensation Advisor feature to produce a user-compensation.

The typical parasitics of a capacitor setup can be described with the following model shown in figure 4. This contains elements representing the inductance and resistance of the leads, and stray capacitance and leakage current between the two sides of the DUT.

*Figure 4: Schematic diagram outlining a model for user-fixture compensation. The model contains elements representing the inductance and resistance of the leads, and the stray capacitance and leakage current between the two sides of the DUT.
*

Once the parasitics have been compensated, the impedance values such as Abs(Z), Img(Z) and phase can be directly read out. To access further impedance parameters such as capacitance, ESR, inductance, loss tangent etc., the user picks a model from the list of equivalent circuit models. The chart in figure 5 shows the process flow from the initial lock-in signals to the required impedance parameters.

*Figure 5: Process flow within the MFIA to get from lock-in measured current and voltage to the desired parameters such as capacitance, Q-factor, resistance etc.
*

A final point on the experimental setup: as super-capacitors are unipolar, in order to avoid damage, a DC bias voltage must be applied to the driving voltage to ensure that the super-capacitor only sees positive voltages. In this case, we applied an offset of 200 mV to our driving AC voltage of 200 mV.

*Results*

The chart in figure 6 shows three different traces. The blue trace is the absolute value of impedance, which shows three distinct regions; from 1 mHz to 100 mHz, the capacitive reactance can clearly be observed as a negative gradient in Abs(Z). The second region is as the blue trace levels out between 100 mHz and 1000 Hz. This is an area where the ESR dominates, and it can be measured to be 0.33 mOhm at 46 Hz (see blue dashed circle). The third region can be observed at frequencies above 1 kHz, where the Abs(Z) becomes positive in gradient, due to the inductive reactance becoming dominant.

*Figure 6: LabOne Sweeper screenshot showing live data taken on the 3000 F capacitor: the graph shows the capacitance (red trace) as a function of frequency, and the absolute impedance (blue trace). The floor of the absolute impedance represents the ESR. The light blue trace is the phase between Re(Z) and Img(Z).
*

The phase between the resistance and the reactance can be observed as the light-blue trace in figure 6. It begins at -90 degrees in the low frequency domain (capacitive reactance) and slowly rises to +90 degree as the reactance is dominated by inductance.

The absolute impedance and phase are base values based on the phase-sensitive voltage and current. Providing a model of the impedance allows us to determine model-derived parameters such as capacitance (red trace). The red trace in figure 4 shows the capacitance to be 2863 F at a bias voltage of 200 mV, as measured at low frequencies (1 mHz). For comparison, the nominal capacity is 3000 F at 2.7 V.

Digging a little deeper, the ESR, which is simply the real part of the absolute impedance, can be plotted along with the absolute value of Z as shown in figure 7. The chart in figure 7 shows the ESR for a larger frequency range than in figure 6, extended by a decade on either side. This means the ESR can be reliably measured from 10 mHz to 10 kHz.

*Figure 7: Post-processed chart showing the absolute value of Z (dark blue trace) and the real part of Z (light blue trace). The real part of Z is equivalent to the ESR.
*

*Conclusion*

The MFIA impedance analyzer has been used to measure the equivalent series resistance (ESR) of a 3000 F super-capacitor. The ESR could be reliably and accurately measured from 10 mHz to 10 kHz, with an example value of the ESR at 46 Hz being 0.33 mOhm. This nicely demonstrates one of the many powerful aspects of the MFIA. Stay tuned for more exciting results!

*A huge thanks to Jürg Schwizer for all his help with these measurements.*