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Rectifiers

# Full-Wave Rectifier

A **full-wave rectifier** is a device that has two or more diodes arranged
so that load current flows in the same direction during each half cycle of the
AC supply.

## The Conventional Full-Wave Rectifier

A diagram of a basic full-wave rectifier is shown in view A of the figure below.
The transformer *Tr* supplies the source voltage for two diode rectifiers,
*D*_{1} and *D*_{2}. This transformer has a
center-tapped secondary winding that is divided into two equal parts (W1 and W2).
W1 provides the source voltage for *D*_{1}, and W2 provides the
source voltage for *D*_{2}. The voltages at the opposite
ends of the secondary windings are 180 degrees out of phase with each other.
For example, when the voltage at point B is positive with respect to ground, the
voltage at point A is negative with respect to ground.
The connections to the diodes are arranged so that the diodes conduct on
alternate half cycles.
Let's examine the operation of the circuit during one complete cycle.

During the first half cycle (indicated by the solid arrows),
the voltage at point A is positive with respect to ground, while the
voltage at point B is negative with respect to ground.
During this alternation, the anode of *D*_{2} is driven negative
and *D*_{2} cannot conduct. For the period of time that the anode
of *D*_{2} is negative, the anode of *D*_{1} is
positive, permitting *D*_{1} to conduct.
As shown, current flows from point A of the
transformer, through diode *D*_{1}, down through the load resistor
(*R*_{L}) to ground (center tap). When *D*_{1}
conducts, it acts like a closed switch so that
the positive half cycle is felt across the load (*R*_{L}).

During the second half cycle (indicated by the dashed lines), the polarity of
the applied voltage has reversed. Now the anode of *D*_{2} is
positive with respect to ground and the anode of *D*_{1} is
negative. Now only *D*_{2} can conduct. Current now flows, as
shown, from point B of the transformer, through diode *D*_{2}, down
through the load resistor (*R*_{L}) to
ground (center tap). Notice that the current flows
across the load resistor (*R*_{L}) in the same direction for both
halves of the input cycle.

View B of the figure above represents the output waveform from the full-wave rectifier. The waveform consists of two pulses of current (or voltage) for each cycle of input voltage. The ripple frequency at the output of the full-wave rectifier is therefore twice the line frequency.

The higher frequency at the output of a full-wave rectifier offers a distinct advantage: Because of the higher ripple frequency, the output is closely approximate to pure DC. The higher frequency also makes filtering much easier than it is for the output of the half-wave rectifier.

In terms of peak value, the average value of current and voltage at the output
of the full-wave rectifier is twice as great as that at the output of the
half-wave rectifier. The relationship between the peak value and the average
value is illustrated in the figure below. Since the output waveform is
essentially a sine wave with both alternations at the same polarity, the
average current or voltage is 63.7 percent (or 0.637) of the peak current
*I*_{peak} or voltage *V*_{peak}.

As an equation:

**Example:**

The total voltage across the high-voltage secondary of a
transformer used to supply a full-wave rectifier is 300 volts. Find the average
load voltage (ignore the small voltage drop across the diode).

**Solution:**

Since the total secondary voltage (*V*_{S}) is 300 volts, each
diode is supplied one-half of this value, or 150 volts. Because the secondary
voltage is an RMS value, the peak load voltage is:

The average load voltage is:

Every electric circuit has advantages and disadvantages. The full-wave rectifier is no exception. In studying the full-wave rectifier, you may have found that by doubling the output frequency, the average voltage has doubled, and the resulting signal is much easier to filter because of the high ripple frequency. The only disadvantage is that the peak voltage in the full-wave rectifier is only half the peak voltage in the half-wave rectifier. This is because the secondary of the transformer in the full-wave rectifier is center tapped; therefore, only half the source voltage goes to each diode.

Fortunately, there is a rectifier which produces the same peak voltage
as a half-wave rectifier and the same ripple frequency as a full-wave rectifier.
This circuit, known as the **bridge rectifier**, will be the subject of our
next discussion.

## The Bridge Rectifier

When four diodes are connected as shown in the figure below, the circuit is
called a **bridge rectifier**. The input to the circuit is applied to
the diagonally opposite corners of the network, and the output is
taken from the remaining two corners.

One complete cycle of operation will be discussed to help you understand how
this circuit works. Let us assume that there is a positive
potential at point A and a negative potential at point B. The positive potential
at point A will forward bias *D*_{3} and reverse bias
*D*_{4}. The negative potential at point B will forward bias
*D*_{1} and reverse bias *D*_{2}. At
this time *D*_{3} and *D*_{1} are forward biased
and will allow current flow to pass through them; *D*_{4}
and *D*_{2} are reverse biased and will block current flow. The
path for current flow is from point A through *D*_{3}, down
through *R*_{L}, through *D*_{1} to point B.
This path is indicated by the solid arrows.

One-half cycle later the polarity across the secondary of the transformer
reverses, forward biasing *D*_{2} and *D*_{4} and
reverse biasing *D*_{1} and *D*_{3}. Current flow
will now be from point B through *D*_{2}, down through
*R*_{L}, through *D*_{4} to point A. This path
is indicated by the broken arrows. You should have noted that the current
flow through *R*_{L} is always in the same direction.
In flowing through *R*_{L} this current develops a voltage
corresponding to that shown in the output waveform. Since current flows
through the load (*R*_{L}) during both half
cycles of the applied voltage, this bridge rectifier is a full-wave rectifier.

One advantage of a bridge rectifier over a conventional full-wave rectifier is that with a given transformer the bridge rectifier produces a voltage output that is nearly twice that of the conventional full-wave circuit.