Full Wave Rectifiers | Analog and Digital Electronics - Electrical Engineering (EE) PDF Download

Full Wave Rectifiers

A wave rectifier circuit is used to convert an input AC signal into DC by rectifying both negative cycles. This process is achieved by utilizing diodes that conduct during each cycle of the input signal. The outcome is a DC output with reduced ripples compared to a half-wave rectifier resulting in a smoother waveform with a value.

Full Wave Rectifier Circuit

Full Wave Rectifier Circuit

An electrical arrangement called a wave rectifier circuit’s employed to convert alternating current (AC) into direct current (DC). It makes use of diodes to ensure that both halves of the AC cycle are transformed into a flow of current, in one direction. This leads to a smoother DC output. The basic implementation can be done using either a center tapped transformer or a bridge rectifier configuration.

Working of Full Wave Rectifier

1. Rectification: Converts AC to pulsating DC by allowing current flow in both halves of the AC cycle using diodes.
2. Bridge Configuration: Often employs a bridge rectifier with four diodes to ensure full-wave rectification.
3. Output Voltage: Produces a pulsating DC output with twice the frequency of the input AC.

We are going to learn about some important formulas as given below :

Center-Tapped Full-Wave Rectifier Formula

A full wave rectifier is a circuit that converts alternating voltage (AC) into (DC) voltage. There are two used types; the center tapped wave and the bridge rectifier.

To calculate the output DC voltage (V_out) of a center tapped full wave rectifier you can use the equation:

Here,

• V_out represents the output DC voltage.
• V_m is the peak value of the AC voltage (the voltage).
• ω refers to the frequency of the AC voltage (2π times the frequency, in Hertz).
• t denotes time.

Bridge Rectifier Formula

There are four diodes used in a bridge rectifier to rectify the AC voltage. The output voltage (V_out) of a bridge rectifier can be calculated using the below equation:

V_out = V_m – V_d

Where:

• V_out is the output DC voltage.
• V_m is the peak value of the AC voltage (maximum voltage).
• V_d is the voltage drop across the diodes (usually around 0.7 volts for silicon diodes).

In both cases, the output voltage is a pulsating DC voltage. To obtain a smoother DC voltage, a filter capacitor is often connected across the output.

Note: Keep in mind that these formulas provide idealized results, and in practical circuits, there may be variations due to factors like diode characteristics, transformer losses, and other real-world considerations.

Peak Inverse Voltage

PIV is the maximum reverse voltage that a diode in a full-wave rectifier must withstand. It is equal to the peak value of the input AC voltage.

PIV= Vm

where, Vm = peak value of the AC input voltage

DC Output Voltage

The DC output voltage of a full-wave rectifier is approximately equal to the peak value of the AC input voltage minus the voltage drop across the diodes.

Vdc ≈ Vm – 2Vd

where, Vd= voltage drop across each diode

RMS Value of Current

The RMS value of the output current in a full-wave rectifier can be calculated using the RMS value of the input current.

where, Im= peak value of the input current

Form Factor

The form factor is the ratio of the RMS value of the output voltage to the average value of the output voltage. For a full-wave rectifier, the form factor is typically around 1.11.

Where, Vrms = RMS value of the output voltage

Peak Factor

The peak factor is the ratio of the peak value of the output voltage to its RMS value.

Rectification Efficiency

Rectification efficiency measures how effectively the rectifier converts AC to DC. It is the ratio of the DC power output to the AC power input. The efficiency of the full wave rectifiers is 81.2%.

Ripple Voltage

Ripple voltage is the AC component super imposed on the DC output voltage. In a full-wave rectifier with a filter capacitor, it can be calculated using the load current (IL) and the capacitance (C) of the filter capacitor.

Filter Circuit Using Full Wave Rectifier

A filter circuit in conjunction with a full-wave rectifier plays a crucial role in converting alternating current (AC) into direct current (DC) with minimal ripple voltage. The full-wave rectifier, typically implemented using diodes, ensures that both halves of the AC input waveform are utilized, effectively doubling the frequency of voltage pulses. However, this rectification process still leaves some residual AC components and produces a pulsating DC output. To smooth out these fluctuations and obtain a relatively constant DC voltage, a filter circuit is employed. This filter typically consists of capacitors and sometimes inductors arranged in various configurations.

Filter Circuit using Full Wave Rectifier

Capacitors store electrical energy and discharge it during the brief gaps between rectified pulses, effectively reducing the ripple voltage. This results in a much smoother and steady DC output that is suitable for powering electronic devices and circuits. The combination of the full-wave rectifier and the filter circuit ensures that the DC output is nearly constant, which is crucial for many applications where stable power supply is essential.

Types of Full Wave Rectifiers

A full wave rectifier is an electronic circuit that converts alternating current (AC) into direct current (DC), and it has two main types:

1. Center-Tapped Full Wave Rectifier: It uses a center-tapped transformer and two diodes to rectify AC, commonly employed in low to moderate power applications.
2. Bridge Rectifier: This type of bridge rectifier utilizes four diodes arranged in a bridge configuration allowing for AC to DC conversion without relying on a center tapped transformer. It is often employed in high power applications and compact circuits.

Centre-Tapped Full Wave Rectifier

Centre-tapped Full Wave Rectifier

A center-tapped full wave rectifier circuit consists of a center-tapped transformer, two diodes, and a resistive load. The center-tapped transformer has a wire connected at the center of its secondary winding, which divides the input AC voltage into two halves. The diodes are connected in parallel to each other, with the load connected at the center tap of the transformer.

During the positive half of the input cycle, one diode conducts (forward bias) while the other diode is non-conducting (reverse bias). This allows current to flow through the load. In the negative part of the cycle, the diodes change their job. The one that was allowing electricity to flow now stops, and the one that was blocking it begins to allow it through. This is unlike a half-wave rectifier that uses only one part of the cycle. Using both parts in a full wave rectifier improves its performance and ensures more efficient conversion of the wavy input into a smooth output.

Working of Centre-Tapped Full Wave Rectifier

Working of Centre-tapped Full Wave Rectifier

In this arrangement the center tapped full wave rectifier effectively converts AC to DC by utilizing two diodes. During the half of the AC cycle one diode allows current to flow through the connected device or load. Conversely during the half of the cycle the other diode takes over. Enables current to flow in the opposite direction. This dual diode action ensures that both positive and negative halves of the input AC cycle are transformed into an flow resulting in a more stable and reliable source of power for electronic devices.

Advantages of Centre-Tapped Full Wave Rectifier

• Some advantages of using a center tapped wave include its higher efficiency compared to a half wave rectifier since it utilizes both halves of the AC cycle.
• It produces an more consistent DC output waveform, which reduces noise in devices.
• This type of rectifier plays a role in converting AC to DC and providing reliable power, for various electronic applications.
• The voltage and current, in the DC are twice as high as those in a half wave rectifier resulting in increased power, for the devices connected to it.

Disadvantages of Centre-Tapped Full Wave Rectifier

• The rectifier necessitates the use of center tapped transformers, which can be more costly to produce and thus raise the circuit expenses.
• Designing and constructing it is more intricate when compared to a half wave rectifier, which makes it less appropriate, for simple applications.
• The transformer utilized in this rectifier can be bigger and heavier which may not be optimal, for portable devices.

Bridge Rectifier Full Wave Rectifier

Bridge Rectifier Full Wave Rectifier

A wave rectifier that doesn’t need a center-tapped transformer is a bridge rectifier circuit. Instead, it converts both of the input cycle’s negative components using four diodes arranged in a bridge arrangement.

In this circuit, the diodes are positioned so that two conduct during one half of the input cycle and the other two conduct during the other. By ensuring that both input cycle halves are rectified, a current (DC) output waveform is produced.

Working of Bridge Rectifier Full Wave Rectifier

Input Image

Input Voltage Waveforms

Output Image

Rectified Output Voltage/Current Waveforms

Consider a square with two diodes on top and two on bottom, making the outline of a bridge. When the AC power goes through this bridge, during each half of the cycle, two of these diodes start working like a team. They let the electric current flow through them and into whatever you’re powering. This clever setup ensures that both the positive and negative parts of the AC electricity get turned into DC, which means you get a smoother and more even kind of electricity that’s great for powering all sorts of things.

So, a bridge rectifier is like a bridge that helps make your power supply smooth and stable.

Advantages of Bridge Rectifier Full Wave Rectifier

• The efficiency of rectifying a bridge is higher when compared to a half wave rectifier.
• The ripple factor is lower which leads to a DC output waveform.
• Bridge rectifiers are a cost option as they eliminate the need, for a center tapped transformer, unlike center tapped rectifiers.

Disadvantages of Bridge Rectifier Full Wave Rectifier

• While using bridge rectifiers there is a decrease, in voltage due to the process of rectification.
• Setting up bridge rectifiers involves a circuit arrangement, which might pose challenges for those who are new to electronics.
• The components used in bridge rectifiers such as diodes can be more expensive compared to rectification methods.
• Multiple diodes in bridge rectifiers can generate heat so it’s important to include heat dissipation solutions like heat sinks.
• Bridge rectifiers may exhibit leakage currents, where a small amount of current flows, in the opposite direction when the diodes are off. This can result in energy wastage and reduced efficiency.

Solved Example of Full Wave Rectifier

Suppose we have an AC voltage source with a sinusoidal waveform:

This AC voltage source is connected to a full-wave bridge rectifier circuit consisting of four diodes. We want to find the output DC voltage Vout across the load resistor (RL=1,000).

Solution

1. The given AC voltage source Vin(t) has a frequency of 60 Hz, which means it completes 60 cycles per second.

2. The full-wave bridge rectifier circuit will convert both the positive and negative halves of the input AC waveform into positive DC voltage.

3. The output voltage Vout can be calculated as follows:

Vout= Vpeak − Vdiode drop

• Vpeak is the peak voltage of the input AC waveform.
• Vdiode drop is the voltage drop across the diodes, which is typically around 0.7 volts for silicon diodes.

4. To find Vpeak, we need to determine the peak value of the sinusoidal waveform. The peak value of a sine wave is times its RMS (root mean square) value.

RMS value = 10/√2 volts

Peak value Vpeak = √2 volts = 10 volts

5. Now, we can calculate Vout:

Vout = 10 volts – 0.7 volts = 9.3 volts

So, the output DC voltage Vout across the load resistor is 9.3 volts when the input AC voltage is a 10-volt sinusoidal waveform with a frequency of 60 Hz. This rectified DC voltage can be used to power electronic devices or circuits.

Full Wave Rectifier With Smoothing Capacitor

A full-wave rectifier with a smoothing capacitor is an electrical circuit designed to convert alternating current (AC) into direct current (DC) while mitigating voltage fluctuations, resulting in a more stable DC output voltage. This configuration is frequently employed in power supply systems to deliver a dependable source of DC voltage for a variety of electronic devices. The rectifier uses diodes to ensure that both halves of the AC cycle are utilized, yielding a pulsating DC output. The smoothing capacitor, connected in parallel, stores energy during peak voltage moments and releases it during lower voltage periods, effectively diminishing voltage ripples, thus furnishing a steadier DC output. This helps ensure consistent power delivery for electronic equipment.

Working

Full Wave Rectifier With Smoothing Capacitor

• Rectification: Converts AC voltage to pulsating DC using a bridge rectifier (four diodes).
• Smoothing Capacitor: Connected in parallel to the load resistor.
• Charging: During the positive half-cycle, the capacitor charges as current flows through the load resistor.
• Discharging: During the negative half-cycle, the capacitor discharges energy into the load resistor, bridging gaps between voltage pulses.
• Output Voltage: This process smooths out the output voltage, reducing ripples to provide a relatively constant DC voltage.
• Larger Capacitance: A larger capacitor reduces ripple and yields a more stable DC output.

Advantages and Disadvantages of Full Wave Rectifier

There are some list of advantages and disadvantages of Full Wave Rectifier given below :

Advantages

• Efficiency: Utilizes both halves of the AC cycle, making it more efficient than half-wave rectification.
• Higher Average Voltage: Provides a higher average output voltage compared to half-wave rectifiers.
• Reduced Ripple: Smoother DC output due to the double frequency rectification, improved further with a smoothing capacitor.

Disadvantages

• Complexity: Requires four diodes in a bridge configuration, making it slightly more complex than a half-wave rectifier.
• Higher Cost: Increased component count can lead to higher manufacturing costs.
• Voltage Drop: Each diode introduces a small voltage drop, which may affect the output voltage slightly.

Full wave rectifiers play a vital role in electronics by converting AC signals to DC signals. Whether it’s a center-tapped rectifier or a bridge rectifier, both types offer advantages such as higher rectification efficiency, smoother DC output waveforms, and increased output voltage and load current values. These rectifiers find applications in power supply units, radio signal detection, electric welding, and high voltage conversion, among others. Understanding the working principles and characteristics of full wave rectifiers is essential for anyone working in the field of electronics.