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A TRIAC is a three terminal device that can operate an AC load, either in On-Off mode, or in modulated mode, such as in a lamp dimmer.

The three terminals are M1, M2, and Gate. The AC source and load are connected in series with M1 and M2. If the Gate is held near the voltage of M1, the device does not turn on. If the Gate voltage is towards the direction of M2, the device turns on. Once the device turns on, it stays on for the duration of that line cycle, i.e. until the voltage between M1 and M2 reverses.

The actual trigger point varies depending on the specific device, so you need to look it up in the specifications for the device.

Note that the positive going trigger point is often not the same magnitude as the negative going trigger point. This can cause asymmetry in the output power, leading to a DC bias that is often not desired. Most designs compensate for this by providing another TRIAC operating in DIAC mode (or just a DIAC) in series with the Gate.

The DIAC is simply a TRIAC with the Gate connected to M2. This mode will trigger based on M2, rather than on Gate, and is symmetrical. Using a DIAC as the trigger for a TRIAC will balance the output waveform, minimizing DC bias.

If you design the controlling circuit so that the trigger point in the cycle is adjustable, you get a variable voltage switch, i.e. dimmer, that can be used for various things. The advantage of this over a rheostat, is that the TRIAC is fully conducting when it is turned on, so the power dissipated by it is relatively small, because the voltage differential is small, whereas a rheostat would need to dissipate at least half the expected power of the load.

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