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9.2.1.3. Rectifiers

Table of Contents

Turning AC into DC

A rectifier is a circuit that uses diodes to convert alternating current, AC, into current that flows mainly in one direction, DC. This is one of the most important practical uses of semiconductor diodes. Many electronic devices need a DC supply, but wall outlets usually provide AC. Rectifiers are the first step in changing that AC into usable DC.

The key idea is simple. A diode conducts easily in one direction and blocks current in the other direction. Because of this one way behavior, a diode can allow only selected parts of an AC waveform to pass.

Why Rectification Works

An AC voltage changes sign periodically. For a sinusoidal source,

$$
v(t) = V_0 \sin(\omega t)
$$

the voltage is positive during one half of the cycle and negative during the other half. A diode placed in series with a load will conduct during one half cycle and block during the other half cycle, depending on its orientation.

If the diode is forward biased during the positive half cycle, current flows through the load. During the negative half cycle, the diode is reverse biased and current is nearly zero.

A rectifier does not usually produce perfectly constant DC by itself. It produces a unidirectional but varying output. Smoothing often requires additional components such as capacitors, which belong to later circuit topics.

Half-Wave Rectifier

The simplest rectifier is the half wave rectifier. It uses one diode and a load resistor.

Half-wave rectifier

When the input voltage is positive enough to forward bias the diode, current flows and the output across the load is positive. When the input voltage becomes negative, the diode blocks and the output becomes nearly zero.

So the output is made only of one half of the input waveform.

Output Shape

If we idealize the diode as perfect, then

$$
v_{out}(t) =
\begin{cases}
V_0 \sin(\omega t), & \sin(\omega t) > 0 \\
0, & \sin(\omega t) < 0
\end{cases}
$$

With a real silicon diode, the output is smaller by about the forward voltage drop when conduction occurs.

For a real diode, the conducting output is approximately
$$
v_{out} \approx v_{in} - V_D
$$
where $V_D$ is about $0.7\,\text{V}$ for a silicon diode, when the diode is on.

Features of the Half-Wave Rectifier

The half wave rectifier is simple and cheap, but it is not very efficient. It uses only half of the AC cycle, so the output contains large gaps and strong ripple.

FeatureHalf-wave rectifier
Number of diodes1
Uses both half cyclesNo
Output smoothnessPoor
Circuit simplicityVery high

Full-Wave Rectification

A better approach is to use both halves of the AC input. This is called full wave rectification. In this case, the output across the load has the same polarity during both half cycles.

There are two common ways to do this. One uses a center tapped transformer and two diodes. The other uses a bridge of four diodes. The bridge rectifier is especially common.

Bridge Rectifier

A bridge rectifier uses four diodes arranged so that current through the load always has the same direction, even though the source polarity reverses every half cycle.

Bridge rectifier

During one half cycle, one pair of diodes conducts. During the next half cycle, the other pair conducts. In both cases, current passes through the load in the same direction.

Main Consequence

Because both halves of the AC wave are used, the output pulses occur twice as often as in half wave rectification. This makes the output easier to smooth.

If the input frequency is $f$, then the ripple frequency after full wave rectification is approximately

$$
f_{\text{ripple}} = 2f
$$

A full wave rectifier uses both half cycles of the input AC. This gives a larger average output and less ripple than a half wave rectifier.

Center-Tapped Full-Wave Rectifier

Another full wave design uses a center tapped transformer and two diodes. Each diode conducts during a different half cycle, and the transformer arrangement ensures the load current keeps the same direction.

This method works well, but it requires a special transformer with a center tap. Because of this, the bridge rectifier is often more convenient in many practical circuits.

Comparison of Rectifier Types

PropertyHalf-waveFull-wave, center tapBridge rectifier
Diodes needed124
Uses both half cyclesNoYesYes
Transformer requirementNone specialCenter tap neededNone special
Output rippleLargeSmallerSmaller
Common practical useSimple low power circuitsSome power suppliesVery common

Average Output Idea

The output of a rectifier is not constant, but it has a nonzero average value. That average value is what makes it useful as a DC source.

For an ideal half wave rectified sine wave, the average output voltage is

$$
V_{\text{avg}} = \frac{V_0}{\pi}
$$

For an ideal full wave rectified sine wave, the average output voltage is

$$
V_{\text{avg}} = \frac{2V_0}{\pi}
$$

where $V_0$ is the peak input voltage.

These formulas show that full wave rectification gives a larger DC level from the same peak AC input.

Important ideal averages for a sinusoidal input:
$$
V_{\text{avg, half}} = \frac{V_0}{\pi}, \qquad
V_{\text{avg, full}} = \frac{2V_0}{\pi}
$$

Real Diode Effects

In real circuits, diodes are not perfect. Their forward voltage drop reduces the output voltage. In a bridge rectifier, current typically passes through two diodes in each conducting path, so the total voltage loss is about

$$
2V_D
$$

for silicon diodes.

This means the peak output of a bridge rectifier is approximately

$$
V_{\text{peak,out}} \approx V_{\text{peak,in}} - 2V_D
$$

For small voltages, this loss can be significant.

Rectified Waveforms

The essential difference between the input and output waveforms is shown below.

Input AC and rectified outputs

Practical Use of Rectifiers

Rectifiers are found in power supplies, battery chargers, adapters, radios, and many household electronic devices. Their role is usually the first stage of AC to DC conversion. After rectification, other parts of the circuit may smooth and regulate the voltage.

For beginners, the central idea to remember is that the diode acts like a one way gate for current, and a rectifier arranges one or more diodes so that the load always receives current in the same direction.

Key Takeaway

Rectifiers use the one way conduction property of diodes to convert AC into unidirectional output. A half wave rectifier uses one half cycle only, while a full wave rectifier uses both half cycles and gives a better result. The bridge rectifier is especially important because it is widely used and does not require a center tapped transformer.

Core rule of rectification: arrange the diode or diodes so that current through the load always has the same direction, even when the source polarity reverses.

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