# Decoupling Capacitor Power Waste

I'm designing for a very power sensitive motor controller, and I'm concerned about the power that will be lost to the ESR of my decoupling capacitors. I have a prototype board as well, but there's no way to tell how much energy is being wasted within the capacitors.

With the capacitors, I expect the current draw into the board to resemble a square wave, because it's a 3-phase BLDC motor. However, with all my nice decoupling, it's become a reasonably sinusoidal wave at my PWM frequency.

Is there any way to determine how much power is being wasted in these capacitors? All of the literature I can find on it seems to be overly complex white papers. Are there rules of thumb or first order approximations I can use?

Could I also perhaps remove the capacitors, capture voltage and current waveforms, and add them back and check the difference? This approach would tell me the results for the current design, but doesn't really help in the design process.

Thanks!

• I would say this power is negligible comparing to the power motor is consuming, or eve the power dissipated on the controllers power stage. In programming it is called "premature optimization". Not sure there is such a term in EE though.. Jul 29, 2016 at 17:27
• Wouldnt leakage current be a bigger concern than ESR? Jul 29, 2016 at 17:31
• I think you would need to buy better quality caps with less ESR. Jul 29, 2016 at 17:36
• is that the ripple current or the load current? your psu/battery should be providing most of it Jul 29, 2016 at 17:38
• "I don't know what will be sourced by the capacitor and what by the battery." Fair enough, but this just points out the fact that if you're going to worry about inefficiencies at this level of detail, you need to worry about all of the parasitic losses in the system. Just as an example, two feet of AWG8 copper wire has a resistance of 1.2 mOhm, and at 50 A, this dissipates 3 W, too. There are dozens of effects like this in even a simple system, and most are going to be more significant than these examples. You need to go for the low-hanging fruit first. Jul 29, 2016 at 19:57

It sounds like you already have a working board. BY FAR the easiest way to study power loss is to use a thermal imaging camera to find hot spots during operation. If the capacitors are not getting warm, they are not dissipating heat. You can now buy low cost IR attachments for your android or iPhone device. There is SEEK thermal camera and FLIR one.

Another tool that could be helpful is a high bandwidth current probe. Sometimes you can insert a wire loop in series with your component and large enough to fit through the current probe. Then you can measure AC current. The dissipation is the RMS current * RMS current * ESR.

• Thanks for the answer. Measuring the current is likely the most accurate way to go. I'd like to be able to calculate and predict in order to confirm, and to design. Aug 2, 2016 at 13:00
• You are an analyticist. I am an empiricist. Both types are needed in this world. But don't let it hold you back from making progress. ;-) Aug 2, 2016 at 15:42
• Sigh. Unfortunately you're correct. It does slow the whole progress thing. Thanks :D Aug 2, 2016 at 17:02

Use polypropylene coupling caps. If they aren't good enough, nothing will work.

• Correct answer, but you need to elaborate as to why polypropylene is the best choice. It has a low dissipation factor even with sharp edged pulses for ultrasonic welding, etc. Single line answers with no details are subject to downvotes or deletion.
– user105652
Jul 30, 2016 at 1:18
• Sorry, Sparky256, that is one of my bad habits. But let me correct myself: Use polypropylene film/foil for best ESR. However, film/foil capacitors will not self-heal, so if "high" voltage is involved, consider a metallized film/foil hybrid that can self-heal (foil on one side of the dielectric and metallization on the other). That will give better reliability. Jul 30, 2016 at 6:50
• Yeah, I hovered over the downvote button for a while here, but it's painful because you may have good reasons for this answer. As it stands, it's worthless and doesn't even answer the question.
– pipe
Jul 30, 2016 at 8:03

The cap conducts AC and is sized for low impedence at the switching frequency giving low ripple voltage .It is reasonable here to neglect leakage losses.Your current draw is a square wave which occurs when system inductance gives high reactance at the switching frequency.We want the AC current to go through the caps and not through the DC power leads in order to make EMC problems less likely so we just calc the RMS value of your AC square wave ripple current .Now it is just I squared R where R is the Cap ESR .The power wasted in the caps will be small compared to the motor power but it can heat up the caps reducing thier lifetime .Remember that a 10 degree temp rise will roughly halve the life of an electrolitic cap .In most applications the cap life is adequate when there is no additional heating due to ripple current .If you find that your ballpark calcs show significant losses that will heat the caps by say 30 degrees C then your reliability could be in jepordy .Placing more caps in parallel is an easy way out of this problem .

• This answer makes sense, except that it is difficult to know what percentage of the current will be drawn from the cap, and which will be sourced over your power delivery path. Aug 2, 2016 at 14:23
• When the switching freq is reasonably high and the power rail has inductance for EMC compliance you can say that all the HF ripple goes through the caps. Aug 3, 2016 at 23:39

A brushless DC motor will NOT have currents of square-wave type, it'll have applied winding voltages of square waves, and the currents will be more triangle-shaped. More to the point, low-ESR capacitors are typically used in 50 kHz power applications, and it's unlikely you are going to get to that high a frequency for a motor drive. It is also unlikely that the measured ESR will be much of a guide, because the skin depth is much greater at low frequency, and your electrical conductivity be better then the as-tested datasheet indications. Your motor's magnetization curve losses are likely to dominate (and those are harder to model than the ESR of capacitors).

If you can put a Hall probe on the capacitor's connecting wiring, it will give you the RMS currents in the capacitors, and you can calculate losses. First, though, you will want to measure ESR of each capacitor at the real frequency-of-interest for your application.

• Thanks for the answer. Interesting information. Is the current draw surely a triangle wave on the DC side of an 3-phase inverter? I understand that it will be triangular in the inductive load itself, and also at the peak of the square wave, but not at the ON/OFF edge of the switching FET. They will quickly go from no to complete conduction. Aug 2, 2016 at 14:24
• One expects any steel-core inductor to have some misbehavior at the highest frequencies (because of conductivity of the steel), but at normal motor-operation frequencies, the stator and/or rotor inductance will make a slow slew of current out of any input voltage step. For efficiency, drive is usually voltage-switch type, though not always. The rapid switching of voltage just puts a square-wave-step voltage into an inductor, making a slow slewing current according to L dI/dt = V. Aug 3, 2016 at 0:27