Boost Converter - Coil energy transfer into Capacitor - Help needed!

Question

I am trying to design my own boost converter and so am learning about coils.

Let’s consider this example:

The switch of our boost converter has just opened, there was 100 mA flowing though the coil, now it has nowhere left to go, so the coil pushes all that energy into the capacitor, charging it up. I want to calculate the capacitor voltage after it’s been charged.

As you can see from my calculations, we should see the capacitor charged to 1 V, however that doesn’t happen. We are working with ideal components so the only route for energy to escape is in the diode. Its voltage drop is exactly 0.7 V.

My approach to calculating the energy lost by the diode looks like this:

We multiply the voltage drop of the diode by the average current that was flowing through it during the entire charge time, and then multiply that by the total charge time. - As you can see in the photo.

The issue is, I don’t know how to calculate both the charge time and the average current, I only know the minimum and maximum values. Also, the current flowing through the coil does not fall linearly, it’s ever so slightly slowing down as we approach zero.

How do I calculate these two values: The total charge time and the average charge current?

Thank you very much for all your help.

Component values, if needed:

• Coil: 1 mH
• Capacitor: 10 uF
• Diode Vdrop: 0.7 V
• Coil current: 100 mA

Answer 1

As you can see from my calculations, we should see the capacitor charged to 1V, however that doesn’t happen.

The capacitor is already charged to the incoming supply via the inductor and diode prior to the MOSFET switch operating so, if you calculate the energy is sufficient to raise the capacitor from 0 volts to 1 volt then, you'll actually be raising the capacitor by nearly 1 volt above the incoming supply.

I say "nearly" because once you have the capacitor pre-charged above 0 volts then, the energy required to lift is another volt is more than the energy to lift it from 0 volts to 1 volt.

There's also the diode drop to take into account.

How do I calculate these two values: The total charge time and the average charge current?

I wouldn't hesitate in using a simulator for this. Even if you wanted to make some approximate hand calculations, the simulator will be more accurate AND give valuable insight into some of the details you missed (such as what I alluded to in the first part of my answer).