# Center Tapped Full Wave Rectifier with capacitor filter

In the previous article, we have seen Halfwave rectifier working principles. Halfwave rectifier converts the only positive half cycle of AC voltages into DC voltage and ignores the negative half cycle. That is why its average output is around 32% of the peak voltage. A full-wave rectifier converts the complete cycle into DC and has higher average output. There are two types of Full-wave rectifier: The Center Tapped rectifier and Bridge Rectifier. We are discussing Center Tapped Full-wave Rectifier here.

## Full wave Center Tapped Rectifier operation:

Because of the fact that a The Center Tapped Rectifier use a center tapped transformer in its circuit that is why it is named as Center Tapped Rectifier. The secondary winding of the center-tapped transformer is divided in half. As the circuit below shows that, the center tap of the secondary winding is grounded and each diode is connected on the remaining terminals of the secondary winding. The load is connected to the common point of both diodes and another side of the load is grounded. #### Positive Half cycle:

For the positive half cycle, the diode D1 becomes forward biased and the diode D2 becomes reverse biased. The current flow through D1 and load resistor. In this situation, notice that the half of the secondary winding provides the voltage to the load. #### Negative Half Cycle:

For the negative half cycle, the diode D2 is forward biased and diode D1 is reverse biased. The current make its path through D2 and the load resistor. Same as the previous case, here also the half part of the secondary winding is driving the load. In both cases, the current through the load is unidirectional or pulsating Direct Current (DC). ## Effect of the turn ratio on rectifier output:

Because of the fact that half of the secondary winding drives the load, only half of the secondary voltage appears across the load in each case. For the transformer ratio of 1:1, the secondary voltage and primary voltage remain the same, so the voltage across the load will be half of the input voltage. To make the full input voltage appear across the load, a transformer ratio should be set to 1:2 and consider the diode forward voltage drop which is 0.7 volts for silicon diode and 0.3 volts for germanium diode.

## Peak inverse voltage of diode:

Both diode forward bias and reverse bias alternatively as the sinusoidal voltage change the direction. Each diode should tolerate the maximum reverse voltage that is called Peak Inverse Voltage (PIV). Consider the positive half cycle, where diode D1 is forward bias and analyze the diode D2 for PIV. As the diode D1 is forward biased so the peak voltage at point O will be

$v_{o}=\frac{v_{p(s)}}{2}-0.7$

Moreover, the voltage at point b will be

$v_{b}=-\frac{v_{p(s)}}{2}$

The inverse voltage across the diode D2 will be

$PIV of D2=v_{o}-v_{b}$

$PIV=\left[ \frac { { v }_{ p(s) } }{ 2 } -0.7 \right] -\left[ \frac { -{ v }_{ p(s) } }{ 2 } \right] \\ PIV={ v }_{ p(s) }-0.7$

The same procedure can be repeated for diode D1 peak inverse voltage equation.

## Average Output of the rectifier:

During the complete sinusoidal input cycle, the output of the center tapped rectifier repeat itself twice. In other words, the time-period of the output is $\pi$ instead of $2\pi$. Therefore, the average of the output waveform will be $v_{avg}=\frac{V_{p(s)}}{\pi }(\int_{0}^{\pi }{\sin t dt} )$

$v_{avg}=\frac{V_{p(s)}}{\pi }(2)$

$v_{avg}=\frac{2V_{p(s)}}{\pi }$

$v_{avg}=0.637 V_{p(s)}$

Notice that the average voltage of the center tapped rectifier is twice of the half wave rectifier which is 0.32.

## Ripple factor of the rectifier:

Ripple factor shows the effectiveness of the filter and defined as

$r=\frac{v_{r(pp)}}{v_{dc}}$

Where vr(pp) is the ripple voltage (peak-peak) and vdc value of the filtered output. The formulas for vdc and v­r(pp) is given below

$v_{r(pp)}=(\frac{1}{fR_{L}C})(\frac{v_{p(s)}}{2}-0.7)$

$v_{dc}=(1-\frac{1}{2fR_{L}C})(\frac{v_{p(s)}}{2}-0.7)$

Notice the frequency of the output waveform of the rectifier is twice of the input frequency. ## Conclusion:

• Center Tapped rectifier convert both halves of the AC input cycle into DC output
• The rectifier uses a tapped transformer and two diodes and the tapping is grounded
• The average output of the center tapped rectifier is twice that of half wave rectifier
• The ripple voltage is less than that of half wave rectifier
• The output voltage can be controlled with a change in turn ratio
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1. victor December 21, 2019