Half Wave Rectifier

A Half-wave rectifier is an electronic device that is used to convert Alternating current (AC) to Direct current (DC). A half-wave rectifier allows either a positive or negative half-cycle of AC to pass and blocks the other half-cycle. Half-wave rectifier selectively allows only one half-cycle of the AC input voltage to pass through, producing a pulsating DC output voltage across the load resistor. While it’s a simple and cost-effective way to convert AC to DC.

In this article, we will go through Half wave Rectifier, First, we will begin with the basics of the rectifier, Then we will go through the definition of the half wave rectifier, then we will go through a diagram of half wave rectifier, and working principle of half wave rectifier, Also we will go through capacitor filter in half wave rectifier and three phase half wave controlled rectifier. At last, we will conclude our Article with Advantages and Disadvantages, Application and Some FAQs on Half Wave Rectifier.

What is a Rectifier?

A rectifier is an electronic device that converts Alternating current (AC) to Direct current (DC). The process of converting AC to DC is called rectification. A p-n junction diode is a primary component that is used as a rectifier. Rectifiers can be broadly classified into two: Half-wave rectifiers and Full-wave rectifiers. Both half-wave rectifiers and full-wave rectifiers consist of p-n junction diodes. Rectifiers are used widely in electrical and electronic circuits. For example, you can find a rectifier inside the LED bulbs we use in our households. An LED only works in DC, that’s why a rectifier is used in LED bulbs whose source is AC. It can also be found in our mobile phone chargers and many other devices.

Rectifier Components

Before we Begin on the working of Rectifier, let us look at the Components of the Rectifier

• P-N junction diode: A p-n junction diode is a device that only allows current flow in one direction. It allows current flow when the P side of the diode has a higher potential than the N side and such a condition is called forward biased. It prevents the flow of current when the N side has a higher potential than the P side and it is known as the reverse biased condition.
• Alternating Current (AC): It is an electric current that changes its direction periodically
• DC Current (DC): It is a type of electric current that does not change its direction periodically.
• Waveform: Waveform is a graphical representation of the magnitude and direction of electric current or voltage.
• V_rms and I_rms: V_rms and I_rms are the root mean square values of voltage and current of AC respectively. It is 1/√2 times the peak voltage or current.
• Capacitor: A capacitor is a two-terminal device that stores energy in the form of electric field. It can charge and discharge in a circuit which helps to reduce fluctuations in the circuit.
• Function Generator: It is a device used to produce electrical waveforms of different mathematical functions. Here it is used to generate AC with the required voltage and frequency.

Types of Rectifiers

Rectifiers are classified broadly into two: Half-wave rectifiers and Full-wave rectifiers.

• Half Wave rectifier: A half-wave rectifier allows one AC half-cycle to pass through it and blocks the other AC half-cycle. Therefore it is called a half-wave rectifier. It is less efficient than a full wave rectifier as one half cycle is wasted. It has a very simple circuit compared to a full-wave rectifier.
• Full wave rectifier: A Full wave rectifier can convert both AC half cycle to DC. It allows a one-half cycle of AC without any modification. And other half cycle is also allowed to pass but it reverses the direction of that half cycle. Thus it can convert AC to DC. It uses the complete half cycle of AC and has no wastage, therefore it is more efficient than Half half-wave rectifier. But it has a complex circuit consisting of more number of diodes.

Half Wave Rectifier

A Half-wave rectifier is a device that converts Alternating Current (AC) to Direct Current (DC). In a Half-wave rectifier, only one half-cycle of AC is converted to DC and the other half-cycle is blocked. Therefore, the output waveform produced by a half-wave rectifier consists of ripples of positive half-cycle of the input waveform and it is called pulsating DC. In a half-wave rectifier, a p-n junction diode is used as a rectifier. It has a relatively simple circuit consisting of a p-n junction diode connected in series to a load.

Half Wave Rectifier Circuit

Given below is the Circuit diagram of the Half Wave Rectifier. The components of the Half Wave Rectifier are P-N Junction diode, Ac supply and the load.

Half wave rectifier circuit diagram

Construction of Half Wave Rectifier

To Construct a half-wave rectifier, the Components are Assembled as the Following

• Function generator serves as input AC source for us. The positive end of the function generator (red colored end) is connected to the positive side of the diode(black side of diode without line).
• Next, The negative terminal of the diode (marked by a grey line or indicator) is connected to the one end of the resistor.
• Now, The other end of the resistor is connected to the remaining terminal of the function generator. This completes the circuit loop and allows the AC signal from the function generator to flow through the diode and resistor.

Working of Half Wave Rectifier

In a half-wave rectifier, the AC supply is connected in series to a p-n junction diode and load resistor. An Alternating current (AC) consists of two half-cycles: Positive half-cycle and Negative half-cycle. Let us take a look at the working of the half-wave circuit at each half-cycle separately.

• In a positive half-cycle, the Diode is forward-biased and hence acts like a short circuit. Therefore in a positive half-cycle, current flows through the circuit and produces whole AC input as such in DC output. In the real world, the output voltage is less than the input voltage considering the Diode voltage drop.

Equivalent circuit in positive half-cycle

• In a negative half-cycle, the Diode is reverse-biased and hence acts like an open circuit. Therefore, in a negative half-cycle current does not flow through the circuit. And output does not consist of input negative half-cycle.

Equivalent circuit in negative half-cycle

This step is repeated in each half-cycle and AC is converted into DC. The waveform of input AC and corresponding rectified DC are shown in the figures below.

Half Wave Rectifier Waveforms

Given below is the Input and output waveform of the half wave rectifier

AC Input Waveform

The below figure shows AC input with a maximum voltage of V_max. This is the Ac Waveform given as the input for the half wave rectifier which is converted to the Dc.

AC input waveform

DC Output Waveform

The below figure shows the output waveform of the DC output waveform of a half-wave rectifier. From the input first a positive half cycle comes and in the positive half cycle diode lets pass the input voltage through it. You can see the positive half cycle in the output waveform as such from the input waveform. Then a negative half-cycle comes, but it does not allow to pass the negative half-cycle and we can see that the negative half-cycle is not present in the output waveform. At that time output voltage is zero. Then again a positive half cycle comes which is passed through the diode and it is visible in the output waveform. After that a negative half cycle comes and it is blocked by the diode and is not present in the output. This process continues to convert AC to DC.

Rectified DC output waveform

Half Wave Rectifier with Filter

we can see that the output of a half-wave rectifier is pulsating DC and pulsating DC cannot be used for many real-world applications. So, To avoid or reduce the ripples in pulsating DC filters are used. Generally, capacitors and inductors are used as filters in half-wave rectifier circuits. These capacitors or inductors reduce ripples in output DC and help in many real-world applications. Although we can reduce ripples in the output of the half-wave rectifier, it is not possible to completely remove ripples in output DC.

Half Wave Rectifier Capacitor Filter

Here’s the circuit diagram of a half-wave rectifier with a capacitor filter.

Half Wave Rectifier with Filter

Working of Half Wave Rectifier with Filter

In a Half-wave rectifier with a filter, the Diode is connected in series to a capacitor and Load resistor which in turn are connected parallelly as shown in the above circuit diagram. In this circuit, the capacitor charges in the positive half-cycle and discharges during the negative half-cycle and reduces ripples in the output. In a positive half cycle, the diode acts as a short circuit and the capacitor charges from the input source. In the negative half cycle when the diode acts as an open circuit, the capacitor discharges providing current flow into the Load. Thus adding a capacitor to the circuit helps to maintain DC output even when AC is in negative half cycle. Given below is the output waveform of the Half wave rectifier with Filter.

Output waveform of a Half wave rectifier with capacitor filter

Thus a capacitor helps to reduce ripples in the DC output of a half-wave rectifier.

Three Phase Half Wave Rectifier

Three-phase connection is used in households and industries with high power requirements. The main advantage of three phases over a single phase is that they are more efficient. A three-phase AC connection consists of three single phases (Red, Yellow and Blue colored wires are used to represent each of the three phases) AC with a phase difference of 120° connected to the load. So at any time voltage of any one of the phases will be greater than zero and therefore machines operate at a better efficiency. To convert a Three-phase AC supply to DC a three-phase half-wave rectifier is used. To convert a three-phase AC supply to DC, a diode is connected in series to each of the three-phase inputs, such an arrangement is called a three-phase rectifier. So it requires three diodes to convert three-phase AC to DC. The circuit diagram of a three-phase rectifier is given below.

Circuit diagram of three-phase rectifier

Working of Three Phase Half Wave Rectifier

The below figure shows the input of a three-phase AC supply. You can see that the input of three-phase AC is like that of three single-phases separated by an equal time gap. So when we place a half-wave rectifier in each phase wire, the half-wave rectifier allows it to pass the positive half cycle and prevents the flowing of current in the negative half cycle. Thus it can convert AC to DC.

Input waveform of Three-phase AC supply

If we consider the red phase alone, In the positive half cycle diode acts as a short circuit and it allows to pass current through it. In a negative half cycle, the diode acts as an open circuit and blocks the flow of current. You can see that in the output waveform given below, red phase voltage is present when it is in the positive half cycle and it is not visible in the negative half cycle.

Similarly, other phases are also rectified by using a diode.

Output waveform of three-phase rectifier

From the output of a three-phase rectifier, You can see that its voltage does not fall into zero like in that of a single-phase rectifier as it uses three phases and at any time any of the three phases will have a positive half-cycle. Thus it has a better supply than that of a single-phase rectifier.

Half Wave Rectifier Formula

Here are some important formulas to calculate various parameters related to Half half-wave rectifier.

Terms used below formulas are: Vp is peak AC voltage, V_d is forward biased voltage drop of the diode, I_dc is the value of DC component of output current, P_out value of output power, P_in is the value of input power and V_avg is the average value of output voltage.

Peak Inverse Voltage of HWR

It is the maximum Voltage Withstand by the diode without getting damage

PIV=V_m

Output voltage (V_out)

The output voltage of a half-wave rectifier for a given AC voltage is given by the formula

V_out = V_p/π -V_d

Form Factor (FF) of a Halfwave Rectifier

Form factor is defined as the ratio of the RMS value of voltage to the average value of output voltage.

FF =RMS Value/Avg Value= V_rms / V_avg

Ripple factor (γ) of Half Wave Rectifier

Ripple factor determines the quality of rectification of AC to DC. The lower the value of the ripple factor, the higher the quality of rectification. We use capacitors and inductors in rectification circuits to decrease the ripple factor.

Ripple Factor(γ)=√((FormFactor)²-1) = √((V_rms / V_avg)²-1) also, γ= (I²_rms – I²_dc)/ I_dc

From the above equation, we can find out that the ripple factor of a half rectifier without any filters is 1.21.

Efficiency (η) of Half Wave Rectifier

Efficiency is defined as the ratio of output DC power to input AC power.

η= (P_out / P_in)x100

RMS Value of Half Wave Rectifier

I_rms and I_dc: I_rms is the average value of the output current and I_dc is output current at load.

I_rms= I_m/2 and I_dc = I_m / π

Solved Examples on Half Wave Rectifier

Calculate the rectification efficiency of a half-wave rectifier that obtained 15 watts of power output on an input power of 40 watts.

Given the input power (P_in) as 40 watts and the output power (Pout) as 15 watts, the rectification efficiency can be calculated using the formula:

Rectification efficiency = (P_out / P_in) * 100

Substituting the given values:

Rectification efficiency = (15 / 40) * 100 ≈ 37.5%

So, the rectification efficiency is approximately 37.5%.

A power supply with a peak voltage of 6v is connected to a diode for rectification and a resistor of 100Ω is connected as load. If the internal resistance of the diode is 6Ω, find the following:

• Find the Peak value of the current, the RMS value of the current and the DC output current.
• Find the input and output power.
• Find the efficiency of rectification.
• Find the output voltage of the DC output.

Given:

Load resistance (RL) = 100Ω

Peak voltage (Vm) = 6V

Diode resistance (RD) = 6Ω

1. Calculate Im (peak current):

I_m= V_m/(R_D+R_L) = 6 / (6 + 100) = 0.057A = 57mA

Calculate I_dc (average current):

I_dc = Im / π = 57mA / π ≈ 18.14mA

Calculate I_rms(root mean square current):

I_rms= Im / 2 = 57mA / 2 = 28.5mA

2. Calculate input power (Pin):

P_in = I²R = (I_rms)² x (R_D+R_L) = (0.0285)² x (6+100) = 0.086 watts

Calculate output power (Pout):

P_out = I²R = (I_dc)² x R_L = (0.01814)² x 100 = 0.032 watts

3. Calculate efficiency:

Efficiency = (P_out/ P_in) x 100 = (0.032W / 0.086W) x 100 ≈ 37.2%

4. Calculate DC voltage (Vdc):

V_dc = I_dcx R_L = 0.01814A x 100Ω = 1.814V

Advantages and Disadvantages of Half Wave Rectifier

Given below are the Advantages and Disadvantages of the half wave rectifier

Advantages of Half Wave Rectifier

• Simplicity of circuit: The half-wave rectifier circuit is simple and easy to Implement.
• Low cost: Components required for a half-wave rectifier are inexpensive, contributing to cost-less designs.
• Easy to manufacture: Due to its Low cost and simple Design, half Wave Rectifiers can be easily manufactured in large quantities.

Disadvantages of Half Wave Rectifier

• High ripple factor: It produces Significant ripple in output Waveform, leading to fluctuations in the DC output voltage.
• High power loss: Efficiency is reduced due to the utilization of only half of the input waveform, resulting in higher power dissipation.
• Low efficiency: Compared to full-wave rectifiers, half-wave rectifiers have lower efficiency because they utilize only one half of the input cycle.
• Low output voltage: The output voltage of a half-wave rectifier is lower than that of a full-wave rectifier, limiting its application in systems requiring higher voltages.

Applications of Half Wave Rectifier

Half-wave rectifiers are widely used in electrical and electronic circuits. Some of such circuits are:

• Pulse generating circuits: Half-wave rectifiers are commonly used in pulse-generating circuits for applications such as triggering switches and driving LEDs.
• Signal demodulation circuits: They are utilized in demodulating AM radio signals to extract the original information signal.
• Signal peak circuits: Half-wave rectifiers can be employed in circuits that require detection of signal peaks or maximum values.
• AC to DC converters: In low-power applications where efficiency is not critical, half-wave rectifiers can be used to convert AC power to DC power.
• Low-power DC chargers: They are suitable for charging low-power devices such as small batteries or capacitors in applications like toys or portable electronics.

Conclusion

A half-wave rectifier is the simplest form of rectifier available. Even though it does not convert the entire AC cycle to DC like a full-wave rectifier, still it has many applications in real life and is one of the important fundamental electronic devices. Also, it serves as the basis of a full wave rectifier. I hope this article helped to create a better understanding of half-wave rectifiers. Share your thoughts in the comments!

Half Wave Rectifier – FAQs

Why is a half-wave rectifier so called?

Half wave rectifier is a device that allows only one of the AC half-cycle to pass through it, blocking the other half-cycle. So, the rectification process occurs only in one of the half cycle therefore, it is called as half-wave rectifier.

Is it possible to remove ripples in a half-wave rectifier?

No, it is not possible to eliminate ripples in the Half-wave rectifier. But we can reduce it by using a filters like capacitors and inductors.

What is pulsating Direct current (DC)?

Pulsating DC is a current that varies its magnitude over time but does not change the direction.

Where are Half-wave rectifiers used?

Half-wave rectifiers are used in low-power DC chargers, Signal peak circuits, pulse generators, signal demodulators etc.