# The Buck Converter

In the part one we discussed about switched mode voltage regulation. Controlling the dc component of a pulsed output voltage may be good for some applications like controlling DC motor, but here the objective is to output purely dc voltage. The way of getting a purely dc voltage is insert a low pass filter after the switch. Here the output voltage is always less than the input voltage. Hence this circuit is called Step-Down converter. Buck converter object is to efficiently reduce DC voltage. According to the law of energy conservation the input power should be equals to the output power. (Assuming ideal circuit). So the P IN = P OUT which means that V IN I IN =V OUT I OUT.  By assuming LP filter is ideal we can say that the output voltage is average of the input voltage to the filter. The input to the filter which is the voltage across the diode, is VS when the switch is closed and is zero when the switch is open, provided that the inductor current remains positive keeping the diode on. Periodic opening and closing of the switch results a VSD voltage at the output. D is the duty ratio. When the buck converter operating in the steady state it has following properties,

1. The Inductor current is periodic
2. The average voltage across inductor is zero. In inductors, the current cannot change instantaneously because inductors tend to keep the current constant. An ideal inductor with infinite inductance act as a constant current source.
1. The average current across capacitor is zero. In capacitors, the voltage cannot change instantaneously because capacitors tend to keep the voltage constant. An ideal capacitor with infinite capacitance act as a constant voltage source.
1. Input power is equals to the output power.

The operation of the buck regulator can be seen by breaking its operation into two periods. Here we assume the continuous conduction mode which the current through inductor never comes down to the zero. In the discontinuous conduction mode, the inductor current eventually hits zero during the switch open state.

1. Power switch is closed
2. Power switch is open

## Power switch is closed for DT seconds During the switch closed, the diode is reverse biased thus the diode is open. A current loop is created that includes the input voltage source, the power switch, the inductor and the load.

VL=L*(diL/dt)

VL=VIN – VOUT

VIN – VOUT= L*(diL/dt)

(diL/dt) = (VIN – VOUT)/L

## Power switch is Open for (1-D) T seconds The property of Inductor is that it tries to oppose sudden change in voltage appears across it. While charging, the inductor terminal near to the switch is positive. When the switch is open the voltage across the inductor reverses (the terminal away from the switch becomes positive). It makes freewheel diode D forward biased. IL continues to flow; thus the diode is closed. This allows the energy stored in the inductor to be delivered to the output. This continuous current is then smoothed by output capacitor.

VL=L*(diL/dt)

VL= -VOUT

-VOUT= L*(diL/dt)

(diL/dt) =(-VOUT)/L

Since the average voltage across L is zero,

VL AVG = D*(VIN – VOUT) + (1-D) *(-VOUT) = 0

DVIN = D*VOUT + VOUT – D*VOUT

VOUT = D*VIN

From the power balance V IN I IN  = V OUT I OUT, so

IOUT = IIN / D

In the next lesson we will discuss how to design a buck converter for the given specifications.

## Summary

he buck converters are used for DC to DC voltage conversions, those are step down converter. LC circuit is used as a filter for the circuit, by using LC circuit the power loss of the conversion can be minimalized.

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