Rectifier
The rectifier is a device that converts alternating current (AC) to direct current (DC). Dc only flows in one direction whereas ac regularly flows in the reverse direction. The Rectifier works on the principle of PN junction diode biasing condition. The diode offers low resistance to current flow in one direction i.e. in forward biased condition and it offers high resistance in other direction i.e. in reverse biased condition. The process of conversion of ac signal to dc is called rectification.
Depending on the arrangements of diode and rectification of ac signal to dc weather only the one-half cycle of ac or both half cycles of ac, rectifiers are divided into two types. They are:
- Half Wave Rectifier
- Full Wave Rectifier
Here we are going to discuss in detail about Half Wave Rectifier.
Half Wave Rectifier
A rectifier that converts the ac signal to the dc signal by passing either a positive or negative half cycle of the ac waveform and blocking the other half cycle is called a half wave rectifier. During construction, a half-wave rectifier circuit uses only one diode for the rectification process. A half-wave rectifier is a simple type of rectifier.
The working of half wave rectifier is based on the fact that the diode allows the current flow only in one direction. Thus it converts the ac signal into a dc signal. When ac voltage is applied across the diode, the diode conducts only on the forward biasing condition. i. e. when the anode side of the diode is positive with respect to the cathode side.
Since a half-wave rectifier passes only half of the input, its efficiency of it is lower than the efficiency of a full-wave rectifier. The maximum efficiency of half wave rectifier is about 40.5 % and that of a full-wave rectifier is twice of half wave rectifier. Half wave rectifier produces more amount of ripple than a full-wave rectifier. Eliminating the ripple content requires much more filtering. So it is rarely used in practice.
Components of Half Wave Rectifier
A half-wave rectifier consists of mainly three components. They are:
- Diode
- Transformer
- Resistive Load
Circuit Diagram
The circuit diagram for the half wave rectifier is shown in the figure below:
In this circuit, a high voltage ac input is applied to the primary side of the transformer. Here, the transformer used is a step-down transformer so that the low output voltage is obtained at the secondary winding. The output from Transformer is applied to the diode. Load resistance is connected in series with the diode as shown in the figure above.
In the rectifier circuit, we will focus on the secondary side of the circuit. If we replace the secondary winding of the transformer with a voltage source, the circuit diagram of the half-wave rectifier is simplified as the diagram below.
Operations
During the positive half cycle of ac voltage, the diode comes in forward biased condition as the anode is positive with respect to the cathode and it conducts current to a resistive load. Due to this current flow, A voltage is developed across the load which is the same as the applied ac input voltage of the positive half cycle.
The circuit becomes closed during the positive half cycle. The circuit diagram during a positive half cycle is shown below.
During the negative half cycle of ac, the diode comes in reverse biased condition as the anode is negative with respect to the cathode and there is no current flow through the diode. No voltage appears across the resistive load in the negative half cycle.
The circuit becomes opened during the negative half cycle. The circuit diagram during a negative half cycle is shown below.
In this regard, it is seen that the diode conducts during positive half cycles and does not conduct during negative half cycles. So, the half-wave rectifier clips off negative half cycles. The obtained waveform is called a half wave signal.
The waveform of input and output signal of Half Wave Rectifier is shown in the figure below:
Here, the input-output waveform shows that the half-wave rectifier only allows the positive half cycles through the diode and blocks the negative half cycles. The voltage waveform of the half wave rectifier before and after rectification is shown in the figure below.
Ripple Factor
The direct current (dc) produced by a half-wave rectifier is not a pure dc but a pulsating dc. There are some ac components remaining when converting the ac signal to dc signal. This unwanted ac component contained in the output side of the rectifier is called ripple. The ripples in the output dc signal can be minimized by using filters such as capacitors and inductors.
The ripple factor gives the number of ripples present in the output dc signal. It is used to measure how well the half wave rectifier can convert ac voltage into a dc voltage. Mathematically, the ripple factor is the ratio of the RMS value of the ac component of output voltage to the dc component of output voltage. Or it is the ratio of ripple voltage to the dc voltage.
For the construction of a good rectifier, the ripple factor should be kept as minimum as possible. Thus, capacitors and inductors are used as filters to reduce the ripples in the circuit.
The ripple factor is denoted by γ and is given by the formula:
By rearranging, we get:
For half-wave rectifiers, the ripple factor comes out to 1.21.
RMS Value
For the derivation of the RMS value of the half wave rectifier, we have to calculate the current across the load.
For instantaneous load current iL = Im*sinωt, the average load current IDC is given by,
Here, Im is equal to maximum instantaneous load current (Imax). Therefore, the output dc current across the load (Idc) is given by:
Where Imax is the maximum amplitude of dc current.
For Half Wave Rectifier, the RMS value of Imax is equal to the average current I_dc multiple of π/2.
Thus, the RMS value of load current Imax for half wave rectifier comes out.
Where Im= Imax is the peak instantaneous current across the load.
Then, The RMS value of output load voltage is given by:
Output DC Voltage (Vdc)
The Output DC Voltage (Vdc) is the voltage that appeared across the load RL. This is obtained by the multiplication of output dc current and load resistance RL.
Mathematically it can be written as:
The Output DC Voltage (Vdc) is given by:
Where, (Vin)max = maximum amplitude of secondary voltage
Efficiency
The efficiency of the rectifier is the ratio of output dc power to the input ac power. IT is denoted by ղ and mathematically written as
For Half Wave Rectifier, The efficiency is equal to 40.6%.
Peak Inverse Voltage (PIV)
Peak inverse voltage (PIV) is the maximum reverse bias voltage that the diode can withstand. The diode will be destroyed if an applied voltage is greater than the peak inverse voltage (PIV).
During the positive half cycle, the diode is forward-biased and allows an electric current to flow. This current is dropped at the resistive load R_L. Whereas, during the negative half cycle, the diode is reverse biased and does not allow electric current. So that the input ac current is dropped at the diode. The maximum voltage dropped at the diode is equal to the maximum input voltage.
Hence, PIV of diode =(Vin)max
Form Factor (FF)
The form factor is defined as the ratio of the RMS value to the DC value or average value. Mathematically, it is given as:
For half Wave rectifier, The form factor is equal to 1.57.
Applications
The Half Wave rectifier is mainly used for the following applications:
- They are used for rectification applications
- They are used for Signal demodulation purpose
- They are used for Signal peak applications
Advantages
The main advantages of the Half Wave Rectifier are as follows:
- Simple: The circuit design of it is simple and completely straightforward.
- Cheap: As it requires and used a minimal number of components, it is cheaper.
- Easy to use: As the construction is easy, the device is easy to use.
Advantages
The disadvantages of Half Wave Rectifier are as follows:
- Power Loss: As they only allow the half cycle of ac signal, and another half cycle is wasted, this leads to power loss.
- Low output Voltage: They produce a low output voltage
- Higher ripple factor: The output dc voltage obtained by the half wave rectifier is not pure dc, and still contains the components of ac called ripple.
- The transformer utilization factor is low.
