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High-Efficiency mmW/THz Oscillator Design - 2: Some Historic Perspectives

10 Jun 2018

Turns out that people have been thinking about this problem from very early on.

In 1968, Vehovec documented in his book a method for optimizing the output power of a transistor oscillator circuit. He formulated the problem in terms of the complex voltage gain across the transistor. Shown in the following figure, a transistor oscillator is considered as a combination of an active device and a passive feedback network. The ratio between the voltage at the output and the input port of the active device is defined as the voltage gain. In the steady state, we use phasors to represent the voltages and therefore the voltage gain is complex.

\begin{equation} A=A_R+jA_I=\frac{V_2}{V_1}, \end{equation} where $A_R$ and $A_I$ are the real and imaginary parts of $A$, respectively.

2-port Description of a Feedback Oscillator

Let $y_{ij}=g_{ij}+jb_{ij}$ denote the Y-parameters of the network. By definition,

The power flowing from the two-port network can be found by

If we assume that $V_1$ is a constant with respect to $A$, then $P_R$ can be normalized

Eqn. 3 shows that the power $P_R$ forms a paraboloid with respect to the real and imaginary parts of the complex voltage gain. Maximum value of $P_R$ is reached at the apex of the paraboloid, and the corresponding optimum complex voltage gain is given by

2-port Description of a Feedback Oscillator