GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Efficient steady-state analysis based on matrix-free Krylov-subspace methods
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
Simulation of high-Q oscillators
Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
Global Optimization Applied to the Oscillator Problem
Proceedings of the conference on Design, automation and test in Europe
Parameter finding methods for oscillators with a specified oscillation frequency
Proceedings of the 44th annual Design Automation Conference
Periodic steady-state analysis augmented with design equality constraints
Proceedings of the conference on Design, automation and test in Europe
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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.