Steady-state analysis of voltage and current controlled oscillators

This paper introduces the problem of finding the steady-state and the numerical value of the controlling voltage or current for oscillators where the frequency of oscillation is known beforehand. These situations are very common when the oscillator is part of a phase-locked loop (PLL). In PLLs, the reference frequency as well as the divide ratios are known at the time of design. Therefore the desired frequency of the voltage (current) controlled oscillator is known but not the controlling voltage (current). We formulate this problem as the solution of an appropriate nonlinear equation. We present robust and efficient numerical techniques for solving this nonlinear equation both in time and frequency domain. We demonstrate using experimental results that this technique is at par with classical methods of calculating oscillator steady-state and period of oscillation for a given control voltage. We show that compared to a search-based approach to calculating the desired control voltage or current, our direct method is a order of magnitude faster for the same accuracy.