Operating Principle Without Smoothing Capacitor Value

The four diodes labeled D1 to D4 are arranged in “series pairs” with only two diodes conducting current during each half cycle.
During the positive half cycle of the supply, diodes D1 and D4 conduct in series while diodes D2 and D3 are reverse biased and the current flows through the load as shown in figure 5.

During the negative half cycle of the supply, diodes D2 and D3 conduct in series, but diodes D1 and D4 are “OFF” as they are now reverse biased.
The current flowing through the load is in the same direction as the positive cycle (see figure 6).
This is a double-way topology. In each half-cycle, the current flows in both directions in the secondary winding, but always in the same direction in the load.

The bridge is fed by a sinusoidal AC voltage so that:

With:

• , the RMS value of the input voltage
• , the peak value of the input voltage

It’s assumed that the four diodes are perfect and identical.

For the positive cycle: 

• D1 and D4 conduct
• D2 and D3 switch “OFF”.

Figure 5: Positive Cycle of the Single-Phase Diode Bridge Rectifier

Thus, we obtain:

For the negative cycle: 

• D2 and D3 conduct
• D1 and D4 switch “OFF”.

Figure 6: Negative Cycle of the Single-Phase Diode Bridge Rectifier

Thus, we obtain:

The output voltage is periodic of period . 
The average output voltage is calculated as follows:

Therefore, it leads to an average output voltage of:

With:

The average output current is obtained using Ohm’s law:

The root-mean-square (RMS) value of the output voltage is:

The root-mean-square (RMS) value of the output current is:

To analyze the performance of a rectifier circuit, the form factor and the ripple factor are often used.

The form factor is the ratio of the RMS output voltage and the average output voltage:

The more F tends to 1, the more the rectified output voltage can be regarded as continuous.

The ripple factor can be calculated as follows:

Where:
is the maximum peak value of the output voltage
is the minimum peak value of the output voltage

The more  tends to 0, the more the rectified output voltage can be considered as continuous.

Operating Principle with Smoothing Capacitor Value

Rectifiers are normally used in circuits that require a steady voltage to be supplied. The raw rectified DC requires a smoothing capacitor circuit to enable the rectified DC to be smoothed so that it can be used to power electronic circuits without large levels of voltage variation.
To smooth the output of the rectifier, a reservoir capacitor is used - placed across the output of the rectifier and in parallel with the load.
This capacitor charges up when the voltage from the rectifier rises above that of the capacitor and then as the rectifier voltage falls, the capacitor provides the required current from its stored charge.

Figure 7: Single-Phase Diode Bridge Rectifier with Smoothing Capacitor

The choice of capacitor value needs to fulfil a number of requirements.
In the first case, the value must be chosen so that its time constant is very much longer than the time interval between the successive peaks of the rectified waveform:

Where :

• , the overall resistance of the load for the supply
• , the value of capacitor
• , the ripple frequency - this will be twice the line frequency when a full wave rectifier is used

The ripple voltage is not only determined by the value of the smoothing capacitor, but the frequency and the load current.
It is calculated as:

Where: 

• , the DC load current
• , the frequency of the ripple or twice the input frequency in Hertz
• , the capacitance 

It can be noted from equation (10) that the ripple voltage is inversely proportional to the resistance.
So, we can conclude that for C constant, the peak-to-peak voltage decreases as the resistance increases and therefore the curve is smoothed.