In Power Supplies

Full-wave bridge rectifier

April 5, 2022

A Full-wave rectifier is a circuit arrangement that makes use of both half cycles of input alternating current (AC) and converts them to direct current (DC). In our tutorial on Half-wave rectifiers, we have seen that a half-wave rectifier makes use of only one-half cycle of the input alternating current. Thus a full-wave rectifier is much more efficient (double+) than a half-wave rectifier. This process of converting both half cycles of the input supply (alternating current) to direct current (DC) is termed full-wave rectification.

The full-wave rectifier can be constructed in 2 ways. The first method makes use of a centre tapped transformer and 2 diodes. This arrangement is known as Center Tapped Full-Wave Rectifier.

The second method uses a normal transformer with 4 diodes arranged as a bridge. This arrangement is known as a Bridge Rectifier.

Full Wave Rectifier Theory

To understand full wave bridge rectifier theory perfectly, you need to learn half wave rectifier first. In the tutorial on the half-wave rectifier, we have clearly explained the basic working of a rectifier. In addition, we have also explained the theory behind a p-n junction and the characteristics of a p-n junction diode.

Full Wave Rectifier – Working & Operation

The working & operation of a full-wave bridge rectifier is pretty simple. The circuit diagrams and waveforms we have given below will help you understand the operation of a bridge rectifier perfectly. In the circuit diagram, 4 diodes are arranged in the form of a bridge. The transformer secondary is connected to two diametrically opposite points of the bridge at points A & C. The load resistance R_L is connected to the bridge through points B and D.

Full-Wave Bridge Rectifier – Circuit Diagram with Input and Output Wave Forms

During the first half cycle

During the first half cycle of the input voltage, the upper end of the transformer secondary winding is positive with respect to the lower end. Thus during the first half cycle, diodes D1 and D₃ are forward biased and current flows through arm AB enters the load resistance R_L, and returns back flowing through arm DC. During this half of each input cycle, the diodes D₂ and D₄are reverse biased and current is not allowed to flow in arms AD and BC. The flow of current is indicated by solid arrows in figure 1.2 above. We have developed another diagram below to help you understand the current flow quickly. See the diagram below – the green arrows indicate the beginning of current flow from the source (transformer secondary) to the load resistance. The red arrows indicate the return path of current from load resistance to the source, thus completing the circuit.

Current path in Bridge Rectifier — The flow of current in the Bridge Rectifier

During the second half cycle

During the second half cycle of the input voltage, the lower end of the transformer secondary winding is positive with respect to the upper end. Thus diodes D₂ and D₄ become forward biased and current flows through arm CB, enters the load resistance R_L, and returns back to the source flowing through arm DA. The flow of current has been shown by dotted arrows in figure 1.3. Thus the direction of flow of current through the load resistance R_L remains the same during both half cycles of the input supply voltage. See the diagram below – the green arrows indicate the beginning of current flow from the source (transformer secondary) to the load resistance. The red arrows indicate the return path of current from load resistance to the source, thus completing the circuit.

Flow of current in Full wave rectifier — Path of current in 2nd Half Cycle

Peak Inverse Voltage of a Full wave bridge rectifier:

Let’s analyse the peak inverse voltage (PIV) of a full-wave bridge rectifier using the circuit diagram. At any instant when the transformer secondary voltage attains positive peak value Vmax, diodes D1 and D3 will be forward biased (conducting) and the diodes D2 and D4 will be reverse biased (non conducting). If we consider ideal diodes in the bridge, the forward biased diodes D1 and D3 will have zero resistance. This means voltage drop across the conducting diodes will be zero. This will result in the entire transformer secondary voltage being developed across the load resistance RL.

Thus PIV of a bridge rectifier = Vmax (max of secondary voltage)

Bridge Rectifier Circuit Analysis

The only difference in the analysis between full wave and centre tap rectifier is that

In a bridge rectifier circuit, two diodes conduct during each half cycle and the forward resistance becomes double (2R_F).
In a bridge rectifier circuit, Vsmax is the maximum voltage across the transformer secondary winding whereas in a centre tap rectifier Vsmax represents that maximum voltage across each half of the secondary winding.

The different parameters are explained with equations below:

Peak Current

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

vs = Vsmax Sin wt

If the diode is assumed to have a forward resistance of R_F ohms and a reverse resistance equal to infinity, the current flowing through the load resistance is given as

i1 = Imax Sin wt and i2 = 0 for the first half cycle

and i1 = 0 and i2 = Imax Sin wt for second half cycle

The total current flowing through the load resistance R_L, being the sum of currents i1 and i2 is given as

i = i1 + i2 = Imax Sin wt for the whole cycle.

Where the peak value of the current flowing through the load resistance R_L is given as

Imax = Vsmax/(2R_F + R_L)

2. Output Current

Since the current is the same through the load resistance RL in the two halves of the ac cycle, the magnitude of dc current Idc, which is equal to the average value of ac current, can be obtained by integrating the current i1 between 0 and pi or current i2 between pi and 2pi.

Output Current of Full Wave Rectifier

3. DC Output Voltage

The average or dc value of voltage across the load is given as

DC Output Voltage of Full Wave Rectifier

4. Root Mean Square (RMS) Value of Current

RMS or effective value of current flowing through the load resistance R_L is given as

RMS Value of Current of Full Wave Rectifier

5. Root Mean Square (RMS) Value of Output Voltage

RMS value of voltage across the load is given as

RMS Value of Output Voltage of Full Wave Rectifier

6. Rectification Efficiency

Power delivered to load,

Rectification Efficiency of Full Wave Rectifier

7. Ripple Factor

The form factor of the rectified output voltage of a full-wave rectifier is given as

Ripple Factor of Full Wave Rectifier

So, ripple factor, γ = 1.11² – 1) = 0.482

8. Regulation

The dc output voltage is given as

Merits and Demerits of Full-wave Rectifier Over Half-Wave Rectifier

Merits – let us talk about the advantages of a full-wave bridge rectifier over a half-wave version first. I can think about 3 specific merits at this point.

Efficiency is double for a full-wave bridge rectifier. The reason is that a half-wave rectifier makes use of only one half of the input signal. A bridge rectifier makes use of both halves and hence double efficiency
The residual ac ripples (before filtering) are very low in the output of a bridge rectifier. The same ripple percentage is very high in a half-wave rectifier. A simple filter is enough to get a constant dc voltage from the bridge rectifier.
We know the efficiency of the full-wave rectifier is double than the half-wave rectifier. This means higher output voltage, Higher transformer utilization factor (TUF) and higher output power.

Demerits – Full-wave rectifier needs more circuit elements and is costlier.

Merits and Demerits of Bridge Rectifier Over Center-Tap Rectifier.

A centre tap rectifier is always a difficult one to implement because of the special transformer involved. A centre tapped transformer is costly as well. One key difference between centre tap & bridge rectifier is in the number of diodes involved in construction. A centre tap full wave rectifier needs only 2 diodes whereas a bridge rectifier needs 4 diodes. But silicon diodes being cheaper than a centre tap transformer, a bridge rectifier is a much-preferred solution in a DC power supply. Following are the advantages of a bridge rectifier over a centre tap rectifier.

A bridge rectifier can be constructed with or without a transformer. If a transformer is involved, any ordinary step-down/step-up transformer will do the job. This luxury is not available in a centre tap rectifier. Here the design of the rectifier is dependent on the centre tap transformer, which can not be replaced.
The bridge rectifier is suited for high voltage applications. The reason is the high peak inverse voltage (PIV) of the bridge rectifier when compared to the PIV of a centre tap rectifier.
The transformer utilization factor (TUF) is higher for the bridge rectifiers.

Demerits of Bridge rectifier over centre tap rectifier

The significant disadvantage of a bridge rectifier over a centre tap is the involvement of 4 diodes in the construction of the bridge rectifier. In a bridge rectifier, 2 diodes conduct simultaneously on a half cycle of input. A centre tap rectifier has only 1 diode conducting on a one-half cycle. This increases the net voltage drop across diodes in a bridge rectifier (it is double the value of the centre tap).

Applications of Full-wave Bridge rectifier

Full-wave rectifier finds uses in the construction of constant dc voltage power supplies, especially in general power supplies. A bridge rectifier with an efficient filter is ideal for any type of general power supply applications like charging a battery, powering a dc device (like a motor, led etc) etc. However, for an audio application, a general power supply may not be enough. This is because of the residual ripple factor in a bridge rectifier. There are limitations to filtering ripples. For audio applications, specially built power supplies (using IC regulators) may be ideal.