Noise Analysis of Nonautonomous Circuits

Abstract

In the previous chapter we developed a noise simulation and characterization technique for oscillators. We found that a mathematically consistent way of representing the output of a noisy oscillator is to view it as a sum of two stochastic processes: a small amplitude noise process arid a large signal output process which is the noiseless oscillator response phase shifted by a Brownian motion process. This new way of characterizing the oscillator output has far reaching impact on the methodology of performing noise simulation for circuits driven by these oscillators. The “traditional” approach for this is to view the oscillator output as a deterministic signal with some additive noise, classified as phase noise and amplitude noise. Therefore, for traditional noise analysis of nonautonomous circuits, it is assumed that the input signal noise can be viewed as a circuit noise source. Since the circuit is driven by a periodic input signal, the circuit response is also periodic. Traditional noise analysis techniques linearize the circuit equations around the periodic response and solve the resulting linear periodic time varying (LPTV) system of equations. Since the circuit is driven by a large periodic signal, the circuit noise statistics and the output noise statistics are also periodically time varying.