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## What is a Full Wave Rectifier?

A full wave rectifier is defined as a type of rectifier that converts both halves of each cycle of an alternating wave (AC signal) into a pulsating DC signal. Full-wave rectifiers are used to convert AC voltage to DC voltage, requiring multiple diodes to construct. Full wave rectification is the process of converting an AC signal to a DC signal.

Circuits that convert alternating current (AC) into direct current (DC) are known as rectifiers. If such rectifiers rectify both the positive and negative half cycles of an input alternating waveform, the rectifiers are full-wave rectifiers.

Full-wave rectifiers achieve this by using a group of diodes. A diode permits current in one direction only and blocks the current in the other direction. We use this principle to construct various rectifiers.

We can classify rectifiers into two types:

- Half Wave Rectifier
- Full Wave Rectifier

When we use a half-wave rectifier, a significant amount of power gets wasted as only one half of each cycle passes through, and the other cycle gets blocked. Moreover, the half-wave rectifier is not efficient (40.6%), and we can not use it for applications that need a smooth and steady DC output. For a more efficient and steady DC output, a full wave rectifier is used.

We can further classify full wave rectifiers into:

- Centre-tapped Full Wave Rectifier
- Full Wave Bridge Rectifier

## Centre-tapped Full Wave Rectifier

### Construction of Centre-tapped Full Wave Rectifier

A centre-tapped full-wave rectifier system consists of:

- Centre-tapped Transformer
- Two Diodes
- Resistive Load

Centre-tapped Transformer: – It is a normal transformer with one slight modification. It has an additional wire connected to the exact centre of the secondary winding.

This type of construction divides the AC voltage into two equal and opposite voltages, namely +Ve voltage (V_{a}) and -Ve voltage (V_{b}). The total output voltage is

The circuit diagram is as follows.

### Working of Centre-tapped Full Wave Rectifier

We apply an AC voltage to the input transformer. During the positive half-cycle of the AC voltage, terminal 1 will be positive, centre-tap will be at zero potential, and terminal 2 will be negative potential.

This will lead to forwarding bias in diode D_{1} and cause current to flow through it. During this time, diode D_{2} is in reverse bias and will block current through it.

During the negative half-cycle of the input AC voltage, terminal 2 will become positive relative to terminal 2 and centre-tap. This will lead to forwarding bias in diode D_{2} and cause current to flow through it. During this time, diode D_{1} is in reverse bias and will block current through it.

During the positive cycle, diode D_{1} conducts, and during the negative cycle, diode D_{2} conducts and during the positive cycle.

As a result, both half-cycles are allowed to pass through. The average output DC voltage here is almost twice the DC output voltage of a half-wave rectifier.

#### Output Waveforms

#### Filter Circuit

We get a pulsating DC voltage with many ripples as the output of the centre-tapped full wave rectifier. We cannot use this pulsating for practical applications.

So, to convert the pulsating DC voltage to pure DC voltage, we use a filter circuit as shown above. Here we place a capacitor across the load.

The working of the capacitive filter circuit is to short the ripples and block the DC component so that it flows through another path and is available across the load.

During the positive half-wave, the diode D_{1} starts conducting. The capacitor is uncharged.

When we apply an input AC voltage that happens to be more than the capacitor voltage, it charges the capacitor immediately to the maximum value of the input voltage. At this point, the supply voltage is equal to capacitor voltage.

When the applied AC voltage starts decreasing and less than the capacitor, the capacitor starts discharging slowly, but this is slower when compared to the charging of the capacitor, and it does not get enough time to discharge entirely, and the charging starts again.

So around half of the charge present in the capacitor gets discharged. During the negative cycle, the diode D_{2} starts conducting, and the above process happens again.

This will cause the current to flow in the same direction across the load.

## Full Wave Bridge Rectifier

### Construction of Full Wave Bridge Rectifier

A full wave bridge rectifier is a rectifier that will use four diodes or more than that in a bridge formation. A full wave bridge rectifier system consists of

- Four Diodes
- Resistive Load

We use the diodes, namely A, B, C and D, which form a bridge circuit. The circuit diagram is as follows.

### Principle of Full Wave Bridge Rectifier

We apply an AC across the bridge. During the positive half-cycle, terminal 1 becomes positive, and terminal 2 becomes negative.

This will cause the diodes A and C to become forward-biased, and the current will flow through it. Meanwhile, diodes B and D will become reverse-biased and block current through them. The current will flow from 1 to 4 to 3 to 2.

During the negative half-cycle, terminal 1 will become negative, and terminal 2 will become positive.

This will cause the diodes B and D to become forward-biased and will allow current through them. At the same time, diodes A and C will be reverse-biased and will block the current through them. The current will flow from 2 to 4 to 3 to 1.

#### Filter Circuit

We get a pulsating DC voltage with many ripples as the output of the full wave bridge rectifier. We can not use this voltage for practical applications.

So, to convert the pulsating DC voltage to pure DC voltage, we use a filter circuit as shown above. Here we place a capacitor across the load. The working of the capacitive filter circuit is to short the ripples and block the DC component so that it flows through another path, and that is through the load.

During the half-wave, the diodes A and C conduct. It charges the capacitor immediately to the maximum value of the input voltage. When the rectified pulsating voltage starts decreasing and less than the capacitor voltage, the capacitor starts discharging and supplies current to the load.

This discharging is slower when compared to the charging of the capacitor, and it does not get enough time to discharge entirely, and the charging starts again in the next pulse of the rectified voltage waveform.

So around half of the charge present in the capacitor gets discharged. During the negative cycle, the diodes B and D start conducting, and the above process happens again. This causes the current to continue to flow through the same direction across the load.

## Full Wave Rectifier Formula

We will now derive the various formulas for a full wave rectifier based on the preceding theory and graphs above.

### Ripple Factor of a Full Wave Rectifier (γ)

‘Ripple’ is the unwanted AC component remaining when converting the AC voltage waveform into a DC waveform.

Even though we try out best to remove all AC components, there is still some small amount left on the output side which pulsates the DC waveform. This undesirable AC component is called ‘ripple’.

To quantify how well the half-wave rectifier can convert the AC voltage into DC voltage, we use what is known as the ripple factor (represented by γ or r).

The ripple factor is the ratio between the RMS value of the AC voltage (on the input side) and the DC voltage (on the output side) of the rectifier.

The formula for ripple factor is:

Where V_{rms} is the RMS value of the AC component, and V_{dc} is the DC component in the rectifier.

The ripple factor of a centre-tapped full-wave rectifier is equal to 0.48 (i.e. γ = 0.48).

Note: To construct a good rectifier, we need to keep the ripple factor as minimum as possible. We can use capacitors or inductors to reduce the ripples in the circuit.

### Efficiency of a Full Wave Rectifier (η)

Rectifier efficiency (η) is the ratio between the output DC power and the input AC power. The formula for the efficiency is equal to:

The efficiency of a centre-tapped full-wave rectifier is equal to 81.2% (i.e. η_{max} = 81.2%).

### Form Factor of a Full Wave Rectifier (F.F)

The form factor is the ratio between RMS value and average value.

The formula for form factor is given below:

The form factor of a centre-tapped full wave rectifier is equal to 1.11 (i.e. FF = 1.11).

## Advantages of Full Wave Rectifiers

The advantages of full wave rectifiers include:

- Full wave rectifiers have higher rectifying efficiency than half-wave rectifiers. This means that they convert AC to DC more efficiently.
- They have low power loss because no voltage signal is wasted in the rectification process.
- The output voltage of a centre-tapped full wave rectifier has lower ripples than a halfwave rectifiers.

## Disadvantages of Full Wave Rectifiers

The disadvantages of full wave rectifiers include:

- The centre-tapped rectifier is more expensive than a half-wave rectifier and tends to occupy a lot of space.