Decoders usually come with varying amounts of function wires for control of various lights and other electrically-operated devices on the loco and train. Most of the them also have a blue (common) wire that provides full-wave power for the function wire to use.

Because of size constraints, some decoders come without the blue wire. In this case, power from one of the rails is used to power the device. Further, some people are tempted to wire lights this way, because of the way the bulbs are designed into the loco, even when the blue wire is available.

Wiring this way is called Half-Wave. This term is used because it describes the portion of electricity a function gets when wired to only one rail. So what does full-wave/half-wave really mean?

The track provides square-wave AC power. One rail has one half of the "full-wave" of that power, the other rail has the other half. A full-wave bridge rectifier inside the decoder converts this AC power to DC. The blue wire is connected to the "+" terminal of that bridge rectifier. When the function wire sinks that power, it is sinking full-wave power. If you wire a bulb or other device directly to one rail, instead of the blue wire, that device will only be getting half of the full AC wave - hence, Half Wave.

Half-Wave wiring is NOT recommended unless there absolutely is no other way. Because the device (bulb) will be getting power from only one rail, that power will vary if an analog loco is run at the same time. Even though you're controlling an analog loco, the manipulation of track voltage for that analog control will affect all Half-Wave-powered lights.

When controlling an analog loco, power on the rails is manipulated in a way that will increase and decrease voltage between the rails. To make an analog loco go one way, one rail increases while the other decreases. To make it go the other way, the other increases while the first decreases. This means that the rail the half-wave bulb is connected to will determine whether the bulb gets brighter or dimmer as the analog loco's speed is increased and decreased.

Any type of diode that can handle the voltage and amperage of the functions (bulbs) will do. Notice that the stripe on each diode is away from the rails. This allows the voltage from one rail to feed the bulbs when positive is on that rail, and voltage from the other rail to feed the bulbs when positive is on that rail - both halves: Full-wave. Remember, the rail has AC voltage, which means polarity alternates back and forth between positive and negative.