Full Wave Bridge Rectifier with Capacitor Filter

 

Bridge Rectifier with Capacitor Filter

A bridge rectifier is a full wave rectifier circuit configuration that converts the full waveform of the AC voltage into DC voltage. In this circuit configuration, four power semiconductor switches are connected in a bridge-like arrangement. 

 

We have published a dedicated article on the basics of bridge rectifiers, where we discussed the circuit diagram, working principle, output waveforms and important formulas of bridge rectifiers. We recommend you to first go through that article, so that you can understand the fundamentals of bridge rectifiers, which will help you to grasp the concepts discussed in this article.

 

To simplify the explanation of bridge rectifiers with filters, we are taking reference of the diode bridge rectifier for resistive load and a capacitor filter.

 

Harmonics on the DC side or the Output side of the Bridge Rectifier

 

In bridge rectifiers, we saw that the rectified output waveform of a diode bridge rectifier with resistive load is pulsating in nature, as shown in figure, “called pulsating DC”. However, it is not desired. Actually, the output waveform of the rectifier depends on the combination of the nature of load and rectifier circuit configuration. 

This pulsating DC waveform is made up of the combination of DC voltage and AC voltage. Since our primary goal is to obtain pure DC voltage, the AC voltage component present in the output waveform is unwanted. This unwanted AC component is called the ripples in the output voltage waveform. 

 

The presence of these ripples in the output waveform can lead to overheating of loads and reduction in the performance of the rectifier. Therefore, it is essential to remove these unwanted ripples from the output waveforms. So, in order to remove these ripples, we must use filters at the output of the rectifiers.

 

But, before moving onto how to remove ripples from the rectified output waveform by using filters, let's first calculate the DC component and AC component present in this waveform. This type of waveform can be expressed using Fourier series in terms of its DC and AC components.

 

 

Fourier Series of Full Wave Bridge Rectifier

With the help of the above expression of Fourier series we can calculate the DC component and AC component of this rectified output waveform. By observing the AC component part, we can conclude that the AC component present in the rectified output waveform consists of fundamental plus higher order harmonics components.

 

 

Bridge Rectifier Ripple Factor

 

Ripple factor is the measure of the ripples or unwanted AC components present in the rectified output waveform of a rectifier. It is defined as the ratio of RMS value of the AC component present in the output waveform to its average value.

RMS value of AC voltage component or ripple voltage of the given waveform is 

Average value of the output waveform is   =     V_o

For Diode bridge Rectifier with resistive load

After substituting these values into ripple factor expression, we find that the ripple factor of diode bridge rectifiers is 0.483. This indicates the AC voltage component or the ripple voltage of the given waveform is 48.3% of its average voltage or DC component, which is quite high.

Form Factor of Bridge Rectifier

 

It is defined as the ratio of RMS value of the waveform to its average value.

After substituting above value in the ripple factor expression we get,

For diode bridge rectifier output waveform form factor is 1.11

 

If we carefully observe the above expression of ripple factor, we see that if FF is equal to 1, then the ripple factor is zero, meaning the output voltage is ripple free or smooth as a pure DC waveform. 

Diode Bridge Rectifier with Capacitor Filter

 

As we mentioned previously, to obtain a smoother DC output waveform, a filter must be used across the load side of the rectifier. Let us take an example of a capacitor filter, connected parallel to the load. This filter capacitance reduces the ripple in the output voltage waveform by charging and discharging itself.

 

Let us understand how the filter capacitance reduces ripples in the output voltage waveform with the help of MATLAB simulation. To make it easy to understand the components used in this circuit are considered ideal.

Given figure shows the diode bridge rectifier circuit with filter capacitor using MATLAB simulation model. In this MATLAB simulation model, we have taken the peak value V_m for the input signal is 100V and the supply frequency is 50Hz.

To make it easy to understand the effect of filter capacitance in a diode bridge rectifier we take the output waveform for three conditions.

In the first condition, we consider the bridge rectifier without a filter. The output voltage waveform and their average and rms values in this condition, is shown in the given figure. 

As we discussed in the bridge rectifier, the fundamental time period of the output waveform of the full bridge diode rectifier is half of the fundamental time period of the AC supply, which is evident in the output waveform illustrated in the given figure. The RMS and average value of the output waveform are also provided in the given figure. 

 

• The fundamental time period of the AC supply is 0.02
• The fundamental time period of the rectified output waveform is 0.01
• RMS value of the output waveform in this condition is 70.56
• Average value of the output waveform in this condition is 63.61

Thus, the form factor is 70.56 / 63.61 that is equal to 1.11 

 

In the second condition, we consider the same rectifier circuit discussed in the previous condition with a 10mf capacitor filter. The output voltage waveform and their average and rms values in this condition, is shown in the given figure.

In this condition during 0 to 0.005 sec, while the rectified voltage goes from 0 to its peak value the capacitor is charged up to the peak value of the input voltage.

 

And during 0.005 to 0.01 sec, while the input voltage goes to 0 from its peak value the capacitor discharges to the load. The discharging speed of the capacitor is slower due to its time constant. So, the output voltage waveform in this case goes to zero slowly as compared to the previous case.

 

And before fully discharging the capacitor or the output waveform going to zero the second pulse of the rectified output waveform again charges the capacitor to its peak value. And this process of charging and discharging of capacitor repeats again and again resulting in the output voltage waveform never going to zero. We can observe this phenomenon in the output waveform of the given figure.

• RMS value of the output waveform in this condition is 79.15
• Average value of the output waveform in this condition is 77.67 (we can see these value in the given figure)

Thus, the form factor is 79.15 / 77.67 that is equal to 1.02 which is not much low but it is low as compared to previous case of without filter capacitance.

In the third condition we take the output voltage waveform of the previously discussed circuit with 50mf filter capacitor.

In this condition, we increase the value of the capacitance from 10 mf to 50 mf. The higher the value of the capacitance, the higher the time constant of the capacitor. This will result in a decrease in the discharging speed of the capacitor. Means the capacitor takes more time to discharge. As a result, less ripples in the output waveform. The output voltage waveform and their average and rms values in this condition, is shown in the given figure.

• RMS value of the output waveform in this condition is 92.65
• Average value of the output waveform in this condition is 92.54 

 

Thus, the form factor is 92.65 / 92.54 that is equal to 1.001 which is quite small as compared to both of the previous cases.

 

Observation and Conclusion

 

In the above discussion of the diode bridge rectifier with filter, we observed the following: 

• Form Factor of diode bridge rectifier without filter  = 1.11 

• Form Factor of diode bridge rectifier with 10mf capacitor filter  = 1.02

• Form Factor of diode bridge rectifier with 50mf capacitor filter  = 1.001

 

By carefully observing these form factor values, we can see that as the capacitance increases then the form factor decreases. As we discussed earlier, when the form factor decreases then the ripples in the waveform decrease leading to the smoother output waveform.

 

So, the overall conclusion of the discussion held in this article is that the introduction of the sufficiently large capacitor in the rectifier circuit results in a smoother output waveform.