# Full Wave Bridge Rectifier Working and Application

The full-wave bridge rectifier is a circuit consisting of four diodes arranged in a bridge-type structured figure as shown. This circuit gives full-wave rectification and is cost-effective as well, thus used in many applications.

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**Construction Of Full Wave Rectifier**

Four diodes are used in the bridge rectifier. All the four diodes are connected in the form of a diamond-shape to the transformer and the load as in the shown circuit diagram.

**Working of Full Wave Rectifier**

The working of the full-wave rectifier is simple. The primary winding of the transformer is supplied with a sinusoidal supply. Whereas, the secondary of the transformer is diametrically connected to the two diametrically opposite points. The load R_{load} is connected to the remaining two points of the bridge.

Now when the AC input is given, during the first half cycle, the upper part of the transformer becomes positive when compared to the lower half of the same. Thus during the first half diodes, D4 and D1 are in forward biased. The currents follow the path 1-2 and enter the load. While returning, the path is 4-3. Similarly, diodes D2 and D3 are reverse biased. Thus, no current flows through the path 2-3 and 1-4.

During the negative half-cycle, i.e. in the next cycle, the upper portion of the transformer becomes negative when compared with the lower portion of the same. Thus diodes D2 & D3 are forward biased and the currents follow the path as 3-2-4-1. The other two, i.e., D1 & D4 are reversed biased for this cycle. So no current flows through the path 1-2 and 3-4. Hence negative cycle is rectified as it appears across the load.

The waveform of the rectified input will look like

Maximum of secondary Voltage = **Peak Inverse Voltage (PIV) of the bridge rectifier**

Thus in the bridge rectifier circuit, two diodes out of four conduct during one half-cycle and henceforward resistance becomes double that is 2RF.

**Peak Current in Full Wave Rectifier**

The value of the instantaneous applied voltage to the rectifier is given as

V_{s} = V_{smax}sin wt

Let us suppose that the diode has a forward resistance of R_{f} ohms and the reverse resistance equals to infinity, hence current through the R_{L} load can be given as :

- I1 = I
_{max}Sin wt and I_{2}= 0 for first half-cycle and - I1 = 0 and I
_{2}= I_{max }Sin wt for the second half-cycle.

The sum of currents I_{1} and I_{2} flows through the load resistance R_{L} which is given as:

I = I_{1} + I_{2} = I_{max} Sin wt for complete cycle

The peak value of load current flowing through the load resistance R_{L} is :

I_{max} = V_{smax}/(2R_{F} + R_{L})

**Output Current of Full Wave Rectifier**

The current through the load RL is the sum of the two halves of the ac cycles. The magnitude of the direct current Idc is equal to the average value of the ac current and is obtained by integrating the current I1 between 0 & Π or current I2 between Π & 2Π.

I_{dc} = 1 / Π ∫ ∫_{0}^{Π} I_{1} d(wt)

= 1/Π ∫ ∫_{0}^{Π} I_{max} sin wt d(wt)

= 2I_{max} / Π

**DC Output voltage**

DC or average value of voltage across the load is given by

Vdc = I_{dc} RL = 2/ (Π I_{max}R_{L})

**Root Mean Square (RMS) Value of Current**

Effective or RMS value of the current flowing through the load resistance RL can be given as:

I^{2}_{RMS} = 1/ Π ∫ ∫_{0}^{Π} I1 d (wt) = I^{2}_{max }/ 2

I_{RMS} = Imax / √2

**Rectification Efficiency of Full Wave Rectifier**

Now the amount of power delivered to the load

Pdc = I^{2}_{dc} R_{L} = 2Im/Π =RLoad

= (4/Π^{2})I^{2}_{m }RL

Alternating (AC) power input to the transformer = power dissipated at the diode + power dissipated from load resistance RL

I^{2}_{RMS}R_{f} + I^{2}_{RMS}R_{Load} = (I^{2}_{m}/2) (R_{f} + R_{Load})

Rectification efficiency,

n = P_{dc }/ P_{ac} = ((4/Π^{2})I^{2}_{m }R_{Load}) / ((I^{2}_{m}/2) (R_{f} + R_{Load})

=0.812(1+R_{f }/ R_{Load})

**Ripple Factor of Full Wave Rectifier**

Rectified output voltage, form factor is given as:

K_{f} = I_{RMS}/ I_{avg} = (I_{m}/√2) / (2I_{m}/ Π) = 1.11

Thus ripple factor, γ = √(1.11^{2} – 1) = 0.482

**Regulation of Full Wave Rectifier**

The DC output voltage is given as

V_{dc} = I_{dc }R_{L}= 2/(I_{m}R_{L})

= (2V_{sm}R_{L }/ (R_{f }+ R_{Load}))

= (2V_{sm }/ Π) – (I_{dc}R_{f})

**Applications of Full Wave Rectifier**

**Conversion of AC Power to DC Power**

In many of the electronics applications, regulated DC Power supply is used. One of the most convenient and reliable ways is to convert the AC supply to DC supply. The said conversion is done through a rectifier which uses a system of diodes arranged in a particular way.

Now if two the diodes are used then the arrangement made is a half-wave rectifier which rectifies only half of the AC signal. Whereas, when four diodes are arranged in a particular way then the circuit is the Full Wave Rectifier which rectifies both the cycles of the AC signal. Also with the help of a center-tapped transformer and with two diodes, we can have a full-wave rectifier.

Here the bridge rectifier is used for the application. The arrangement consists of 4 diodes arranged in a way that the anodes of the two adjacent diodes are connected together to give the positive supply to output and the cathodes of the other two are connected together to give the negative supply to the output. The cathode and anode of two adjacent diodes are connected together at the positive of AC supply whereas cathode and anode of another two diodes are connected at the negative of the AC supply. Hence, the four diodes are arranged in a bridge-type configuration such that in each half-cycle two alternate diodes conduct producing a DC voltage with some repels.

**Uses of Rectifier while Soldering**

Half-wave rectifiers are used in soldering iron type of circuit and are also used in mosquito repellent to drive the lead for the fumes. In electric welding, the bridge rectifier circuit is used to supply polarized and steady DC voltage.

**In AM Radio**

A half-wave rectifier is used in AM radio as a detector because the output consists of an audio signal. Due to the less intensity of the current, it is if very less use to more complex rectifiers.

**For Modulation**

For demodulating amplitude of a modulated signal, a half-wave rectifier is used. In a radio signal, for detecting the amplitude of a modulating signal, a full-wave bridge rectifier is used.

Also, a half-wave rectifier is used for the purpose of voltage multiplier.

**Other applications are as follows:**

- Because of the low cost (when compared with center-tapped), these are widely used in power supply circuits.
- It can be used to detect the amplitude of the modulated radio signals.
- To supply polarised voltage in welding, the bridge rectifiers can be used.
- A bridge rectifier with a filter is ideal for many general power supply applications like charging a battery, powering a dc device, maybe LED, motor, etc

**Full Wave Bridge Rectifier with Capacitor Filter**

As we know, the output voltage of the full-wave rectifier is not constant, it is always pulsating and thus can’t be used in real-life applications. In other words, we require a DC supply with a constant output voltage. This need can be fulfilled by using an adequate filter with an inductor or a capacitor to make the output voltage smooth and constant.

Here capacitor is connected in parallel to the load resistance in a linear power supply. The capacitor is used to increase the DC voltage and to reduce the ripple voltage components of the output obtained. This capacitor is also called a reservoir or smoothing capacitor. Generally, this is followed by a voltage regulator which eliminates the remaining ripples so that the required output can be achieved.

Till the time, the rectifier conducts and the potential is higher than the charge across the capacitor, the capacitor would store the energy from the transformer. But when the output of the rectifier falls below the charge across the capacitor, the capacitor would discharge its energy into the circuit. As the rectifier conducts current only in the forward direction, all the energy discharged by the capacitor will flow into the load. This makes the output a sawtooth wave which is a convenient linear approximation to the actual waveform as shown below:

**Advantages of Full Wave Bridge Rectifier**

- In terms of rectification, the efficiency of the full-wave rectifier is double that of a half-wave.
- Higher transformer utilization factor, higher output power and higher voltage in case of a full-wave rectifier.
- In the case of the bridge rectifier, the transformer used is simple when compared to the center-tapped one and even the transformer can be eliminated if voltage up and down is not required.
- The ripple voltage is lower and of high frequency in case of the full-wave rectifier, so even simple filtering is enough.
- For a certain power output, a smaller power transformer can be used in the case of a bridge rectifier because the current in both primary and secondary winding of the transformer flows for the entire AC cycle.

**Disadvantages of Full Wave Bridge Rectifier**

- The requirement of four diodes (two in case of a center-tapped)
- Additional voltage drops because of the two extra diodes thereby reducing the output voltage.

**Ajay Dheeraj**

**(Technical Content Developer)**