# Charge storage capacitor dissipation

New for December 2018.  Back in 1992, James Carville coined the phrase "It's the economy, stupid", for Bill Clinton's successful Presidential candidacy against George H.W. Bush.  In case you only get your news from Microwaves101, Bush passed away on November 30, 2018 and led a remarkable life and was an all-around decent human being. We want to offer a variation on Carville's Law.  When you are asked to troubleshoot electrical hardware, remember:

# It's the capacitor, stupid!

Go ahead and print that out and display it proudly somewhere in your lab, and work it into tonight's dinner conversation: Maybe nine out of ten calls for air-conditioning service are due to failed caps.... and maybe you were hosed when the AC tech "replaced the motherboard". Replacing a capacitor on a motor requires only a screwdriver, a twenty dollar bill and knowledge of how to shut the power off, especially when dealing with 220 volts, which can kill you. Pass the meatloaf!

Capacitors fail for several reasons, one big reason is temperature (other reasons include voltage, humidity, mechanical damage, aging and witchcraft). That is why you need to understand mechanisms that heat up capacitors. In Tucson, the major culprit is sunshine, in Oregon, it's humidity. Check out this vintage distributed amplifier, it will likely need new capacitors if it is going to operate again.

In a pulsed power application, self-heating needs to be examined. For capacitors subject to AC voltage (not charge storage). It's trivial to calculate dissipation, you just need to plug the equivalent series capacitance into the I^2R equation. We'll add some equations for that later.

What about capacitors that are tied to a DC supply to smooth out voltage in a pulsed power application, so-called charge-storage capacitors?  Below we present a simple method of calculating dissipation without resorting to transient analyis.  It should be accurate enough for preliminary designs, you can follow up with Spice analysis for critical designs.  Note: there is a previous Microwaves101 page on this topic, which has a small error in the calculation.  Eventually we'll clean that mess up, get rid of it, or merge it. Meanwhile, don't believe everything you read on the world wide web!

Charge storage capacitors are decoupled from a power supply with some longish leads (some inductance) and connected to a device that draws a lot of current when it is tuned on, and draws smaller amount (or possibly zero) when it is switched off.  In this manner, the  power supply only has to be rated for the average current, not the peak current. This needs a figure...

The way to calculate dissipation is to first be sure you have sufficient capacitance so that voltage droop duing the pulse is acceptable, then calculate the sum of the inrush and outrush charge in Coulombs, then divide by the pulse period to get average (RMS) current in Amperes. Note that conservation of charge enforces that inrush and outrush charge are the same. We made a spreadsheet that does all this, it is available in our download area.  Below is an image of the spreadsheet for an example power amplifier running at 48 volts (can you say gallium nitride?) The user needs to enter data in the blue boxes, for duty cycle and pulse repetition frequency (PRF) and allowable voltage droop.  If your requirement is given in units of pulse width and pulse period and you cannot figure out how to convert to PRF and duty, consider a career in the gig economy....

How do you know what is an acceptable voltage droop?  It comes down to how much power droop you can stand.  Typically, power should not drop more than 0.5 dB.  For all but the shortest pulse widths, the power amplifier will heat up in the pulse and power will drop maybe 0.2 dB if you mounted it with a good heat sink design (ask your power amplifier supplier for data on this).  That allows 0.3 dB droop for voltage.  In a power amplifer, drain current will remain near-constant for minor voltage excursions, so you can calculate voltage droop based on power-proportional-to-voltage*. Below is a table for percent voltage droop and accompanying power droop in this case.  For 0.3 dB power droop, you can allow ~6.5% voltage droop, or about 5 volts for a 48 volt power amplifier. In the example we tightened that up to 2.5V, because, why not?

 Voltage droop power droop percent dB 0% 0.00 1% -0.04 2% -0.09 3% -0.13 4% -0.18 5% -0.22 6% -0.27 7% -0.32 8% -0.36 9% -0.41 10% -0.46

* Power droop is not simple, it depends on load line and nonlinear behavior.  You might actually see power proportional to square of voltage which would imply that the dB droop shown above should be doubled...

With all this talk about Droop, it is time to watch Droopy Dog, a cartoon from the 1950s. Fair warning, many of the gags in this series involve Blackface, another ugly chapter in the US history.  Maybe that's why MGM (Droopy Dog's content owner) tries to keep Droopy off of Youtube...

The spreadsheet user has to enter quiescent and peak currents for the power amplifier.  In drain-pulsed applications quiescent power is zero. In our example we used 1A and 10A respectively. The spreadsheet calculates inrush charge (Q=CV), then time-averages it twice over the pulse period to get avarage current (inrush plus outrush). The power amplifier is found to need 3800uF of capacitance.  The amplifier is operating at 48V, so you should derate the caps to 100V, then select some from a catalog. In this imaginary case we found two 1600uF caps with ESR of 0.125 ohms and entered them into the spreadsheet, and the pulse droop is close enough for Government Work. The result is shown the each capacitor is dissipating 0.4W.  Congratulations, you have now done a critical calculation that is often ignored by your co-workers.

You will need to do a thermal calculation to determine the temperature rise.  If you are an RF engineer, find a thermal engineer and throw her the charge number for a couple of hours.

Author : Unknown Editor