## half wave rectifier

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Half wave rectifier (HWR) is the first type in the rectifiers which rectifies the full wave input AC signal in to half wave pulsating DC signal. That’s y this is called half wave rectifier.

### Construction of HWR:

The diode is the first component used in rectifiers which is a uni-directional device i.e. it allows the signal in one direction and blocks the signal flow in opposite direction. In HWR, the diode is placed in series with the input AC  sinusoidal signal which consists of positive ad negative peaks. If the diode is placed in the normal direction then it rectifies the negative peak and produces positive peak as output. If it placed in reverse direction then it acts as positive clipper and produces negative HW output.

Half wave Rectifier circuit diagram

Transformer is placed at the input to step down the input AC signal to the corresponding output DC voltage. I.e. normally AC input voltage will be high which can break the diodes so that it needs to step down. The output voltage is measured across the resistor placed at output terminals.

#### Operation of HWR

The operation of HWR is same as diode that it rectifies half of the input wave form and allows other half. When the input voltage is greater than diode built-in potential then it starts conducting and the input signal is produced at the output. i.e. until the diode is conducting state the output will be same as input. During the negative pulse, once again when the input voltage is less than built-in potential, the diode is reverse biased and stops conducting which blocks the input signal. So the resultant output during this period will be zero. The ideal input and output waveforms are shown in the above figure.

HWR input and output wave forms

##### Specifications of the Half wave Rectifier

1) Average output Voltage(VDC): Measure of DC content in  the output Voltage. Consider above output wave form of HWR with Vm as output peak voltage and period is 0 to 2∏.

Vdc        =            $\frac{Average&space;Value}{Period}$

=          $\frac{1}{2\pi}\int_{0}^{\pi}Vm&space;sin\theta&space;d\theta$

=           $\frac{V_{m}}{2\pi&space;}\left&space;|&space;-cos\theta&space;\right&space;|_{0}^{\pi&space;}$

=           $\frac{V_{m}}{2\pi&space;}\left&space;[&space;1+1&space;\right&space;]$

Vdc            =            $\frac{V_{m}}{\pi&space;}$

2) RMS Value of output (Vrms) :  It measures the AC content in the output pulsating DC Voltage. RMS  value means Root Means Square value i.e. square root of mean Value square. So,

Vrms               =            $\sqrt{\left&space;[&space;Mean&space;Value&space;\right&space;]^{2}}$

=            $\sqrt{\frac{1}{2\pi}\int_{0}^{2\pi}[]Vm&space;sin\theta]^{2}&space;d\theta}$

=           $\sqrt{\frac{Vm^{2}}{2\pi}\int_{0}^{2\pi}[sin\theta]^{2}&space;d\theta}$

=      $\frac{Vm}{\sqrt{}2\pi}\sqrt{\int_{0}^{2\pi}[\frac{1-cos2\theta&space;}{2}]&space;d\theta}$

=        $\frac{Vm}{\sqrt{}2\pi}\sqrt{\frac{\theta&space;}{2}\left&space;|_{0}^{2\pi&space;}&space;+&space;\frac{sin2\theta&space;}{4}_{0}^{2\pi}}$

=           $\frac{Vm}{\sqrt{}2\pi}[\frac{2\pi&space;-&space;0}{2}]$

Vrms    =         $\frac{Vm}{\sqrt{}2}$     = 0.707 Vm

3) Form factor: It measures the percentage of RMS AC voltage to the Average DC Voltage

$Form&space;Factor&space;=&space;\frac{RMS&space;Value}{Average&space;Value}$

= $\frac{\frac{Vm}{\sqrt{2}}}{\frac{Vm}{\pi}}$

= $\frac{0.707Vm}{0.636Vm}$

=  1.11

4) Peak Inverse Voltage:  The maximum voltage reading across the diode is called peak inverse  voltage. Half wave rectifier consists of one diode and in reverse bias the total peak voltage VM will be dropped across diode. So the peak inverse voltage of the half wave rectifier is Vm.

PIV = Vm

5) Regulation of HWR:

% Regulation        =         $\frac{V_{NL}-V_{FL}}{V_{FL}}&space;*&space;100$

VNl = No load Voltage i.e with out any losses at the output. The total Average voltage is the no load voltage.

VNL = vdc = $\frac{Vm}{\pi}$

VFL = Full load voltage is the output DC voltage under full load condition.

VFL = $\frac{Vm}{\pi}&space;-&space;I_{DC}R_{f}$

% Regulation        =     $\frac{\frac{Vm}{\pi}&space;-[\frac{Vm}{\pi}&space;-&space;I_{DC}R_{f}]}{\frac{Vm}{\pi}&space;-&space;I_{DC}R_{f}}$

=    $\frac{\frac{Vm}{\pi}&space;-\frac{Vm}{\pi}&space;+&space;I_{DC}R_{f}}{\frac{Vm}{\pi}&space;-&space;I_{DC}R_{f}}$

=   $\frac{I_{DC}R_{f}}{\frac{Vm}{\pi}&space;-&space;I_{DC}R_{f}}$

=   $\frac{1}{\frac{Vm}{\pi&space;I_{DC}R_{f}}&space;-&space;1}$

We know that

I$I_{DC}&space;=&space;\frac{Vm}{\pi(R_{f}+R_{L})}$

By substituting IDC in the above equation

=        $\frac{1}{\frac{Vm}{\pi}&space;*&space;\frac{\pi}{V_{m}}*\frac{R_{f}+R_{L}}{R_{f}}&space;-&space;1}$

%Regulation     =       $\frac{R_{f}}{R_{L}}&space;*&space;100$