Electronics

# Half Wave Rectifier (HWR) : Circuit Diagram, Formula & Working Principle

A Half wave rectifier is a simplest type of rectifier or first stage of rectifier that required only one PN junction diode for construction. While full wave rectifier use more than one PN junction diode. The use of rectifier is to convert alternating current (AC) to pulsating direct current (DC). Here we will full study of rectifier.

## What is a Half Wave Rectifier?

Half wave rectifier is rectifier circuit that allows the Alternating current (AC) voltage signal, in Alternating current (AC) voltage signal half wave rectifier allow the positive cycle of signal and block the negative cycle of the signal. The rectifier is constructing by a single P-N junction diode.

OR

The half wave rectifier is allowing the Alternating current (AC) voltage and converts the Alternating current (AC) voltage signal to pulsating Direct current (DC) signal. The pulsating direct current is that in which it has some part of alternating signal and some part of direct current. Half wave rectifier is a simplest type of rectifier or first stage of rectifier that required only one PN junction diode for construction. While full wave rectifier use more than one PN junction diode. Here we will full study of rectifier.

### Half wave rectifier circuit

Half wave rectifier circuit has consists following components:

• Resistor at the load section
• Alternating current source
• P-N junction diode
• Step-down transformer

#### Resistor at the load section

This is the component that is block the electric current flow only to a specified level.

#### Alternating current sources

This alternating current source is for the hole circuit supply and it is represented as a sine signal.

#### PN junction diode

It is the simple P-N junction semiconductor silicon diode. The silicon made semiconductor diode breakdown voltage is 0.3V.

#### Step-down transformer

When we need to increase or decrease the alternating voltage is done by transformer. When low alternating voltage is required we often use the step down transformer. It decrease the alternating voltage, the region behind the use of step down transformer is that, the simple PN junction diode is not capable to bear the high voltage, it damage the PN junction diode. In a few case, a step-up transformer can also be used.

Step down transformer, the secondary winding has minimum turns than that of the primary winding. Because the work of step-down transformer is decreases the voltage level from primary to the secondary winding.

### Working of Half Wave Rectifier

When the positive cycle of the alternating voltage is applies during the positive cycle the diode is forward bias condition and the diode is conduct. The voltage produce across the load resistance (RL) is the same of alternating voltage positive cycle signal of the input.

When the negative half cycle of the alternating current occurs the diode input terminal. The diode is not conduct it means circuit is open. There is no voltage induce across the load resistance.

Output DC voltage of a half-wave rectifier is
Vrms = Vpeak / 2
Vdc = Vpeak / ᴨ
Where
VdcVav, DC or average output voltage,
Vpeak, Peak value of the phase input voltages,
Vrms, Root mean square (RMS) output voltage.

### Characteristics of Half wave Rectifier

#### Peak Inverse Voltage (PIV)

Peak inverse voltage are those voltage in which when the diode are in reverse biased condition, the diode is withstand because of maximum reverse voltage before breakdown. Peak inverse voltage also known peak reverse voltage.

PIV = VMAX

#### Average and Peak Currents in the Diode

The voltage across of the secondary transformer is sinusoidal and its maximum value of sinusoidal is VMAX. The instantaneous voltage of the half wave rectifier is

V = VMAX Sin θ

IMAX = VMAX / (RF+RL)

#### Regulation

It is the difference of no load and full load voltage and the percentage is finding by the  given formula in below

### Efficiency of half wave rectifier

The efficiency of rectifier is the ratio of DC power output to the applied input AC power is known as rectifier efficiency.
i.e. efficiency, η = DC power output/ AC power input
let the alternating voltage sine wave is V= VMAX sin θ is appear the secondary side of the transformer. The diode is conduct when the +ve cycle are arrive and it is off when the –ve cycle is arrive.

This shows that in half wave rectification, a maximum 40.6% of the alternation current power is converted in to direct current power

## Half Wave Rectifier Formula

### Ripple Factor of Half wave rectifier

In any rectification process the ripple factor Ripple content is defined as the amount of AC content present in the output DC. If ripple factor is low, the rectifier performance will be good. The ripple factor is 1.21. The alternating current component of the output of rectifier is filtered by the using filter devices like inductors and capacitors. Ripple factor is represented as γ.
Mathematical equation of ripple factor is
Ripple factor = rms value of AC/ rms value of DC

### Calculation of ripple factor

I2 = I2dc + I21 + I22+ I2= I2dc+ I2ac
γ = Iac / Idc
= (I2 – I2dc) / Idc
= {(Irms /I2dc)-1}
= kf2-1
Kf is the form factor
Kf  = Irms/ Iavg = (Imax /2)/ (Imax /ᴨ) =ᴨ/2 = 1.57
Ripple factor (γ)= (1.572 – 1)
= 1.21

### Efficiency of Half wave rectifier

It is the ratio of output DC power to the input AC power. Efficiency is denoted by “η”.
The efficiency formula is given below

### RMS value of Half Wave Rectifier

The RMS value of the load current for a half wave is given by the formula:

### Form factor of a Half wave Rectifier

Form factor is the ratio of RMS value to the average value and is given by the formula:

### Transformer Utilization Factor (TUF)

Transformer utilization factor is the ratio of Alternating Current power delivered to the load and transformer secondary AC rating. The transformer utilization factor is 0.287.

## Advantage of half wave rectifier

• The cost is low
• The circuit design is simple
• It is easy to use
• It has less no of component use

## Disadvantage of half wave rectifier

• The output current of rectifier is pulsating current whose frequency component is equal to the supply frequency.
• Alternating supply deliver power only half the time, due to this region the output is low.
• Transformer utilization factor is minimum.
• It has high power losses

## Applications

The application of rectifier is used in power supply in almost of the electronics device. Here some application are given below:

• It is used in firing and pulse generation circuits
• In voltage amplifier and modulation devices.
• In AM radio device for the detection purposes

## Limitation of half wave rectifier

There are the some limitation of rectifier. If the load resistance values are low for a given capacitor, when the high current follow through the load capacitor is discharge quickly and ripple are increases.

The value of RC constant is much greater than the period capacitor remains almost fully charged, get perfect direct current output voltage. For grater RC time constant we use the large value of capacitor. This is not possible because limitation on both the cost and capacitor size. It has also limitation when the negative half cycle are arrive there is no output voltage.

Due to these type of limitation it rarely used most of the time full wave rectifier is used.

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