20.2.2 Full Wave Rectification | Alternating Current | Physics 12

What is Full-Wave Rectification?

Full-wave rectification converts both the positive and negative half-cycles of an AC input into a unidirectional (DC) output. Unlike half-wave rectification, no part of the input waveform is wasted, resulting in higher efficiency and a smoother output.

The Bridge Rectifier

The most common full-wave rectifier circuit is the bridge rectifier, which uses four diodes ( $D_{1}$ , $D_{2}$ , $D_{3}$ , $D_{4}$ ) arranged in a bridge configuration. It does not require a centre-tapped transformer.

Circuit Operation

During the positive half-cycle of the AC input:

Diodes $D_{1}$ and $D_{2}$ are forward biased and conduct.
Diodes $D_{3}$ and $D_{4}$ are reverse biased and do not conduct.
Current flows through the load $R_{L}$ in a fixed direction.

During the negative half-cycle of the AC input:

Diodes $D_{3}$ and $D_{4}$ are forward biased and conduct.
Diodes $D_{1}$ and $D_{2}$ are reverse biased and do not conduct.
Current still flows through the load $R_{L}$ in the same fixed direction.

In both half-cycles, two diodes conduct in series, so the voltage drop across the load is: $V_{l o a d} = V_{in} - 2 V_{D}$ where $V_{D} \approx 0.7 V$ is the forward voltage drop of each diode.

Output Frequency

Because both half-cycles are utilised, the output pulsates twice per input cycle. If the AC input frequency is $f$ , the output ripple frequency is: $f_{o u t} = 2 f$ For a 50 Hz supply, the ripple frequency is 100 Hz.

Advantages over Half-Wave Rectification

Property	Half-Wave	Full-Wave (Bridge)
Diodes used	1	4
Output frequency	$f$	$2 f$
Efficiency	~40.6%	~81.2%
Ripple	High	Lower

The Smoothing Capacitor

The output of a bridge rectifier is a pulsating DC — it rises and falls with each half-cycle. A smoothing capacitor $C$ is connected in parallel with the load $R_{L}$ to reduce these ripples.

How It Works

Charging phase: When the rectified voltage rises toward its peak, the capacitor charges up to the peak voltage $V_{p e ak}$ .
Discharging phase: When the rectified voltage falls below $V_{p e ak}$ , the capacitor discharges through the load, maintaining the output voltage at a nearly constant level.
The capacitor then recharges on the next peak, and the cycle repeats.

The result is a nearly steady DC voltage with a small residual ripple voltage $Δ V$ .

Factors Affecting Smoothing

Larger capacitance $C$ : Slower discharge → smaller ripple → smoother output.
Larger load resistance $R_{L}$ : Slower discharge → smaller ripple.
Higher ripple frequency (full-wave vs half-wave): Less time between peaks → capacitor discharges less → inherently smoother output.

The ripple voltage is approximately: $Δ V \approx \frac{I}{f _{r i ppl e} \cdot C} = \frac{V _{D C}}{f _{r i ppl e} \cdot R _{L} \cdot C}$

where $I$ is the load current and $f_{r i ppl e}$ is the ripple frequency.

The Bridge Rectifier

The most common full-wave rectifier circuit is the bridge rectifier, which uses four diodes (

D_{1}

D_{2}

D_{3}

D_{4}

) arranged in a bridge configuration. It does not require a centre-tapped transformer.

During the positive half-cycle of the AC input:

Diodes

D_{1}

and

D_{2}

are forward biased and conduct.

Diodes

D_{3}

and

D_{4}

are reverse biased and do not conduct.

Current flows through the load

R_{L}

in a fixed direction.

During the negative half-cycle of the AC input:

Diodes

D_{3}

and

D_{4}

are forward biased and conduct.

Diodes

D_{1}

and

D_{2}

are reverse biased and do not conduct.

Current still flows through the load

R_{L}

in the same fixed direction.

In both half-cycles, two diodes conduct in series, so the voltage drop across the load is:

V_{l o a d} = V_{in} - 2 V_{D}

where

V_{D} \approx 0.7 V

is the forward voltage drop of each diode.

Because both half-cycles are utilised, the output pulsates twice per input cycle. If the AC input frequency is

f

, the output ripple frequency is:

f_{o u t} = 2 f

For a 50 Hz supply, the ripple frequency is 100 Hz.

Property	Half-Wave	Full-Wave (Bridge)
Diodes used	1	4
Output frequency	$f$	$2 f$
Efficiency	~40.6%	~81.2%
Ripple	High	Lower

The Smoothing Capacitor

The output of a bridge rectifier is a pulsating DC — it rises and falls with each half-cycle. A smoothing capacitor

C

is connected in parallel with the load

R_{L}

to reduce these ripples.

Charging phase: When the rectified voltage rises toward its peak, the capacitor charges up to the peak voltage

V_{p e ak}

Discharging phase: When the rectified voltage falls below

V_{p e ak}

, the capacitor discharges through the load, maintaining the output voltage at a nearly constant level.

The capacitor then recharges on the next peak, and the cycle repeats.

The result is a nearly steady DC voltage with a small residual ripple voltage

Δ V

Larger capacitance $C$ : Slower discharge → smaller ripple → smoother output.

Larger load resistance $R_{L}$ : Slower discharge → smaller ripple.

Higher ripple frequency (full-wave vs half-wave): Less time between peaks → capacitor discharges less → inherently smoother output.

The ripple voltage is approximately:

Δ V \approx \frac{I}{f _{r i ppl e} \cdot C} = \frac{V _{D C}}{f _{r i ppl e} \cdot R _{L} \cdot C}

where

I

is the load current and

f_{r i ppl e}

is the ripple frequency.