Half wave rectifier

Half Wave Rectifier

A half-wave rectifier is the simplest rectifier that uses a single diode and load resistor to rectify the ac signal to the dc signal. the half-wave rectifier is a single-phase rectifier of type of rectifier.as shown in the figure the circuit of the half-wave rectifier.

The diode is forward bias during each positive half cycle causing current to flow in the circuit. This current results in voltage Vout across the resistor  RL. The waveform of Vout with respect to Vs is a half-wave rectifier shown in the figure.

The output voltage of the half-wave rectifier is pulsating DC which has a significant AC component and DC component which is the average value of VOUT. This kind of voltage is not suitable as a DC supply. A simple way to make the output voltage smooth is to connect a filter capacitor across the output terminals.

During the positive half-cycle as Vs increases, the diode D conducts allowing the capacitor to charge to peak voltage of the sinusoid. After the peak, the voltage Vs start decreasing making the anode of the diode at lesser voltage than cathode as capacitor C holds the voltage at cathode at the peak voltage. This reverse biases the diode D and the capacitor C starts discharging through RL till the voltage across (which is the voltage at the cathode) it becomes less than Vs which is rising sinusoid. The diode then gets forward biased and starts conducting till the peak is reached and this cycle continues. The charging and discharging of the capacitor causes ripple voltage in the output. A larger capacitor (and /or RL) results in slower discharge and “flat” output giving rise to less ripple content. 

Ripple factor: 

Ripple factor is a measure of the effectiveness of a rectifier circuit. It is defined as the ratio of RMS value of the AC component (ripple component) Irrms in the output waveform to the DC component VDC in the output waveform. 

We can measure the value of the RMS component of the overall output waveform from which we can estimate the value of Irrms. 

We get, 

           

                            

                                                                           

 For half wave rectifier ;

This leads to ripple factor r =1.21 for a half-wave rectifier. The ripple factor can be significantly reduced using a filter capacitor. 

For a half-wave rectifier with a filter capacitor, the ripple factor is given by,

Where f is the frequency of pulsating DC which in this case is the same as that of AC mains. 

The value of the ripple factor can also be estimated from the waveform of the output voltage. 

Where Vp is the peak value of the output voltage and Vrpp is peak to the peak value of the ripple voltage.