Bridge rectifiers are essential components in many electrical circuits and devices that require the conversion of AC voltage to DC voltage. They are widely used in power supplies, battery chargers, and various other applications that require a steady DC voltage. In this article, we will explore the various formulas and calculations that are used to design and analyze bridge rectifiers.

What is a Bridge Rectifier?

A bridge rectifier is a circuit that uses four diodes arranged in a bridge configuration to rectify AC voltage. It rectifies both the positive and negative half cycles of the AC voltage, and the output is a pulsating DC voltage with some ripple. The bridge rectifier is an improvement over the half-wave rectifier, which only rectifies the positive half cycle of the AC voltage.

Bridge Rectifier diagram

To start explaining full wave bridge rectifier ac to dc conversion operation. As shown in the figure the total no of diodes in a bridge rectifier diagram is four.  Input is sinewave and single phase which is fed into a step-down transformer primary coil and downconverted to a required voltage level. Input AC voltage is alternating its polarity and amplitude periodically. To gain a steady state DC voltage we are using a full wave bridge rectifier circuit without a filter or capacitor filter. After understanding, we will use a filter capacitor and different configurations to attain a ripple-free DC output. Each transformer’s secondary terminal is connected to two diodes: anode and cathode. And other terminals of two diodes with the same polarity are connected. One pair of diodes through Positive voltage from transformer secondary coil. At the same time another diode through negative voltage from secondary coil to RL load resistance. In the following full bridge rectifier circuit diagram.

Working of a bridge rectifier

 we can see positive and negative half cycles of input sinewave are distinguished by orange and green colors. Different colors explain the working of a full wave bridge rectifier and better demonstrate the current flow concerning time and input waveform.  normally shown circuit is used with a domestic electric supply which is 110V/220V AC 60Hz/50Hz pure sinewave. So, this article explained the working of bridge rectifiers with relevant waveform or pure sinewave. In future and advanced topics, we may describe working on a full wave bridge rectifier with other types of input waveform signals. But here we will only discuss sinewave input. The calculation of rectified output with sinewave input is different than other waveform types like square and sawtooth waveform signals. Our AC power sources follow the sinewave so it is standard to study with a sinewave input supply. The diodes D1 to D4 are connected in series with only two diodes forward biased during each half cycle. During the positive half cycle of the supply, diodes D2 and D4 in series forward biased while diodes D1 and D3 are reverse biased and the current flows through the RL or load resistance as described in the figure

. During the negative half cycle of the supply, diodes D1 and D3 are in series forward biased while diodes D2 and D4 are reverse biased.

Bridge rectifier Formulas and Calculations

1. Peak Output Voltage:

The peak output voltage of a bridge rectifier can be calculated using the following formula:

Vp = Vrms x 1.414

where Vp is the peak output voltage, and Vrms is the root-mean-square (RMS) value of the AC input voltage.

2. Average Output Voltage:

The average output voltage of a bridge rectifier can be calculated using the following formula:

Vavg = Vp/π

where Vavg is the average output voltage, and π is the mathematical constant pi (3.14).

3. Ripple Voltage:

The output of a bridge rectifier has some ripple voltage due to the pulsating DC voltage. The ripple voltage can be calculated using the following formula:

Vr = (Vp – Vavg)/2

where Vr is the ripple voltage.

4. Efficiency:

The efficiency of a bridge rectifier can be calculated using the following formula:

η = (Vavg^2)/(2 x Vrms^2)

where η is the efficiency.

5. Power Dissipation:

The power dissipation in a bridge rectifier can be calculated using the following formula:

Pd = 2 x Vrms^2/RL

where Pd is the power dissipation, and RL is the load resistance.

Full wave bridge rectifier with filter capacitor 

A capacitor is connected across the load. capacitor continuously charges with rectifier output voltage variations. at each peak, the capacitor is charged to that level. when output voltage decreases capacitor starts to discharge current to load. during each period, the capacitor delivers its charged voltage to the load. this voltage also decreases continuously which depends on load resistance and capacitance of the filter capacitor. for high currents and low frequency, high capacitance is required to acquire smooth DC.

Bridge rectifier with LC Pi Filter

In figure 7 filter capacitors C1 and C2 are used to store electric charge and provide backup to load when the rectifier output voltage is low. thus these capacitors dampen pulsating DC voltage. An inductor blocks high-frequency noise and attenuates the ripple voltage. After attenuation of the AC component by the inductor, C2 flattens the output waveform.

Bridge circuit output filtration with Common Mode Choke 

in a pulsating DC power, AC components always have di/dt equal to a non-zero value. So at the choke or inductor terminal, a L*di/dt AC voltage is induced. in common mode choke voltage induced, across both coils are equal due to equal inductance. but resultant magnetic flux is summed up and a mutual inductance develops a very high inductive reactance against AC voltage. DC voltage is not faced by inductive reactance or high impedance. in figure 8 C1 smooths the pulsating voltage. after passing through a common mode choke, attenuated ripple voltage is further smoothened by a C2 capacitor. common mode choke suppresses high-frequency noise produced by EMI interference. The filter capacitor also absorbs load current transients. current transitions from the load side also induce high-frequency noise. without filtration, noise radiates and injects into a power line. common mode choke also prevents those noise signals to travels the rectifier side.

A full wave bridge rectifier LC pie filter is a circuit that can be used to smooth the output voltage of a bridge rectifier, which is a circuit that converts AC voltage to DC voltage. The LC filter is made up of a capacitor (C) and an inductor (L) connected in parallel with each other and in series with the load (R) and the rectifier output. The capacitance and inductance values of the LC filter can be calculated using the following formulas:

C = 1/(4π^2f^2R) L = R/(4π^2f^2C)

Where C is the capacitance value in farads, L is the inductance value in henries, R is the load resistance in ohms, and f is the frequency of the AC input voltage in hertz.

The ripple voltage of the filtered output can be calculated using the following formula:

V_r = I/(2fC)

Where Vr is the ripple voltage in volts, I is the DC load current in amperes, f is the frequency of the AC input voltage in hertz, and C is the capacitance value in farads.

The efficiency of the filter can be calculated using the following formula:

η = 1/(1 + R^2/(2π^2f^2L^2))

Where η is the filter efficiency and R, L, and f are as defined above.

The ripple voltage can be reduced by increasing the capacitance and/or inductance of the filter. However, increasing the capacitance can increase the time it takes for the filter to charge and discharge, which can result in slower response times. Similarly, increasing the inductance can increase the filter’s resistance, which can decrease the efficiency of the filter. Therefore, a balance must be struck between minimizing ripple voltage and maintaining a reasonable response time and efficiency.

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