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Introduction

Engineering

Robert Tang to fill out when the time comes

Background Knowledge

Buck Converter

DC-DC Step-down voltage regulator.

image-20240918-190305.png

Components:

  • Source (Vin)

  • Switch

    • Usually a MOSFET, because manually switching on/off the switch is tooo slow

  • Diode

    • In synchronous buck converter, a second MOSFET is added

  • Inductor

    • Stores and release energy (as current)

  • Capacitor

    • Smooth the voltage output

Calculating the conversion factor in CCM

*In this application we are only interested in Continuous Conduction Mode (CCM), where essentially i_L is larger than 0 for all time during CCM.

Some assumptions to be made before the calculation:

  1. Assume CCM

  2. Average steady state (Over period, the average values will be constant)

  3. Vin and Vout constant with respect to time

  4. Diodes and FETs are ideal

The calculation:

When the switch is on, during a time T_on the circuit looks like the following, where the diode acts like a open circuit (because of the reverse polarity).

image-20240919-141416.png

The Inductor voltage, and the rate of change of current through the inductor can be tested using the following equation, their graphs are also shown.

image-20240919-141944.png

When the switch is off, (after T_on) for a time T_offthe diode acts like a wire, and the voltage source (Vin) is replaced by an open circuit, the inductor is supplying current to the rest of the circuit.

image-20240919-142202.png

Here the inductor voltage and the current will change

image-20240919-142327.png

Combine the two we can get the graphs for the change in inductor voltage and current over a period T, and we also know that T_on+T_off=T

image-20240920-134855.png

Since we have assumed 'average steady state', which implies that the change in current are the same, so we can equate the two changes in current

image-20240920-135546.png

Finally we get the transfer function Vout/Vin=D, the duty cycle

As for how to design a buck converter, I referred

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