# Picking input and output capacitance

A project log for Nixie Tube 170 V flyback DC-DC power converter

Design walkthrough and evaluation of a flyback converter from scratch

The capacitance added at the input and output of the converter will impact the voltage ripple.

## Output capacitance

There are some different ways to choose the output capacitance. One approach is determine the voltage ripple of the converter, and solve for the capacitance needed to meet the ripple spec. From the circuit diagram in the details section, the capacitor discharges during the on state. Using the small ripple approximation that the current is about constant during this interval, the voltage ripple can be expressed as

Solving for C:

Nixie tubes don't need perfect DC, so a peak-to-peak ripple of 1 V is more than sufficient. Under the target load of 30 mA and the maximum duty cycle at 5 V input of .773, the required output capacitance is 66 nF.

Another way to pick output capacitance is by the desired load transient over/undershoot. When output current jumps, the output voltage briefly drops before the feedback loop returns things to regulation. How sharply the voltage undershoots is a function of both the output capacitance and the bandwidth of the feedback loop.

A crude way to estimate the load transient is to observe that below the crossover frequency, the feedback loop reduces the effective output impedance of the converter, and at high frequencies, the output impedance of the converter is also low because of the output capacitance. The converter's output impedance is likely at a maximum near the crossover frequency, and this can be used to estimate the magnitude of the load transient:

Skipping ahead to the results of the compensation section I'll talk about soon, I ended up picking 8 kHz as the crossover frequency. Let's say I want to keep the voltage undershoot to 1 V when the load goes from 50% to 100% (15 mA to 30 mA). The required output capacitance from this formula is 298 nF.

I ended up using the latter method and rounded this up to 2 x 220 nF capacitors with a 10 nF ceramic capacitor to handle very high frequency transients. The larger capacitors are film type for their low ESR/dissipation factor and high voltage ratings. In this capacitance, film capacitors are available using either PP or PET plastic. PP has superior dissipation factor, but I'm not sure it matters for this application, so I picked a package where I could try both.

## Input capacitance

One way to size the input capacitance is to imagine the input capacitor alone supplies current to the inductor during the on-state, and gets recharged instantly when the switch turns off. How much capacitance would be needed to meet the desired ripple spec? The voltage ripple of a capacitor sourcing the average inductor current during the on period is:

I want the input voltage to drop no more than 1% or 50 mV. Using the maximum current and duty cycle conditions (Vg = 5 V, D = .773, IL = 1.4 A), then the required input capacitance is 62 µF. I rounded this up to 2 x 47 µF aluminum poly bulk capacitors. In addition, a few ceramic 10 µF or smaller caps will help reduce high frequency spikes.

## Discussions 