Mason's Invariant - Importance

Importance

Mason's Invariant, or U, is the only device characteristic that is invariant under lossless, reciprocal embeddings. In other words, U can be used as a figure of merit to compare any three-terminal, active device. For example, a factory producing BJTs can calculate U of the transistors it is producing and compare their quality to the other BJTs on the market. Furthermore, U can be used as an indicator of activity. If U is greater than one, the two-port device is active; otherwise, that device is passive. This is especially useful in the microwave engineering community. Though originally published in a circuit theory journal, Mason's paper becomes especially relevant to microwave engineers since U is usually slightly greater to or equal to one in the microwave frequency range. When U is smaller than or considerably larger than one, it becomes relatively useless.

While Mason's Invariant can be used as a figure of merit across all operating frequencies, its value at ƒ_max is especially useful. F_max is the maximum oscillation frequency of a device, and it is discovered when . This frequency is also the frequency at which the maximum stable gain G_ms and the maximum available gain G_ma of the device become one. Consequently, ƒ_max is a characteristic of the device, and it has the significance that it is the maximum frequency of oscillation in a circuit where only one active device is present, the device is embedded in a passive network, and only single sinusoidal signals are of interest.