Two-phase boost converter output capacitor selection

Question

I am designing a boost converter for my board. Here I am planning to have a smaller capacitance at the output. So I am using the IC from linear technologies ie. LTC3787. This can be configured as two-phase or multi-phase mode boost converter. I tried getting the waveforms for the output capacitor current and derive the capacitor value. But somehow i feel i am in the wrong direction. Could somebody help me on this ?

Here is the equivalent model of for the 2-phase boost converter.

and the waveforms i figured out at various points:

Please check and correct me if i am wrong anywhere.

Answer 1

If you look at your last waveform, the output current is the average of that waveform. So the capacitor current is that same waveform offset such that the average is at zero. That is, half positive and half negative per triangular waveform period.

If the circuit is at 100% duty cycle at 100% load and for small ripple voltage, then approx:

C = (1/8) * i * dT / dV

• i = current at 100% load
• C = capacitance
• dT = half period (pulse width of T1 or T2)
• dV = ripple voltage (p-p)

For example, i = 1A; dT = 2us; dV allowable = 0.02V

• C = (1/8) * 1 * 2e-6 / 0.02
• => C = 12.5e-6 or 12.5uF

Answer 2

Try this configuration in in Matlab: