## 3 Setup  
EIS determines the impedance, i.e., the AC resistance, of electrochemical systems as a function of the frequency of an AC voltage or current. Electrochemical systems are, for example, batteries. EIS can be used to obtain precious information about the system under investigation and the processes taking place in it. Usually, EIS is performed on batteries by imposing an alternating current, that is, the current of the working electrode is sinusoidally modulated and the resulting voltage and its phase are measured. The DC component of the modulated current is usually set to 0 so that the EIS is charge neutral and the state of charge of the cell is not influenced. Due to the three-electrode technology used in our zinc-air cells, the charge-neutral method cannot be used, as the DC component must be at least as large as the AC amplitude so that there is no switching between charging and discharging during an impedance measurement. The concept of impedance and the complex alternating current theory assume that there is a linear relationship between the amplitudes of voltage and current. In electrochemical systems, this is only the case approximately for small amplitudes, e.g., 1 mV to 10 mV [32]. Significantly larger voltage amplitudes, therefore, must not be used for measurement.  
In particular, the necessary DC component during an impedance measurement and the three-electrode technology prevent the use of an existing instrument for the measurement of impedance spectra. Therefore, developments for the measurement of impedance spectra of zinc-air, cells as well as adaptations for existing measuring instruments, are presented in this section.  
In this article, a rechargeable zinc-air cell from the company 3e Batteriesysteme is used. The cell can be seen in Figure 6 and has a capacity of 100 Ah. Figure 6 also shows the schematic diagram of the internal structure. The cell has a symmetrical structure in order to increase the active surface area. Inside the electrolyte there are nickel nets which serve as positive contacts during the charging process.  
Figure 5: Impedance spectra of zinc-air batteries at different working points and SoCs.  
Figure 6: Used zinc-air cell and schematic structure.  
The overall structure of the developed circuit is shown in Figure 7. The entire EIS process is controlled by a microcontroller, so that the setup is rather small and field applications are possible. The STM32F4 microcontroller represents the centerpiece of the schematic that controls all of the other peripherals. One of its two digital analog converters is used to output a sine wave at the frequency that is measured. The other digital analog converter creates several constant voltages using a sample and hold circuit that enables the duplication of numbers of outputs as long as constant voltages are being output. These voltages control the amplitude and the offset of the signal. The accuracy of the output signal is kept high, as amplitude and offset are controlled separately. A galvanostatic impedance measurement is preferred, as it is easier to control the current than such a small voltage. Therefore, the output signal is used as input of a current controller that applies the AC current to the battery under test. Last but not least, an external analog digital converter is used to measure both the actual applied AC current and the resulting voltage response of the battery under test. According to [PERSON] the amplitude of the voltage response has to remain less than 10 mV [32]. Therefore, a high precision, high speed analog digital converter, AD7768-4, is used so that the voltage response can be measured with sufficient accuracy despite the voltage offset of the battery. Offset compensation is thus not necessary.