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# Half Wave Rectifiers

Rectifiers are the circuits used to convert alternating current (AC) into direct current (DC). Half-Wave Rectifiers are designed using a diode (D) and a load resistor (RL) as shown in Figure 1. In these rectifiers, only one-half of the input waveform is obtained at the output i.e. the output will comprise of either positive pulses or the negative pulses only. The polarity of the output voltage so obtained (across RL) depends on the direction of the diode used in the circuit of half-wave rectifier. This is evident from the figure as Figure 1a shows the output waveform consisting of only positive pulses while the Figure 1b has only negative pulses in its output waveform. This is because, in Figure 1a the diode gets forward biased only during the positive pulse of the input which causes the current to flow across RL, producing the output voltage.

Further for the same case, if the input pulse becomes negative, then the diode will be reverse biased and hence there will be no current flow and no output voltage. Similarly for the circuit shown in Figure 1b, the diode will be forward biased only when the input pulse is negative, and thus the output voltage will contain only the negative pulses. Further it is to be noted that the input to the half-wave rectifier can be supplied even via the transformer. This is advantageous as the transformer provides isolation from the power line as well as helps in obtaining the desired level of DC voltage. Next, one can connect a capacitor across the resistor in the circuit of half wave rectifier to obtain a smoother DC output (Figure 2). Here the capacitor charges through the diode D during the positive pulse of the input while it discharges through the load resistor RL when the input pulse will be negative. Thus the output waveform of such a rectifier will have ripples in it as shown in the figure. Different parameters associated with the half wave rectifiers are

1. Peak Inverse Voltage (PIV): This is the maximum voltage which should be withstood by the diode under reverse biased condition and is equal to the peak of the input voltage, Vm.
2. Average Voltage: This is the DC content of the voltage across the load and is given by Vm/π. Similarly DC current is given as Im/π, where Im is the maximum value of the current.
3. Ripple Factor (r): It is the ratio of root mean square (rms) value of AC component to the DC component in the output and is given by Further, for half-wave rectifier, rms voltage is given as Vm/2 which results in the ripple factor of 1.21.
4. Efficiency: It is the ratio of DC output power to the AC input power and is equal to 40.6 %.
5. Transformer Utilization Factor: It is the ratio of DC power delivered to the load to the AC rating of the transformer secondary and is equal to 0.287.
6. Form Factor: This is the ratio of rms value to the average value and is thus equal to 1.57 for half-wave rectifier.
7. Peak Factor: It is the ratio of peak value to the rms value and is equal to 2.
Half wave rectifiers are advantageous as they are cheap, simple and easy to construct. These are quite rarely used as they have high ripple content in their output. However they can be used in non-critical applications like those of charging the battery. They are also less preferred when compared to other rectifiers as they have low output power, low rectification efficiency and low transformer utilization factor. In addition, if AC input is fed via the transformer, then it might get saturated which inturn results in magnetizing current, hysteresis loss and/or result in the generation of harmonics. Lastly it is important to note that the explanation provided here applies only for the case where the diode is ideal. Although for a practical diode, the basic working remains the same, one will have to consider the voltage drop across the diode as well as its reverse saturation current into consideration during the analysis.

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