July 31, 2019

Frequency dependence of Batteries

There are three frequency regimes to consider when dealing with batteries:

1.        Ultra low frequencies. These are frequencies measured in inverse hours or days. In this regime the battery acts like you would expect it to. At low frequency a battery will act like a current source plus resistance. All of the energy transfer will be due to ion movement through the electrolyte and none will be due to surface charge or capacitive storage.

2.        Medium frequencies, 1kHz to 1 Hz you are dealing in the regime of ion movement. If you are trying to pull a 10 mSec pulse out of a battery you will be accessing surface charge and capacitive storage, but also charge due to charges moving across the electrolyte. By the induced charge theorem a charged particle doesn’t need to move all the way across from one electrode to another to realize this energy, an ion with a charge of one unit will induce a charge on the anode of 1/10 of a unit as it moves 1/10th of the distance from the cathode to the anode. But these ions move slowly compared to the electrons in a wire, and this shows up as an increased resistance. The shorter the pulse and the higher current drawn the more the internal resistance of the cell will show itself.

3.        High frequencies for batteries are above 1kHz. In this regime impedance is a better term than resistance because capacitance and inductance come to play. Many types of batteries are spiral wound, which introduces more inductance than flat plates would, and of course all batteries are capacitors, having parallel plates separated by a distance. If the current is drawn from the battery in a series of short pulses at high frequency strange things can happen. For example you can get crazy oscillations in a feedback situation such as a switching power supply. In these kind of applications a capacitor across the battery lets the battery move into a lower frequency regime. However, in a sealed lead acid battery the high frequency impedance is mostly the DC resistance because the chemistry cannot react at these frequencies.

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