Half Wave Rectifier

HALF WAVE RECTIFIER

In half wave rectifier, diode conducts only during positive half cycle of input ac supply. The negative half cycle of ac supply are eliminated from the output. This rectifier circuit consists of resistive load and transformer for step down the input voltage.

During positive half cycle of the ac input supply, diode D conducts. The current IL flows through load resistor RL. During negative half cycle of the ac input supply, diode D reverse biased. It does not conduct. No current flows through load resistor RL. The result is that output voltage consist of positive half cycles of input ac voltage while negative half cycles are suppressed. It may be seen that output across load resistor RL is pulsating d.c.

1. Average DC Load Current (I DC)

The average (or) dc value of alternating current is obtained by integration. For finding out the average value of an alternating signal we have to determine the area under the curve over one complete cycle.(i.e) from 0 to 2л and then dividing it by the base (i.e) 2.

Mathematically current waveform can be expressed as,

Where Rs - Winding resistance

Rf - Diode resistance

RL - Load resistance

2. Average DC Load Voltage (EDC or VDC)

It is the product of average D.C. load current and the load resistance RL

Substitute equation (3) in (2)

3. Mean Square Value of Load Current (IRMS)

RMS value of the set of values is square root of the arithmetic mean of the squares of the original values (or square of the function that defines the continuous waveform.)

4. DC Power Output (PDC)

The dc power output can be determined as,

5. AC Power Input (PAC)

The power input taken from the secondary of transformer is the power supplied to three resistances namely load resistance RL the diode resistance Rf and winding resistance RS.

The ac power is given as,

PAC = I2RMS (RL + Rf + Rs)

6. Rectifier Efficiency (η)

The rectifier efficiency is defined as the ratio of output dc power to input ac power.

7. Ripple Factor (γ)

Mathematically, ripple factor is defined as the ratio of R.M.S value of the ac component to the dc component in the output.

Iac = RMS value of ac component present in output

Idc = DC component present in output

IRMS = RMS value of total output current

The ripple factor for half wave rectifier is very high which indicates that the half wave rectifier circuit is a poor converter of ac to dc.

The ripple factor is minimized using filter circuits along with the rectifiers.

8. Transformer Utilization Factor (TUF)

The TUF is defined as the ratio of dc power delivered to the load to the ac power rating of the transformer.

We know that.

Substitute (11) in (10),

Since from equation (4)

9. Voltage Regulation

When we are neglecting 'RS' value voltage regulation = Rf/RL since RS << Rf

Less the value of voltage regulation, better is the performance of rectifier circuit.

10. Peak Inverse Voltage

The peak inverse is the voltage across the diode in the reverse direction. When the diode is reverse bias the current across the diode is zero. Hence maximum value of reverse voltage which occurs at the peak of the input cycle when the diode is reverse biased.

Peak inverse voltage of half wave rectifier is