# Frequency of the standard battery discharge curve

What can we say about the frequency of the discharging battery? You know that batteries, for example Li-Po, have a characteristic charge and discharge voltage curve. And under a certain rate of discharge and a certain load, the voltage drops for a time, for example from 4.2 V to 3.7 V in 1 hour. I wonder how can we calculate this frequency? The change can be very slow but imagine a battery goes 4.2 V to 3.7 V in a second and we measure the voltage with an oscilloscope.

• What frequency? I don't think "frequency" means what you think it means. Why did you tag oscilloscope and fft and then not even mention either in your question? Mar 20, 2021 at 15:11
• Right, FFT was obsolete but I mentioned about oscilloscope in question. Frequency of the signal? Why can't we regard the discharging curve as a signal? I mean we sample it, doesn't it resemble an analog sensor output? Mar 20, 2021 at 15:19
• yes, but anything but a harmonic oscilaltion doesn't have a single frequency. I really don't think you got the term "frequency" right. Do you mean spectrum? Mar 20, 2021 at 15:31
• yes exactly spectrum, but I think there may be characteristic peaks. Mar 20, 2021 at 15:44

Imagine as I have demonstrated in prior answers that a Li Ion battery has at least 2 time constants of a main capacitance of around 10kFarads and 50mOhm ESR depending on the C charge max rating. Where C is not capacitance but inverse to the ESR such that the max charge rate in 1hr is C times the Amps for a given Ah spec.

Now realize some batteries have more “memory” than others such that a longer time constant ESR2 * C2 = Tau2 is the recovery time from a pulsed short circuit greater than 10kF *ESR(=~50mOhm)= 0.5s this can be dangerous if temp rise causes thermal runaway and explosion so don’t try it, yet you know a shorter duration has some memory just like all e-caps (see Maxwell’s specs) and more dominantly on all double-layer electric supercaps, both have some memory to an instant change in current, so the frequency response of impedance from 1kHz to 1 cycle per hour so the impedance will change. (Still with me?). Ultimately it is the internal Temp rise and voltage dependent chemical “corrosion” factors that determine wear-out.

Rather than use a very slow sweep generator to measure the “frequency response” use dV/dt = Ic/C to measure the capacitance and watch it rise with ESR as the battery depletes and more rapidly below 10% where any prudent Battery abuser often goes past.(and marketting types who want to boast about their high capacity. So Amp hours with thresholds for CV and cutoff voltage can be directly correlated with this ultra-capacitance and ESR.

Also study the dI/dt during CV charging to measure the effective change in C and ESR with pulses. C increases marginally as ESR reduces marginally as stored charge increases only slightly (10%) at 4.1 vs 4.2 vs 4.3 for CV. Cutoff is often designed from 5 to 15% of the CC level to either gain slightly more capacity at the expense of greater loss in life expectancy.

WHat is more important than the frequency of recycling rated say 500 cycles as the temperature rises of the cells which degrades lifespan 50% or so for every 10 degrees C rise of the internal junction (Arhennius Law) but that overcharge CV >4.0 and undercharge <xx% SoC also degrades cycle counts for useful life.

Reading from Battery University, I recall if you had 2 sets of batteries instead and only used 1/2 of the rated capacity from 90% to 40% SOC you will get 10x the charge cycle life span or 5000 cycles and keep them in a state of 60% for long periods when not in use like Lenova does on the battery power management options when leaving a laptop charger on all the time. (Thus being powered by the charger instead of floating between 95 or more and 100% which might get you <5 yrs if lucky.)

Thus the frequency of charging depends on your budget for getting the max Ah performance and the cycle count of life expectancy from temp rise and over/under charging.

Also learn how to measure ESR for different currents as this changes due to the double-layer effects from the primary and secondary ESR * C equivalent circuit. In reality there are more than 2 parallel RC circuits, but I have digressed long enough....

Sorry if I lost you after the 1st paragraph, (lol) but I am addressing a wider audience.

• I basically know the calculations of capacitors, I'll read them a little more. I actually thought of it as an imaginary battery, regardless of the physical state of the battery. My main problem was about the frequency of this signal if we think of the battery voltage output as an analog sensor. Is it unreasonable to observe the discharge curve directly with the oscilloscope? Or recording it with a fast data logger and then doing DFT and looking at the spectrum? Mar 20, 2021 at 15:55
• You can , but that’s MB or GB of data, and remember that for a 16% voltage swing from 3.7 to 3.1 is 0.6V and taking the pre#loaded voltage start at 3.7 V or 3.8 if preferred using the 90% to 10% limit risetime vs Half power -3dB BW is Tr= 0.35 / f-3dB. But more important is load regulation error from a power supply %ESR/Load R and RC time constants using two asymptotic slopes with a constant current load (active cct). BTW that is used to spec DSO BW too but 0.35 assumes a 1st order LPF and not a 2nd order double-layer effect Mar 20, 2021 at 16:04
• Here’s a quick and dirty Lithium battery charge with the secondary absorption capacitance. See if you can create a model for your model of battery and age and post your values. tinyurl.com/yzg8qusm Mar 20, 2021 at 19:49