 # Half Wave Rectifier & Applications

A rectifier can be a simple diode or a group of diodes that converts the AC (Alternating Current) to DC (Direct Current). As the diode allows electric current only in one direction and blocks in another direction, therefore, this principle is used to construct the various types of rectifiers. Broadly, rectifiers are classified as Half Wave Rectifiers & Full Wave Rectifiers.

### Half Wave Rectifier

An HWR (Half Wave Rectifier) circuit is the one that allows only one cycle of input of the AC signal and blocks the other. In general, we can say that it converts the positive half cycle of the sinusoidal wave of the input to pulsating DC output signal, though the conversion of the positive or negative cycle depends on the way the diode is connected.

### Construction of Half Wave Rectifier

In HWR, we use only one diode which is more than sufficient to do the desired work. As we want the DC at the output for the AC sinusoidal signal given at the input, so the single diode placed in series does the work for us. This is not all but when we talk about the whole construction of  Half Wave Rectifier circuit, it consists of  mainly three components (without filter):

1. A Transformer (step down)
3. A Diode

### Theory of Half Wave Rectifier

Now, we’ll see how the HWR circuit converts the AC voltage to DC voltage. First, high voltage AC voltage is applied at the primary side of the step-down transformer and correspondingly a low voltage is obtained at the secondary which is given to the diode.
The diode will be in Forward Biased mode during the positive half cycle of the AC voltage, thus the current flows through it. During the next half-cycle, i,e., negative cycle, the diode becomes reverse biased and blocks the current through it. Thus, when seen at the final output we can see that input has been traced as output for the positive half cycle only as shown in the figure below. Let us try to understand this concept in a more convenient way by taking a sinusoidal voltage instead of the step down transformer. For the positive half cycle, the circuit looks like: This is because during the positive half cycle, the diode is in forward bias and allows the current to pass through it (diode acts as a short circuit) and we get the same voltage as at input.

For the negative half cycle, the circuit becomes open circuit as the diode becomes reverse biased and bocks the current, thus the output voltage is zero as shown below: The input-output waveform of the above-mentioned situation is shown by the waveform below. This happens very fast depending on the frequency of the incoming voltage (for 50 hertz, 20ms of time). The above graph shows the positive half-wave rectifier which allows only the positive cycle and blocks the negative one.
Similarly, if the polarity of the diode is reversed then the same rectifier becomes the negative half-wave rectifier which allows only the negative cycle and blocks the positive one.

### Half Wave Rectifier with Capacitor Filter

The output waveform obtained from the half-wave rectifier circuit without filter explained above is a pulsating DC waveform.

Now, as we know that all the circuits that we use practically need a constant DC and not the pulsating one thus we use filters to get the desired form of DC signal. Filters do so by suppressing the DC ripples in the waveform.

Hence to get smoother DC output waveform we can either use a capacitor or an inductor, but HWR (Half Wave Rectifier) along with capacitive filter is most commonly used. The below diagram shows how  the capacitor filter smoothens the waveform. Capacitor is connected in parallel with the resistive load. HWR with capacitor filter

Let us now see a few formulas of Half Wave Rectifier based on the above explanations and waveforms.

### Ripple Factor of Half Wave Rectifier

When converting the AC voltage waveform to DC, the remaining unwanted AC component is called ripple. Even after all the filtration, we are still left out with some AC component which pulsates the DC waveform. This unwanted AC component is called ripple.

Ripple Factor (represented by ‘ɣ’) is used to quantify the quality of the conversion from AC voltage to DC voltage. The Ripple Factor is given by the ratio of the RMS value of the AC voltage (at input) to the DC voltage at output of the rectifier.

The formula for the ripple factor goes like:

ɣ = √[(Vrms/VDC)2 – 1]

Alternatively,  ɣ = (I2RMS – I2DC )/IDC    = 1.21(for sinusoidal waveform)

Actually, for a good rectifier the ripple factor should be as less as possible that is why capacitor or inductor filter(s) are used to die out the ripples in the circuit.

### Efficiency of Half Wave Rectifier

Rectifier efficiency (ɳ) is the ratio of output DC power to the input AC power, the formula goes like:

ɳ = (Pdc/Pac)

The efficiency of HWR is 40.6% (ɳmax = 40.6%)

### RMS value of Half Wave Rectifier

To find the rms value of the half-wave rectifier, we need to calculate the current across the load. If the instantaneous load current, iL = Imsinwt, then the average of load current (Idc) equals to:

Idc = (1/2 π) ∫0π  Imsinwt = (Im / π)

Here Im represents the peak instantaneous current across the load (Imax). This the DC current obtained across the load (output) is

IDC = Imax/ π        ; where Imax =maximum amplitude of dc current

For a half-wave rectifier, the RMS load current, Irms is equal to the average current, Idc multiplied with π/2. Thus,  Irms = Im/4

Where Imax = Im which is equal to the peak instantaneous current across the load.

### Peak Inverse Voltage of Half Wave Rectifier

It is the maximum voltage that the diode can withstand during the reverse bias condition. If a voltage is applied more than the PIV then the diode will be destroyed.

### Form Factor of Half Wave Rectifier

Form factor is the ratio of rms value to the average value.

F.F = RMS value/ Average value

The form factor of HWR is 1.57, i.e., FF = 1.57

### Output DC Voltage

The output voltage (VDC) across the load resistor is denoted by

VDC = Vsmax/ π  , where Vsmax is the maximum amplitude of secondary voltage

### Advantages of Half Wave Rectifier

• Simple circuit with less number of components
• Economical at initial state. Although there is a higher cost over time due to more power losses

### Disadvantages of Half Wave Rectifier

• Converts only one cycle of the sinusoidal input given to it and the other cycle gets wasted. Thus, giving more power loss.
• HWR produces lower output voltage.
• The output current thus obtained is not purely DC and it still contains a lot of ripple (i.e. it has a high ripple factor)

### Applications of Half Wave Rectifier

In day-to-day life, the half-wave rectifier is mostly used in low power applications because of its major disadvantage being the output amplitude which is less than the input amplitude. Thus power is wasted and output is pulsated DC resulting in excessive ripple.

Some of the uses and applications of rectifiers are in :

• Appliances
• Used with transformers
• Soldering
• Pulse generated circuits
• Single demodulation
• Voltage multiplier

#### Use of Rectifier for powering appliances

As we know that all electrical appliances use DC power supply to function thus using a rectifier in the power supply helps in converting AC to DC power supply. Bridge rectifiers are used widely for large appliances, where these are capable of converting high AC voltage to lower DC voltage.

Used with Transformer

With the help of half wave rectifier we can achieve the desired DC voltage with the use of step up or step down transformers. Even Full Wave Rectifiers are used for powering up motors an LEDs that works on DC voltage.

#### Uses of Rectifier While Soldering

Half Wave Rectifiers are used in soldering iron types of circuit and is also used in mosquito repellent to drive the lead for fumes. In electric welding, rectifiers with bridge configurations are used to supply steady and polarized DC voltage.

Half wave diode rectifiers are used in AM radio as a detector because the output contains an audio signal. Due to the less intensity of the current, it is of very little use to the more complex rectifier.

#### Uses of Rectifier in Circuits

Pulse generating circuits and firing circuits use half-wave rectifiers.

#### Used for Modulation

In a modulating signal, for demodulating the amplitude, a half-wave rectifier is used. To detect the amplitude of modulating the signal, in a radio signal, a full-wave bridge rectifier is used.

#### Used in Voltage Multiplier

For the purpose of voltage multiplier circuit, a half-wave rectifier circuit is used.

### 3 Phase Half Wave Rectifier

Although, the principle and theory of 3 phase HWR are the same as single-phase HWR but the characteristics are different. The waveform, ripple factor, efficiency, and output RMS values are not the same.

The three-phase half-wave (diode) rectifier is used for the conversion of 3 phase AC power to the DC power. Since the diodes are used as switches here hence are uncontrolled switches, implying that there is no way controlling the ON OFF times of these switches.

Generally, the 3-phase half-wave diode rectifier is constructed with a three-phase supply connected to a three-phase transformer where the secondary winding of the transformer is always connected as a star connection. This is done because of the reason that the neutral point is required to connect the load back to the transformer secondary windings, providing a return path for the flow of power.

A typical 3 phase transformer supplying a purely resistive load is shown below. Here, each phase of the transformer is used as an individual alternating source. The measurement and simulation of voltages are as shown in the fig below. Also, we have connected individual voltmeters across each source as well as across the load.  So from the above waveform that the diode D1 conducts when the R phase has the voltage value that is higher than the value of the voltage of the other two phases and the stated condition starts when the R phase is at 300 repeats itself after every complete cycle. So, D1 conducts next at 3900. Similarly, diode D2 starts conducting at 1500 as voltage in B phase becomes maximum (when compared with other two phases) at that instant. Therefore, each diode conducts for 1500 – 300 = 1200.

The average of the output voltage across the resistive load is given by

Vo = (3/2π) Vm line

Where Vm line = √6 Vphase

The RMS value of the output voltage can be given by

Vo rms = 0.84068 Vm phase

And the voltage ripple factor equals

Vr/Vo = 0.151/0.827 = 0.186 = 18.26%

Thus voltage ripple is significant and thus undesirable as it leads to power loss.

Efficiency, ɳ = (Po/Pi) = 0.968 = 96.8%

Even after better efficiency also, a three-phase half-wave diode rectifier is not commonly used as the power loss here is more significant.

Ajay Dheeraj

Technical Content Developer

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