10.2 Rectifier circuits

Rectifier Types

Rectifier circuits convert AC (alternating current) into DC (direct current). Nearly every electronic device with a wall plug uses one, since the power grid delivers AC but most electronics run on DC. This section covers the main rectifier topologies, their key characteristics, and the components that improve their output.

Half-Wave and Full-Wave Rectifiers

A half-wave rectifier is the simplest rectifier: a single diode in series with the load. The diode only conducts during the positive half-cycle of the input AC waveform, so the output is zero for the entire negative half-cycle. That means you're only using 50% of the input signal, which makes it inefficient. You'll mostly see half-wave rectifiers in low-power or cost-sensitive applications.

A full-wave rectifier uses two diodes with a center-tapped transformer to conduct during both half-cycles. Each diode handles one half-cycle, and the center tap serves as the common return path. The result is a pulsating DC output that's present 100% of the time, roughly doubling the average output voltage compared to a half-wave rectifier for the same transformer secondary voltage.

Bridge Rectifiers

A bridge rectifier is a full-wave rectifier that doesn't need a center-tapped transformer. It uses four diodes arranged in a diamond (bridge) configuration.

Here's how it works:

1. During the positive half-cycle, two diodes (on opposite corners of the bridge) are forward-biased and conduct, routing current through the load in one direction.
2. During the negative half-cycle, the other two diodes conduct, routing current through the load in the same direction.
3. The load sees pulsating DC during both half-cycles, just like a center-tapped full-wave rectifier.

The bridge rectifier is the most common topology in practical power supplies (phone chargers, laptop adapters, battery chargers) because it's compact and uses the full transformer secondary winding, giving better transformer utilization than the center-tapped design. The trade-off is that two diodes are always in the current path, so you lose about twice the forward voltage drop (roughly $2 \times 0.7\,\text{V} \approx 1.4\,\text{V}$ for silicon diodes).

Rectifier Characteristics

Ripple Voltage

Ripple voltage is the small AC variation that remains on top of the DC output after rectification. It exists because the rectified waveform isn't perfectly flat; it rises and falls with each half-cycle.

• In a half-wave rectifier, the ripple frequency equals the input AC frequency (e.g., 60 Hz for a 60 Hz source), because there's one pulse per cycle.
• In a full-wave rectifier (center-tapped or bridge), the ripple frequency is twice the input frequency (e.g., 120 Hz), because there are two pulses per cycle.

Higher ripple frequency is actually easier to filter, which is one more reason full-wave rectifiers produce cleaner DC. Ripple can be reduced further with filtering components like smoothing capacitors and inductors (covered below).

Peak Inverse Voltage (PIV)

Peak inverse voltage (PIV) is the maximum reverse voltage a diode experiences when it's not conducting. If the reverse voltage exceeds the diode's PIV rating, the diode can break down and be destroyed.

PIV depends on the rectifier type:

• Half-wave rectifier: PIV equals the peak voltage of the AC input, $V_{\text{PIV}} = V_p$.
• Center-tapped full-wave rectifier: PIV is twice the peak voltage across each half of the secondary, $V_{\text{PIV}} = 2V_p$. This is because when one diode conducts, the full secondary voltage appears across the non-conducting diode.
• Bridge rectifier: PIV equals the peak secondary voltage, $V_{\text{PIV}} = V_p$, because the reverse voltage is shared across the bridge.

When selecting diodes, always choose a PIV rating with a comfortable margin above the expected maximum reverse voltage. A common rule of thumb is to pick a diode rated at least 1.5 to 2 times the calculated PIV.

Rectifier Components

Smoothing Capacitors

A smoothing capacitor (also called a filter capacitor) is connected in parallel with the load to reduce ripple voltage.

1. When the rectified voltage rises to its peak, the capacitor charges up to that peak value.
2. When the rectified voltage drops between pulses, the capacitor discharges through the load, filling in the "valleys."
3. The result is a much smoother DC output with smaller voltage fluctuations.

The size of the capacitor determines how much ripple remains. A larger capacitance stores more charge and keeps the voltage steadier between peaks, producing lower ripple. A smaller capacitance discharges faster, resulting in higher ripple but quicker response to sudden load changes. You can estimate the ripple voltage with:

$V_{\text{ripple}} \approx \frac{I_{\text{load}}}{f \cdot C}$

where $I_{\text{load}}$ is the load current, $f$ is the ripple frequency, and $C$ is the capacitance. This formula shows why full-wave rectifiers (with their doubled ripple frequency) need a smaller capacitor than half-wave rectifiers for the same ripple level.

Transformers

Transformers in rectifier circuits serve two purposes: they step the AC voltage up or down to the level needed by the circuit, and they provide electrical isolation between the mains supply and the output, which is critical for safety.

A transformer has two windings (primary and secondary) on a shared magnetic core. The primary connects to the AC source, and the secondary delivers the adjusted voltage to the rectifier. The voltage ratio follows:

$\frac{V_s}{V_p} = \frac{N_s}{N_p}$

where $N_s$ and $N_p$ are the number of turns on the secondary and primary windings.

A center-tapped transformer has a tap at the midpoint of the secondary winding, splitting it into two equal halves. This is what allows a two-diode full-wave rectifier to work: each half of the secondary feeds one diode, and the center tap acts as the ground reference. The downside is that only half the secondary voltage is available to each diode at a time, so you need a larger transformer for the same output voltage compared to a bridge rectifier.