There is a widespread belief that the stability of oscillators can be determined by the following criterion: "When the phase of the transfer function is zero and the magnitude (at the same frequency) is larger than one, then the system is unstable." For the circuit shown in Figure 1, this criterion is usually presented as two equations: arg(S_n) = -arg(S_r) (1) |S_n S_r| > 1 (2) where S_n = reflection coefficient of the circuits active part S_r = reflection coefficient of the resonator Moreover, Equations 1 and 2 are commonly related to the following steady-state oscillation conditions equations: arg(S_n) = -arg(S_r) (3) |S_n S_r| = 1 (4) Both sets of equations have been widely cited and incorporated in many software packages.
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