The Half wave rectifier is a circuit which converts the ac input voltage to a pulsating D.C voltage. In the Half wave rectifier circuit, a diode is connected in series with a load (RL). The circuit diagram of half wave rectifier is given below.
Where,
Now we discuss, What will happen when the A.C voltage ( V_{s} ) is applied to the half wave rectifier circuit. During the positive half cycle of A.C supply ( V_{s} ) the diode D is forward biased that means it conducts, and a current i_{L} will flow through the load R_{L}.
And during negative half-cycle ,the diode D, being reverse biased that means it does not conduct , hence no current will flow through the Load (R_{L}). So, i_{L} current flows in one direction and develop output voltage V _{out} which is a pulsating wave of one polarity and is called pulsating D.C voltage.
The wave from of the applied voltage V_{s} and out put voltage V _{out} and current i_{L} is shown in fig.
The current i_{L} in the diode or load R_{L} is given by
Assuming that the open circuit voltage from the secondary of the transformer is given by
Where, V_{m} is the peak value of the secondary voltage, the peak value of load current is given.
Where R_{f} is the dynamic Resistance of the diode.
The average value I_{av} or the dc value I dc of current through the load R_{L} is given by
The average value or dc value of out put voltage is given by
The rms value of current flowing through the load R_{L} in a Half –wave rectifier is given by –
The pulsating load current i_{L} is the combination of dc and ripple (ac) components. The instantaneous value of the ripple (ac) component i is the difference between the instantaneous value of i_{L} and the dc value of current I_{dc}. Therefore, the instantaneous value of the ripple components is given by--
i=i_{L} - I_{dc}
Therefore , the rms value of the ripple ( ac ) current of Half – wave rectifier is given by.
Therefore,
Similarly,
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