## Half Wave Rectifier, Full Wave Rectifier And Bridge rectifier

Table of Contents

**RECTIFIERS** –Half Wave Rectifier, Full Wave Rectifier And Bridge rectifier

**RECTIFIERS**

An electronic device called a rectifier uses one or more P-N junction diodes to change alternating current into direct current. Diodes function as one-way valves that only let current flow in one direction. This action is referred to as rectification.

### RECTIFIER Types

Rectifiers are classified according to the period of conduction. They are

** Half Wave Rectifier**

**Full Wave Rectifier**

**1. Half Wave Rectifier:**

The half wave rectifier is a type of rectifier that rectifies only half cycle of the waveform. This describes the half wave rectifier circuit working. The half rectifier consist a step-down transformer, a diode connected to the transformer and a load resistance connected to the cathode end of the diode.

The circuit diagram of half wave transformer is shown below:

The transformer receives the main supply voltage and uses it to raise or lower the voltage before passing it to the diode. The step down transformer is typically used to lower the supply voltage; in this instance, the output of the step down transformer will also be AC. This reduced AC voltage is applied to the diode, an electronic component that only permits forward bias current and not reverse bias current, and it is connected serially to the transformer’s secondary winding. We will obtain the pulsating DC from the diode and supply it to the load resistance RL.

**2. Working of Half Wave Rectifier:**

The input given to the rectifier will have both positive and negative cycles. The half rectifier will allow only the positive half cycles and omit the negative half cycles. So first we will see how half wave rectifier works in the positive half cycles.

**Positive Half Cycle:**

In the positive half cycles when the input AC power is given to the primary winding of the step down transformer, we will get the decreased voltage at the secondary winding which is given to the diode.

The diode will allow current flowing in clock wise direction from anode to cathode in the forward bias (diode conduction will take place in forward bias) which will generate only the positive half cycle of the AC.

The diode will eliminate the variations in the supply and give the pulsating DC voltage to the load resistance RL. We can get the pulsating DC at the Load resistance.

**Negative Half Cycle:**

The diode will enter reverse bias and the current will flow counterclockwise during the negative half cycle. And The diode won’t operate properly in the reverse bias; no current will flow from the anode to the cathode, and we won’t be able to overcome the load resistance. The diode only flows a tiny amount of reverse current, and even that current is hardly noticeable. Additionally, there is no voltage across the load resistance.

**3. Characteristics of Half Wave Rectifier:**

There are some characteristics to the half wave rectifier they are

**Efficiency: **The efficiency is defined as the ratio of input AC to the output DC.

Efficiency, Ƞ = P dc / Pac

DC power delivered to the load, Pdc = I2dc RL = ( Imax/pi ) 2 RL

AC power input to the transformer, Pac = Power dissipated in junction of diode + Power dissipated in load resistance RL

= I2rms RF + I2rms RL = {I2MAX/4}[RF + RL]

Rectification Efficiency, Ƞ = Pdc / Pac = {4/ 2}[RL/ (RF + RL)] = 0.406/{1+ RF/RL } If R**F** is neglected, the efficiency of half wave rectifier is 40.6%.

##### **Ripple factor: **It is defined as the amount of AC content in the output DC. It nothing but amount of AC noise in the output DC. Less the ripple factor, performance of the rectifier is more. The ripple factor of half wave rectifier is about 1.21 (full wave rectifier has about 0.48). It can be calculated as follows:

The sum of the rms values of the harmonic currents I1, I2, I3, and I4 and the DC current Idc represents the effective value of the load current I.

I2 =I2dc+I2 1+I22+I24 = I2 dc +I2ac

Ripple factor, is given as γ = I ac / Idc = (I2 – I2dc) / Idc = {( I rms / Idc2)-1} = Kf2 – 1)

Where Kf is the form factor of the input voltage. Form factor is given as

Kf = Irms /Iavg = (Imax/2)/ (Imax/pi) = pi/2 = 1.57

So, ripple factor, γ = (1.572 – 1) = 1.21

**Peak Inverse Voltage is the highest voltage a diode can tolerate when biassed in the reverse direction. Total voltage drops across the diode during reverse bias because the diode is not conducting. Inverse peak voltage therefore equals input voltage Vs.**

**Transformer Utilization Factor (TUF): **The TUF is defined as the proportion of delivered DC power to the load divided by the secondary transformer’s AC rating. Full wave rectifier has approximately 0.693, while half wave rectifier has approximately 0.287.

Half wave rectifier is mainly used in the low power circuits. It has very low performance when it is compared with the other rectifiers.

**FULL WAVE RECTIFIER**

Full wave rectifiers correct both the positive and negative cycles in the waveform, or the entire cycle in the waveform. The features and operation of a half wave rectifier have already been seen. This Full Wave rectifier has an advantage over the Half Wave in that it produces an average output that is higher. The output has fewer AC components than the input, on average.

The full wave rectifier can be further divided mainly into following types.

- Center Tapped Full Wave Rectifier

2. Full Wave Bridge Rectifier

**1. Centre Tap Full Wave Rectifier**

We’ve already talked about the Full Wave Bridge Rectifier, which transforms the input alternating current (AC) in both half cycles to direct current using four diodes arranged in a bridge (DC).

Only two diodes are required for a centre-tap full wave rectifier, and they are connected to the opposite ends of a secondary transformer with a centre tap as shown in the figure below. Typically, the centre tap is regarded as the ground or zero voltage reference point.

**Working of Centre Tap Full Wave Rectifier**

An ac input is applied to the transformer’s primary coils, as depicted in the figure. With this input, the secondary ends P1 and P2 alternately become positive and negative. The secondary point D1 is positive for the positive ac signal, while P2 is negative and GND has zero volts. Diode D1 will be forward biassed at this moment, while diode D2 will be reverse biassed. According to the Theory Behind P-N Junction and Characteristics of P-N Junction Diode, during the positive half cycle, diode D1 will conduct while D2 does not. As a result, the direction of the current flow will be P1-D1-C-A-B-GND. Thus, across the load resistance RLOAD, the positive half cycle is visible.

During the negative half cycle, the secondary ends P1 becomes negative and P2 becomes positive. At this instant, the diode D1 will be negative and D2 will be positive with the zero reference point being the ground, GND. Thus, the diode D2 will be forward biased and D1 will be reverse biased. The diode D2 will conduct and D1 will not conduct during the negative half cycle. The current flow will be in the direction P2-D2-C-A-B-GND.

When comparing the current flow in the positive and negative half cycles, we can conclude that the direction of the current flow is the same (through load resistance RLOAD). When compared to the Half-Wave Rectifier, both the half cycles are used to produce the corresponding output. The frequency of the rectified output voltage is twice the input frequency. The output that is rectified, consists of a dc component and a lot of ac components of minute amplitudes.

**Peak Inverse Voltage (PIV) of Centre Tap Full Wave Rectifier**

PIV is the maximum voltage that can be applied to a diode while it is being reverse biassed. From the circuit diagram, let’s examine the PIV of the center-tapped rectifier. The diode D1 conducts and offers zero resistance during the first half, or the positive half, of the input ac supply. Thus, the load resistance RLOAD receives the full voltage Vs developed in the upper half of the ac supply. The situation with diode D2 for the lower half of the transformer secondary is comparable.

Therefore, PIV of D2 = Vm + Vm = 2Vm

PIV of D1 = 2Vm

Centre-Tap Rectifier Circuit Analysis

**Peak Current** **of Centre Tap Full Wave Rectifier**

The instantaneous value of the voltage applied to the rectifier can be written as

Vs = Vsm Sinwt

Assuming that the diode has a forward resistance of RFWD ohms and a reverse resistance equal to infinity, the current flowing through the load resistance RLOAD is given as

Im = Vsm/(R**F** + R**Load**)

**Output Current** **of Centre Tap Full Wave Rectifier**

Since the current is the same through the load resistance RL in the two halves of the ac cycle, magnitude od 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 centre Tap rectifier

**DC Output Voltage** **of Centre Tap Full Wave Rectifier**

Average or dc value of voltage across the load is given as

DC Output Voltage of centre Tap Rectifier

**Root Mean Square (RMS) Value of Current** **of Centre Tap Full Wave Rectifier**

RMS or effective value of current flowing through the load resistance R**L** is given as

RMS Value of Current of centre Tap Rectifier

**Root Mean Square (RMS) Value of Output Voltage** **of Centre Tap Full Wave Rectifier**

RMS value of voltage across the load is given as

RMS Value of Output Voltage of Centre Tap Rectifier

**Rectification Efficiency** **of Centre Tap Full Wave Rectifier**

Power delivered to load,

Rectification Efficiency of Centre Tap Rectifier

**Ripple Factor** **of Centre Tap Full Wave Rectifier**

Form factor of the rectified output voltage of a full wave rectifier is given as

Ripple Factor of centre Tap Rectifier

**Regulation** **of Centre Tap Full Wave Rectifier**

The dc output voltage is given as

**2. Full wave bridge rectifier**

A full wave rectifier is a circuit configuration that utilises both input alternating current (AC) half cycles and converts them to direct current (DC). One half cycle of the input alternating current is all that a half wave rectifier uses, as we learned in our tutorial on half wave rectifiers. As a result, a full wave rectifier is significantly (double+) more efficient than a half wave rectifier. Full wave rectification is the process of converting both alternating current (AC) half cycles of the input supply to direct current (DC).

Full wave rectifier can be constructed in 2 ways. The first method makes use of a center 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**

You must first learn about half wave rectifiers in order to fully understand the theory of full wave bridge rectifiers. We have outlined a rectifier’s fundamental operation in the tutorial for half wave rectifiers. Additionally, we have discussed the pn junction theory as well as the characteristics of a pn junction diode.

**Full Wave Rectifier Working & Operation**

The working & operation of a full wave bridge rectifier is pretty simple. The circuit diagrams and wave forms 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 RL is connected to bridge through points B and D.

**During the first half cycle**

During 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 RL, and returns back flowing through arm DC. During this half of each input cycle, the diodes D2 and D4 are reverse biased and current is not allowed to flow in arms AD and BC. The flow of current is indicated by solid arrows in the figure above. We have developed another diagram below to help you understand the current flow quickly. See the diagram below – the green arrows indicate beginning of current flow from source (transformer secondary) to the load resistance. The red arrows indicate return path of current from load resistance to the source, thus completing the circuit.

**During the second half cycle**

The secondary winding of the transformer is positive with respect to the upper end during the second half cycle of the input voltage. As a result, diodes D2 and D4 become forward biassed. Current enters the load resistance RL through arm CB before flowing back through arm DA to the source. Dotted arrows in the figure depict the direction of the current. Thus, during both halves of the input supply voltage, the direction of current flow through the load resistance RL remains constant. The green arrows in the diagram below show the start of the current flow from the source (the transformer secondary) to the load resistance.

The red arrows indicate return path of current from load resistance to the source, thus completing the circuit.