# Rectifier

The electric power is usually available in a.c supply. The supply voltage varies sinusoidal and has a frequency of 50Hz and used for different purposes such as lightning, heating and electric motors. But there are many applications such as electronics circuit where d.c supply is needed. When such a d.c supply is requires, the mains a.c supply is rectified. Thus, rectifiers converts a.c to d.c.

There are two types of rectifiers:

1. Half-wave rectifier
2. Full wave rectifier

## 1.Half-wave rectifier

In a half-wave rectification, the rectifier conducts current only during the positive half-cycles of input a.c supply. The negative half-cycles of a.c supply are suppressed i.e during negative half-cycles, no current is conducted and hence no voltage appears across the load. Therefore, current always flows in one direction(i.e. dc) through the load through after every half-cycle. During the positive half-cycle of a,c input ,the diode is forward biased and conducts current. During negative half-cycle ,the diode is reverse biased and conducts no current. This result is that output consists of positive half-cycles of input a.c voltage while negative half-cycles are suppressed.

when the diode is forward biased, it behaves like a closed switch and connects the a.c supply to the load RL. However ,when the diode is reverse biased, it behaves like an open switch and disconnects the a.c supply form the load RL. This switching action of diode permits only the positive half-cycles of input a.c voltage to appear across RL.

Suppose v=Vm sinθ be the alternating voltage that is to be rectified. Let rf and RL be the diode resistance and load resistance respectively. The diode conducts during positive half-cycles of a.c supply while no current conduction takes place during negative half-cycles.

(i) (ii) (iii) (iv) (v) The efficiency will be maximum when rf is negligible as compared to RL. Neglecting rf/RL ,we have,

Maximum efficiency,ηmax=40.6%

## 2.Full wave Rectifier

In full wave rectifier ,for the positive half-cycle of input voltage, one diode supplies current to the load and for the negative half-cycle, the other diode does. The current always flows through the load in the same direction for both half-cycles of input a.c voltage. Therefore ,a full-wave rectifier utilizes both half-cycles of input a.c voltage to produce the d.c output.

There are mainly two circuits used for full-wave rectification:

• center-tap full-wave rectifier
• Full-wave bridge rectifier

## Centre-tap Full wave Rectifier The center-tap full-wave rectifier employs two diodes D1 and D2.A center tapped secondary winding AB is used with two diodes connected so that each uses one half-cycles of input a.c voltage. Diode D1 utilizes the a.c voltage appearing across the upper half(OA) of secondary winding for rectification while diode D2 uses the lower half winding OB.

During Positive half-cycles of a.c supply ,diode D1 is forward biased and diode D2 is reverse biased. During negative half-cycle, diode D2 is forward biased and diode D1 is reverse biased. The current in load RL is in the same direction for both half-cycles of input a.c voltage. Therefore, d.c is obtained across load RL.  ## Full-wave Bridge Rectifier Full-wave bridge rectifier contains four diodes D1 ,D2,D3 and D4 connected to form bridge. The a.c supply to be rectified is applied to the diagonally opposite ends of the bridge through the transformer. Between other ends of the bridge, the load resistance RL is connected. (i) During positive half-cycle of input a.c voltage ,end A of secondary is positive and end B is negative. Therefore, diodes D1 and D3 are forward biased while diodes D2 and D4 are reverse biased. Therefore, positive half of a.c is conducted through load RL via diodes D1 and D3.

(ii) During negative half-cycle of input a.c voltage , diodes D2 and D4 are forward biased while diodes D1 and D3 are reverse biased. Therefore, negative half of a.c is conducted through load RL via diodes D2 and D4 in the same direction as in (i) ## Efficiency of Full-wave Rectifier Suppose v=Vm sinθ be the alternating voltage that is to be rectified. Let rf and RL be the diode resistance and load resistance respectively. The rectifier will conduct current through the load in the same direction for both half-cycles of input a.c voltage. The instantaneous current i is given by: (i) (ii) (iii) (iv) (v) The efficiency will be maximum when rf is negligible as compared to RL. Neglecting rf/RL ,we have,

Maximum efficiency,ηmax=81.2%

## Ripple Factor

The output of a rectifier consists of a d.c component and a.c component. The a.c component is undesirable and accounts for the pulsations in the rectifier output. The effectiveness of a rectifier depends upon the magnitude of a.c component in the output; the smaller this component, the more effective is the rectifier.

The ratio of r.m.s value of a.c component to the d.c component in the rectifier output is known as ripple factor i.e Ripple factor helps in deciding the effectiveness of a rectifier. The smaller the ripple factor ,the lesser the effective a.c component and hence more effective is the rectifier.

(i) For half-wave rectification: The a.c  components exceeds the d.c component in the output of a half-wave rectifier. This results in greater pulsations in the output. Therefore, half-wave rectifier is ineffective for conversion of a.c into d.c.

(ii) For full-wave rectification: In the output of a full-wave rectifier, the d.c component is more than the a.c component. The pulsations in the output will be less than in half-wave rectifier. Full-wave rectification is invariably used for conversion of a.c to d.c.

## Comparison of Rectifiers

 S.N Particular Half-wave Centre-tap Bridge type 1 No. of diodes 1 2 4 2 Transformer necessary No Yes No 3 Max. efficiency 40.6% 81.2% 81.2% 4 Ripple factor 1.21 0.48 0.48 5 Output frequency fin 2fin 2fin 6 Peak inverse voltage Vm 2Vm Vm

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