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Step-by-step derivation of Buck Converter voltage conversion ratioBuck converter is a step-down converter, and it operates under the principle of inductor.
Let’s derive the voltage conversion ratio for a Buck converter.Buck Converter CircuitFirst, write the volt-second balance equation for a single cycle inductor. It is:
$$V_{in}DT_s=V_{out}(1-D)T_s$$
Where, D: Duty cycle of the Buck converter.Ts: Switching period of the Buck converter.
Rearrange the above equation and find the voltage conversion ratio:
$$\frac{V_{out}}{V_{in}}=\frac{D}{1-D}$$
Derivation of BuckBoost Converter Voltage Conversion RatioBuckBoost converter is a type of DC-DC converter, which can step up or step down the output voltage. The voltage conversion ratio for BuckBoost converter is given as:
$$\frac{V_{out}}{V_{in}}=\frac{1}{1-D}$$
For BuckBoost converter, the inductor is connected to the input and output of the converter. The capacitor is connected between the inductor and the switch.
The operating principle is as follows: When the switch is closed, the input voltage is applied across the inductor and capacitor. This charges the capacitor and causes the inductor to store energy.The switch is opened, and the voltage across the inductor reverses polarity. The stored energy in the inductor is transferred to the capacitor.The output voltage across the capacitor is equal to the input voltage when the switch is closed, and it is equal to the voltage across the inductor when the switch is opened. The voltage conversion ratio for the BuckBoost converter is therefore given by the above equation.
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