# Filters

## Need of filter circuit

1. Filters are the electronic circuits used along with rectifiers to get a pure dc voltage.
2. From all the rectifiers circuits get pulsating dc o/p. Where pulsating means some ac part or some ripples are present in the output.
3. But we need a pure dc voltage. Hence for removing the ac part or ripples from the o/p. We use filters circuit at the o/p of the rectifiers.
4. Therefore we can say that filter circuits are used to obtain the pure dc voltage o/p.

## Types of filters

There are five types of filter circuits depending on the type of components used and how they are connected.

• Capacitor i/p filter (Shunt capacitor filter)
• Series inductor filter (Choke i/p filter)
• ∏ type filter
• RC filter

## Capacitor i/p filter (Shunt capacitor filter)

1. To obtain a pure dc voltage a capacitor i/p filter is used along with rectifier ckt.
2. C is the filter capacitor which is connected across the load resistance RL and the value of c is very large. i. e. few hundred microfarads.
3. Generally electrolytic capacitors are used as a capacitor filter.
4. The filter capacitor is connected in shunt with load. Hence it is called as shunt capacitor filter.

Operation of FWR with shunt capacitor filter can be explained in four different intervals.

## Operation for O-A

1. The initial voltage on capacitor is zero.
2. In first positive half cycle of the supply D1 is forward bias and starts conducting and diode D2 is reverse bias and acts as a open switch.
3. Therefore capacitor C charges through diode D1.
4. At the end of this interval i.e. at point A. Capacitor charges to the peak value of secondary. Vc = Vm
5. After point A the instantaneous secondary voltage Vm starts reducing and this will reverse bias the diode D1. Hence at instant A the diode D1 turns off.

## Operation in the interval A to B

1. During this interval the voltage on capacitor is higher than rectifier o/p. Which results in both D1 and D2 are in off state.
2. The capacitor discharges through load resistor RL.
3. As the value of RL is much higher, the capacitor discharges slowly. Due to large value of RL. The value of C is also large. Therefore the discharging time constant as large as possible.
4. This will reduce the ripple content in the o/p voltage.

## Operation in the interval B to C

1. At instant B the instantaneous rectified voltage is equal to the voltage on capacitor and after ‘B’ it is greater than Vc.
2. Therefore diode D2 starts conduction at instant B.
3. The capacitor starts charges through D2 and at the end of this interval at point the voltage on capacitor is again equal to + Vm.
4. Therefore the diode D2 is reverse biased and stops conducting at point C.

## Operation in the interval C to D

1. During this interval voltage on the capacitor is higher than rectifier o/p.
2. Hence diode D1 and D2 both remain off and capacitor discharges through load resistance RL.
3. The value of RL and C is large. Hence capacitor discharges slowly through RL. Which makes the discharging time constant as large as possible.
4. This will reduce the ripple content in the o/p voltage.

Ripple factor r = 1 /4√3 fcRL for FWR.

r = 1 / 2√3 fcRL for HWR.

f – Supply freq. in H2

1. Easy to design.
2. Reduction in ripple content of the o/p voltage.
3. Increase in the average load voltage.
4. Small size and low cost.

1. Ripple factor is dependent on the load.
2. Regulation is relatively poor.
3. Diodes have to handle large peak currents.

## Half Wave Rectifier with Shunt Capacitor Filter

1. For the interval o to A and B to C the diode is forward biased and starts conducting.
2. Hence the capacitor charges through the diode.
3. For the interval A to B and for C to D the capacitor voltage Vc is higher than the instantaneous secondary voltage.
4. This will reverse biased the diode and makes it off.
5. Due to this the capacitor discharges through RL. Slowly to the lower voltage than FWR.
6. Hence the ripples increases and the ripple factor of this circuit is higher than that of capacitor. Filter with FWR.

## Bridge Rectifier with Shunt Capacitor Filter

Note: – The operation for bridge is same as that of FWR.

But instead of single diode two diodes are conducted in bridge operation.

## Series Inductor Filter

1. An inductor L is connected in series with the load RL.
2. The properly of an inductor is that it opposes any change in current through it hence it is used to reduce current ripple.
3. The diode D1 and D2 conducts alternately in the positive and negative half cycles to produce a unidirectional current through the load.
4. Due to the series connection of inductor L with load. The current ripple reduces to a great extent and the load current is smooth.
5. Higher the value of inductor, lower will be the peak to peak ripple in the load current.
6. The load voltage waveform is same as the load current waveform.
7. RF = 1/3√2 R/WL.

## Dependence of Ripple Factor on Loads

1. Ripple factor is directly proportional to the load RL.
2. This filter is suitable for high load current application.
3. The ripple factor can be improved (reduced) by increasing the value of inductor L.
4. The RF is maximum at no load and increases with increase in the load current. Which is exactly opposite to capacitor input filter.

1. Low ripple factor at heavy load currents.
2. No surge current through diode.
3. Reduces ripple in the o/p.

1. It is bulky.
2. It is more costly.

## Bridge Rectifier with Series Inductor Filter

Operation is same as that of FWR with series inductor filter.

## Comparison of Shunt Capacitor and Series Inductor Filter

Parameter Shunt Capacitor Series Inductor
Useful in Reducing ripple in load voltage Reducing ripple in load current
Surge current Very high and must be controlled Low and need not be control
Ripple factor R = 1/ 4√3 FCR R = R/3√2 WL
Size of filter Small and compact Bulky

## L. C. Filter

1. L. C. filter is a combination of inductor filter and capacitor filter.
2. Inductor filter is preferred for low values of RL and capacitor filter is preferred for high values of RL.
3. LC. Filter given low ripple factor irrespective of the load as it is a combination of two filters.
4. The series inductor offers high reactance to the ripple in the o/p and attenuates them and parallel capacitor offers a low reactance by pass path for them.

This will reduce the ripples.

## Importance of Bleeder Resistance (RB)

1. The resistance RB connected across the capacitor is called as bleeder resistance. It is used to maintain a continuous current through the filter inductance L.
2. If the current through L is not continuous i. e. if it is interrupted then a large back emf. Will be developed across the inductor.
3. This voltage may be exceed the PIV rating of the rectifier diode and damage them.
4. This voltage may exceed the maximum rated voltage of capacitor also.
5. Hence the induced back EMF is dangerous for diodes as well as capacitor.
6. The back EMF will not appear if current through L is continuous.

This RB will maintain a continuous current through L.

Ripple Factor of L.C. filter is RF r= 1/6√2 W2LC.

Which shows that the load resistance RL is not present in the expression. Hence, the ripple factor of LC filter does not depend on the load resistance it remains constant for all values of load.

This is the biggest advantages of LC filter so we can use it for the heavy as well as light loads.

2. Ripple factor is low and does not depend on the load.
3. This filter is suitable for light as well as heavy loads.
4. Diodes do not have to carry surge current.

1. Audible noise is produced by the inductor.
2. Large values of L and C makes ckt costly.
3. Due to use of inductor the filter is bulky.
4. Bleeder resistance increases the rating of rectifier ckt.
5. Power loss takes place in the series inductor L due to its dc resistance.

## ∏ Type Filter (CLC. Filter)

The ∏ type filter is a combination of capacitor i/p filter LC filter. It consist of two capacitors C1 and C2 along with the inductance L generally both the capacitor are of same value.

1. A full wave rectifier drives the ∏ type filter.
2. As C1 comes first, looking from the rectifier side the ∏ type filter behaves in a very similar way as the capacitor i/p filter.
3. All the advantages and disadvantages of capacitor i/p filter are all applicable to the ∏ type filter as well.
4.  ∏ type filter can be considered as a combination shunt capacitor filter and LC. Filter.
5. This improves the effectiveness of ∏ filter as for as of ripple is concerned.
6. Due to use of three filtering elements (C1 L and C2) the ripple factor of the ∏ type filter is very low as improved to the other filter.
7. The capacitor C1 and C2 provide a low reactance path for the ripple where as the series inductor L. Provides high reactance to the ac ripple. The combined effect of this is reduction in ripple and improvement in the output waveform.