Full Wave Rectifier | Bridge Rectifier With Smoothening Capacitor

In the half-wave rectification circuit, you have seen, negative half cycle wastes. In this circuit, we use bridge rectifier configuration to obtain full wave at the output.

During the positive half cycle, diode D2 is forward biased. The current flows through D2 then the load resistor and finally through D3. Hence positive half cycle appears at the output.

During the negative half-cycle, diode D1 is forward biased. Current flows from D1 then load resistor and finally through D4. Hence negative half cycle also rectifies and appears at the output.

Figure 1 The Bridge Rectifier

Figure 2 Output of bridge rectifier

We are considering practical diodes, peak output voltage (VP (out)) is given by

VP (out) = VP (in) -0.7

Average DC Value:

VDC = 0.636 VP

It means the output DC is 63.6% of the peak value.

VRMS = 0.707*VP

Adding A Smoothing Capacitor:

You have seen I  the above figure, the output DC is pulsating which is not smooth. It is undesirable in most cases. Adding a capacitor of a suitable value is used to smooth the output at the load resistor.
 The capacitor charges to peak value and discharges between peaks. The rate at which capacitor discharges is exponential. To minimize the ripples or pulses in the DC we need to choose a proper capacitance value. Now it's time to evaluate the equation.

Figure 3 The Bridge Rectifier With Smoothening Capacitor

Figure 4 Output of bridge rectifier. Fewer ripples, but still needs some improvements (capacitance value 50uF)

Figure 5 Output of bridge rectifier The result is better than above (capacitance value 500uF)

VP = peak voltage

Vr = ripple voltage

T = time period

R = load resistor

C = Smoothing capacitor

\[V_O = V_P e^{\frac {-t}{RC}}\]
 
At t= T >> Vo = VP - Vr

Apply Taylor series and expand e-t/RC

Neglecting higher powers we get

Set  Vr
With the help of the above equation, we can get the value of the capacitor.