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Assume CCM
Average steady state (Over period, the average values will be constant)
Vin and Vout constant with respect to time
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).
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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.
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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.
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Here the inductor voltage and the current will change
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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
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