TABLE OF CONTENTS We now consider autonomous circuits, ones that have no external RF excitation. (They do have dc bias, however. ) In practice, sinusoidal oscillators are the only autonomous circuit we regularly deal with. Although much of the theory in Section 6.2 is useful in the analysis of oscillators, such circuits have a special set of problems that we must address.
As with nonautonomous circuits, our approach is to perform a nonlinear analysis, linearize it, and perform the noise analysis of the linearized, time-varying circuit. The first problem involves the nonlinear analysis, where we face three fundamental difficulties. First, all oscillatory circuits have a zero solution; that is, a nonoscillating state satisfies the circuit equations. Unless we do something special to avoid it, a harmonic-balance analysis of an oscillator (as well as a time-domain analysis) invariably finds this zero solution and blithely terminates the solution process. In effect, we are dealing with a circuit that, by its very nature, has multiple solutions. Circuit simulators do not deal with such circuits very well, partly because of their inability to read the user's mind and determine which solution he is interested in. [3] Second, the initial phase of the solution is indeterminate. In nonautonomous circuits, the phase is defined by the excitation, but in oscillators, any value of phase is acceptable; there is no inherent zero value of time. This lack of a time reference and the resulting indeterminacy of the solution implies...
