# Half wave Rectifier using Diode

Rectifier is an electronic circuit which convert the ac input voltage to dc output voltage. There are two types of rectifier – half wave rectifier and full wave rectifier.

#### Circuit Diagram of Half wave Rectifier

Circuit consist of Diode D, a resistor R and an ac voltage supply.

#### Working of half wave rectifier

In the given circuit we apply ac input voltage. And we know that the ac voltage consist of positive and negative half cycle.

During the positive half cycle of input voltage, Diode D is forward bias. As there is positive voltage at anode and negative at the cathode. So diode D conduct and offer no resistance as diode is ideal. Due to this the whole voltage drop across the resistor R. We get the same positive half voltage waveform as input ac voltage across R.

During negative half cycle of input voltage, there is negative voltage at anode(A) of diode and positive at cathode (K). Due to this the diode is in reverse bias mode and diode does not conduct or in off state. There is no current flow through the circuit. As there is no current flow, so there is no voltage drop across resistor R. Output voltage is zero during whole negative cycle of input voltage.

So overall in one complete cycle of input ac voltage, we have a half positive cycle in output wave. That’s why we called it half wave rectifier.

#### Derivation of Average Value or dc voltage

Average value or Vdc = $\frac{1}{T}\int_{0}^{\pi}$$V_{m}\sin wt{\mathrm{d} t}$

= $\frac{V_{m}}{2\pi}$$\int_{0}^{\pi}\sin wtdt$

= $\frac{V_{m}}{2\pi}$ [ 2 ] = $\frac{V_{m}}{\pi}$

= 0.318 Vm

#### RMS value of output voltage of half wave rectifier

The ac voltage component of a signal containing a dc level is
vac = v – Vdc
the rms value of the ac component is
Vr(rms) =  sqrt{  $\frac{1}{2\pi}\int_{0}^{2\pi}$ $v_{ac}^{2}$dt   }

After solving above we get

Vr(rms)  = 0.385 Vm

#### Ripple factor & Fill Factor of half wave rectifier

Ripple factor defined as:

r = Vr(rms) / Vdc

= 0.385 Vm / 0.318 Vm

= 1.21 or in percentage 121%.

Fill Factor FF = square root( 1.21×1.21 +1)

= square root(2.46)

= 1.57

#### Peak Inverse Voltage(PIV) of half wave rectifier

Peak inverse voltage or peak reverse voltage is define as the voltage across the diode in reverse bias mode which does not exceed otherwise the diode will go in breakdown region and may get damage.

PIV => Vm means PIV must be greater than or equal to Vm.