Close-in Phase Noise of a Digitally Tuned VCO

Here we present analysis and simulation of the close-in phase noise of a digitally tuned VCO, tunable only in discrete frequency steps. By rapidly tuning between two closely spaced discrete frequencies with a variable duty cycle any average frequency can be achieved. This process will result in increased phase noise and spurs if a strictly periodic duty cycle modulation is used. Ideally a randomly varying digital control signal with the appropriate duty cycle should be used to eliminate spurs and smooth the close-in phase noise. Here we use continuous-phase-frequency-shifting-key (CPFSK) modulation results from communication theory to analytically predict the effect of a random modulation at 50% duty cycle. Next the use of a sigma-delta modulator to produce a randomly varying digital signal with continuously variable duty cycle is simulated and compared to our analytical result. The use of a simple repetitive duty cycle modulation produced by a phase detector controlling the VCO in a PLL is also investigated. We present a comparison of the close-in phase noise for these possible approaches to the realization of an all digital PLL and demonstrate the improvement possible with the use of sigma-delta modulation.