What are the purpose of C38 to C51 in this design?

Question

I came across a BLDC drive circuit design and you can find the design here (https://danstrother.files.wordpress.com/2011/01/danstrother_mtrdrv1_20080629.pdf), and here are the picture of the finished PCB.

Basically, it is a simple design, but I couldn't understand the purpose of C38 to C51 in this design. It already has a electrolytic capacitor for DC link. If a bypass capacitor is needed, why are there so many 10uF capacitor? If they are used to help the electrolytic capacitor to filter out the switching noises in the inverter part, what kind of calculation should be used to get the proper capacitor values or the number of capacitor in parallel?

Answer 1

The short answer is lower supply ripple.from switched load regulation noise which is caused by DC Ω's = DCR of the motor

If you look closely at the switched load and RdsOn of the switches and ESR of the Caps, you should expect the ESR of the the string of Caps to be much less so than the load DCR. ... Perhaps near the RdsOn of the full bridge.

If you look at any family of caps you should expect as parts get bigger in value the ESR gets smaller but also the self resonant frequency gets smaller. In fact for the same voltage and size the ESR * C is fairly constant in any one design family of caps.

Also each cap has a small ESL [nH] which can affect ringing in the commutation and controls the self resonant freq (SRF) and having a parallel bank of caps also reduces ESL by N caps

Note the large top side copper plane on each side of the caps. These are also important design aspects to reduce power source inductance which can affect load regulated supply noise.

With low profile ultra low ESR caps as I expect these are I would expect the low ESR*C time constant to be in the 1-10 µs range and std caps in the 100 `300µs range. THis changes with cap design of materials, size and voltage over a wider range. This is just a rule of thumb that is 100x better than 40 years ago.

Thus for a good design of caps, T=ESR*C = 1 µs and C= 10uF each cap could have an ESR hypothetically of 100 mΩ and thus 14 parallel caps will be ~ 7 mΩ.

Not looking into the actual load impedance of this design, if you examine the specs for these cap and motor switches and motor ESR, you should find the caps make an adequate voltage source so step pulse ripple is < 5% for example. From this spec you can work out the ESR : Rds + DCR of motor ratios to minimize heat losses in the switches and caps for a reliable design.

Answer 2

C38 thru C51 is a way to make a very low ESR (equivalent series resistance) 140 µF capacitor. Single caps at such capacitance and voltage would need to be electrolytic to be practical. However, those have fairly high ESR. Ceramic caps have very low ESR, but don't come in suitably large values at that voltage.

In this case, the solution was to parallel a bunch of ceramic caps. That costs more than the equivalent electrolytic, but in this case the designer decided it was worth it to get the low ESR.

Ceramic caps also have other advantages, although these were probably nice to have as apposed to necessary requirements. They can operate at much higher temperatures, and aren't degraded by operation close to the rated temperature or voltage, as electrolytics are. They can handle much higher ripple current (which goes together with ESR, since the real limit on ripple current is heating), and have much higher lifetimes. Other than out of spec voltage, about the only thing that kills ceramic caps is mechanical abuse, usually due to board flexing.