Rectifiers

Wall sockets supply alternating voltage, but phone chargers and radios need direct current. A diode, which only lets current through one way, is the first step in converting one into the other.

Half-wave rectifier#

A rectifier turns an alternating voltage into a one-way (direct) voltage. The simplest has an AC source, one diode and a load resistor R in series. Let the source voltage be V = V₀ sin ωt.

• Positive half-cycle: the diode is forward-biased, so its resistance R_j is small. The current is i = V₀ sin ωt/(R + R_j) ≈ (V₀/R) sin ωt, and nearly the whole source voltage appears across R.
• Negative half-cycle: the diode is reverse-biased and its resistance is huge, so the current is practically zero.

The load current always flows the same way, but only for half of each cycle: half-wave rectification.

Full-wave rectifier#

To use both halves, take the AC from a transformer secondary with a centre tap C. Each end, A and B, goes through its own diode (D₁ and D₂) to a common point E, and the load sits between E and C.

• When A is positive relative to C (and B negative), D₁ conducts and D₂ blocks: current flows A → D₁ → E → load → C.
• Half a cycle later B is positive: D₂ conducts and D₁ blocks: current flows B → D₂ → E → load → C.

Either way the current goes through the load from E to C. The output is a train of positive humps, twice as many as before.

Average output

Averaged over a cycle, a half-wave output gives V₀/π, and a full-wave output 2V₀/π. Real silicon diodes need about 0.7 V before they conduct well, which trims a little off every hump. In practice a large capacitor across the load smooths the humps into a nearly steady voltage.