# Half wave Rectifier

A rectifier is nothing but a simple diode or group of diodes which converts the Alternating Current (AC) into Direct Current (DC).
We know that a diode allows electric current in one direction and blocks electric current in another direction. We are using this principle to construct various types of rectifiers.
Rectifiers are classified into different types based on the number of diodes used in the circuit or arrangement of diodes in the circuit. The basic types of rectifiers are: half wave rectifier and full wave rectifier.
Let's take a look at the half wave rectifier....

## Half wave rectifier definition

A half wave rectifier is a type of rectifier which converts the positive half cycle (positive current) of the input signal into pulsating DC (Direct Current) output signal.
or
A half wave rectifier is a type of rectifier which allows only half cycle (either positive half cycle or negative half cycle) of the input AC signal while the another half cycle is blocked. For example, if the positive half cycle is allowed then the negative half cycle is blocked. Similarly, if the negative half cycle is allowed then the positive half cycle is blocked. However, a half wave rectifier will not allow both positive and negative half cycles at the same time.
Therefore, the half cycle (either positive or negative) of the input signal is wasted.

## What is half wave rectifier?

The half wave rectifier is the simplest form of the rectifier. We use only a single diode to construct the half wave rectifier.
The half wave rectifier is made up of an AC source, transformer (step-down), diode, and resistor (load).  The diode is placed between the transformer and resistor (load). AC source
The AC source supplies Alternating Current to the circuit. The alternating current is often represented by a sinusoidal waveform.
Transformer
Transformer is a device which reduces or increases the AC voltage. The step-down transformer reduces the AC voltage from high to low whereas the step-up transformer increases the AC voltage from low to high. In half wave rectifier, we generally use a step-down transformer because the voltage needed for the diode is very small. Applying a large AC voltage without using transformer will permanently destroy the diode. So we use step-down transformer in half wave rectifier. However, in some cases, we use a step-up transformer.
In the step-down transformer, the primary winding has more turns than the secondary winding. So the step-down transformer reduces the voltage from primary winding to secondary winding.
Diode
A diode is a two terminal device that allows electric current in one direction and blocks electric current in another direction.
Resistor
A resistor is an electronic component that restricts the current flow to a certain level.

## Half wave rectifier operation

### Positive half wave rectifier

When high AC voltage (60 Hz) is applied, the step-down transformer reduces this high voltage into low voltage. Thus, a low voltage is produced at the secondary winding of the transformer. The low voltage produced at the secondary winding of the transformer is called secondary voltage (VS). The AC voltage or AC signal applied to the transformer is nothing but an input AC signal or input AC voltage.
The low AC voltage produced by the step-down transformer is directly applied to the diode. When low AC voltage is applied to the diode (D), during the positive half cycle of the signal, the diode is forward biased and allows electric current whereas, during the negative half cycle, the diode is reverse biased and blocks electric current. In simple words, the diode allows the positive half-cycle of the input AC signal and blocks the negative half-cycle of the input AC signal.
The positive half-cycle of the input AC signal or AC voltage applied to the diode is analogous to the forward DC voltage applied to the p-n junction diode similarly the negative half-cycle of the input AC signal applied to the diode is analogous to the reverse DC voltage applied to the p-n junction diode.
We know that diode allows electric current when it is forward biased and blocks electric current when it is reverse biased. Similarly, in an AC circuit, the diode allows electric current during the positive half cycle (forward biased) and blocks electric current during the negative half cycle (reverse biased).
The positive half wave rectifier does not completely block the negative half cycles. It allows a small portion of negative half cycles or small negative current. This current is produced by the minority carriers in the diode.
The current produced by the minority carriers is very small. So it is neglected. We can’t visually see the small portion of negative half cycles at the output.
In an ideal diode, the negative half cycles or negative current is zero.
The resistor placed at the output consumes the DC current generated by the diode. Hence, the resistor is also known as an electrical load. The output DC voltage or DC current is measured across the load resistor RL.
The electrical load is nothing but an electrical component of a circuit that consumes electric current. In half wave rectifier, the resistor consumes the DC current generated by the diode. So the resistor in half wave rectifier is known as a load.
Sometimes, the load is also refers to the power consumed by the circuit.
The load resistors are used in half wave rectifiers to restrict or block the unusual excess DC current produced by the diode.
Thus, the half wave rectifier allows positive half cycles and blocks negative half cycles. The half wave rectifier which allows positive half cycles and blocks negative half cycles is called a positive half wave rectifier. The output DC current or DC signal produced by a positive half wave rectifier is a series of positive half cycles or positive sinusoidal pulses.
Now let’s take a look at the negative half wave rectifier........

### Negative half wave rectifier

The construction and working of negative half wave rectifier is almost similar to the positive half wave rectifier. The only thing we change here is the direction of a diode.
When AC voltage is applied, the step-down transformer reduces the high voltage to low voltage. This low voltage is applied to the diode.
Unlike the positive half wave rectifier, the negative half wave rectifier allows electric current during the negative half-cycle of input AC signal and blocks electric current during the positive half-cycle of the input AC signal. During the negative half cycle, the diode is forward biased and during the positive half cycle the diode is reverse biased, so the negative half wave rectifier allows electric current only during the negative half cycle.
Thus, the negative half wave rectifier allows negative half cycles and blocks positive half cycles.
The negative half wave rectifier does not completely block the positive half cycles. It allows a small portion of positive half cycles or small positive current. This current is produced by the minority carriers in the diode.
The current produced by the minority carriers is very small. So it is neglected. We can’t visually see this small positive half cycles at the output.
In an ideal diode, the positive half cycle or positive current is zero.
The DC current or DC voltage produced by the negative half wave rectifier is measured across the load resistor RL. The output DC current or DC signal produced by a negative half wave rectifier is a series of negative half cycles or negative sinusoidal pulses.
Thus, a negative half wave rectifier produces a series of negative sinusoidal pulses.
In a perfect or ideal diode, the positive half cycle or negative half cycle at the output is exactly same as the input positive half cycle or negative half cycle. However, in practice, the positive half cycle or negative half cycle at the output is slightly different from the input positive half cycle or negative half cycle. But this difference is negligible. So we can’t see the difference with our eyes.

Thus, the half wave rectifier produces a series of positive sinusoidal pulses or negative sinusoidal pulses. This series of positive pulses or negative pulses is not a pure direct current. It is a pulsating direct current.
The pulsating direct current changes its value over a short period of time. But our aim is to produce a direct current which does not change its value over a short period of time. Therefore, the pulsating direct current is not much useful.

### Half wave rectifier with capacitor filter

A filter converts the pulsating direct current into pure direct current. In half wave rectifiers, a capacitor or inductor is used as a filter to convert the pulsating DC to pure DC.
The output voltage produced by a half wave rectifier is not constant; it varies with respect to time. In practical applications, a constant DC supply voltage is needed.
In order to produce a constant DC voltage, we need to suppress the ripples of a DC voltage. This can be achieved by using either a capacitor filter or inductor filter at the output side. In the below circuit, we are using the capacitor filter. The capacitor placed at the output side smoothen the pulsating DC to pure DC. ## Characteristics of half wave rectifier

### Ripple factor

The direct current (DC) produced by a half wave rectifier is not a pure DC but a pulsating DC. In the output pulsating DC signal, we find ripples. These ripples in the output DC signal can be reduced by using filters such capacitors and inductors.
In order to measure how much ripples are there in the output DC signal we use a factor known as ripple factor. The ripple factor is denoted by γ.
The ripple factor tells us the amount of ripples present in the output DC signal.
A large ripple factor indicates a high pulsating DC signal while a low ripple factor indicates a low pulsating DC signal.
If the ripple factor is very low then it indicates that the output DC current is closer to the pure DC current. In simple words, the lower the ripple factor the smoother the output DC signal.
Ripple factor can be mathematically defined as the ratio of rms value of AC component of the output voltage to the DC component of the output voltage.
Ripples factor = rms value of AC component of the output voltage / DC component of the output voltage
Where, rms = root mean square
or

The ripple factor is also simply defined as the ratio of ripple voltage to the DC voltage

Ripple factor  = Ratio of ripple voltage / DC voltage
The ripple factor should be kept as minimum as possible to construct a good rectifier.
The ripple factor is given as Finally, we get
γ = 1.21
The unwanted ripple present in the output along with the DC voltage is 121% of the DC magnitude. This indicates that the half wave rectifier is not an efficient AC to DC converter. The high ripples in the half wave rectifier can be reduced by using filters.

### DC current

The DC current is given by, Where,
Imax = maximum DC load current

### Output DC voltage (VDC)

The output DC voltage (VDC) is the voltage appeared at the load resistor (RL). This voltage is obtained by multiplying the output DC current with load resistance RL.
It can be mathematically written as,
VDC = IDC RL
The output DC voltage is given by, Where, VSmax = Maximum secondary voltage

### Peak inverse voltage (PIV)

Peak inverse voltage is the maximum reverse bias voltage up to which a diode can withstand. If the applied voltage is greater than the peak inverse voltage, the diode will be destroyed.
During the positive half cycle, the diode is forward biased and allow electric current. This current is dropped at the resistor load (RL). However, during the negative half cycle, the diode is reverse biased and does not allows electric current, so the input AC current or AC voltage is dropped at the diode.
The maximum voltage dropped at the diode is nothing but an input voltage.
Therefore, peak inverse voltage (PIV) of diode = VSmax

### Rectifier efficiency

Rectifier efficiency is defined as the ratio of output DC power to the input AC power.
The rectifier efficiency of a half wave rectifier is 40.6%

### Root mean square (RMS) value of load current IRMS

The root mean square (RMS) value of load current in a half wave rectifier is ### Root mean square (RMS) value of output load voltage VRMS

The root mean square (RMS) value of output load voltage in a half wave rectifier is ### Form factor

Form factor is defined as the ratio of RMS value to the DC value
It can be mathematically written as
F.F = RMS value / DC value
The form factor of a half wave rectifier is
F.F = 1.57

## Advantages of half wave rectifier

• We use very few components to construct the half wave rectifier. So the cost is very low.
• Easy to construct

## Disadvantages of half wave rectifier

• Power loss
The half wave rectifier either allows the positive half cycle or negative half cycle. So the remaining half cycle is wasted. Approximately half of the applied voltage is wasted in half wave rectifier.
• Pulsating direct current
The direct current produced by the half wave rectifier is not a pure direct current; it is a pulsating direct current which is not much useful.
• Produces low output voltage.

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