ESR and LIC when use as a battery substitute

GH Crash

Member
I need some electronic expertise on the value (importance) of ESR for lithium-ion capacitor when the capacitor will be used as battery replacement for small brushed DC motors.

In model aviation, there is a class of aircraft that are referred to as free flights. One group of free flight aircraft use a small DC motor that is powered from a small, usually Lipo, battery. Part of the electric free flight group have replaced the battery with a 10 to 100F supercapacitor (EDLC). The higher voltage, higher capacitance and low self-discharge of the LIC seem to offer advantages over the EDLC. Several individuals feel that the relatively high ESR of a LIC make them unsuitable as an EDLC replacement. Other individuals feel that the ESR may not be a significant factor since the capacitor will be operating at virtually zero frequency.

I would be interested to hear your ideas concerning ESR when using a LIC as if it were a battery. Remember that we are talking about capacitors with a capacitance greater than ten Farads.

Please, don't bother to tell me that a battery would be a better choice. For the sake of this thread (posting) assume a battery cannot be used for reasons that are outside this discussion.
 
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For applications where high current pulses have to be handled, supercapacitors are often used and then their low ESR is really important.

However the ESR is only important where the voltage drop due to ESR matters, so where a model aircraft is flying for several minutes, the ESR will make next to no difference.

If the brushed motors are being controlled using PWM, it will be the motor current, which will equal the peak current taken from the capacitors, that has to be considered, and that can be a lot more than the the average current.

The other consideration is ESL, or equivalent series inductance. The current will not be steady, either due to PWM or due to the switching each time a brush connects with or disconnects from a commutator segment. The ripple current can cause significant voltage spikes. I have no idea how the ESL of a supercapacitor compares with that of an LIC, but it's always a good idea to put generous amount of low ESR capacitors on the input to any PWM controller, so that inductance of the supply, including any wires, has less effect.
 
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ESR, or Equivalent Series Resistance is not dependent on frequency. It will be the same for DC or AC.

ESL, or Equivalent Series Inductance, is frequency dependent, and will be lowest for DC.

Any resistance in the total power loop will have a current dependent voltage drop across it, and will reduce the total power efficiency of the system.
 
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Doing a quick search on Digikey, the ESR tends to be lower with higher value LICs - but for a given value (eg. 50F) the ESR can be anything from 26 milliohms to 450 milliohms, through the different types.

The lower the ESR, the more energy will get to the motor & less wasted. How much is lost depends on the current drawn from the capacitor.

eg. If the motor draws half an amp, the high ESR one would drop almost a quarter of a volt at the terminals due to the ESR, while the 26mR one drops by just 13mV.
If you are only running at around 3V, that's around 8% energy wasted vs. 0.5% waste. The losses are worse at lower voltages and higher currents.

An appropriate plastic film film or ceramic cap across the supercap can reduce the current peaks to nearer the average, so improve efficiency to some extent, in a PWM system.

Lower ESR types are likely rated for higher current, so should also have a longer life in any given application - but they are also generally larger, heavier and more expensive that the ones with high ESR.

The price may be compensated by a far longer life?

eg. Two 50F ones at the extremes; 450mR and 250mA rating vs. 26mR and 5.27A:-
 
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What you say is true, but the example you give is for two different EDLCs.
 
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Good information. All of it. Thanks.

"low ESR capacitors on the input to any PWM controller" Are you talking about micro farad capacitors? Would they still be necessary if the controller is powered from a capacitor?

It seems that your posting is implying that ESR ought to be treated as if it were simple internal resistance. Is that correct?

From what I've read, frequency has an effect on the ESR. ( Do you agree?) It seems that most of the published ESR values are measured at 1 or 2 Khz. What is the ESR at lower, or higher, frequencies?

Attached is a schematic of a circuit that might e used in capacitor powered free flight. An ATTiny85 does PWM duty and provides a run-time motor shutoff. The 4-pin connector at the top is used by a separate programmer circuit to set motor power and run-time. If ESR is an important factor, What changes to the circuit would you suggest?
 

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GH Crash said:
"low ESR capacitors on the input to any PWM controller" Are you talking about micro farad capacitors? Would they still be necessary if the controller is powered from a capacitor?
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Yes, I am talking about microfarad capacitors.

They will probably be needed because the ESR and ESL of the main capacitor, and of the wires connecting the main capacitor to the PWM controller, are most likely a lot more than the ESR and ESL of some small capacitors that you can put directly on the input of a PWM controller.

It's much the same as decoupling capacitors on every IC, not all in one corner of a circuit board.
 
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