This paper presents a technique for automated design and optimization of low-noise oscillators. A sensitivity analysis for oscillators guides the reduction of oscillator noise intensities and improvement of oscillator's immunity to noise. A design-oriented approach to circuit analysis efficiently handles design constraints and reduces the dimensionality of the optimization problem. The perturbation projection vector based phase noise computation makes the proposed optimization technique general and applicable to all types of oscillators, independent of circuit topology. Several examples illustrate the benefits of the new optimization approach.

A design-oriented periodic steady-state analysis is presented in this paper. The new analysis finds the values of circuit parameters that result in a desired circuit performance specified by a set of equality constraints. This is done by including the design equality constraints and the circuit parameters directly in the steady-state analysis as additional equations and unknowns. A time-domain finite difference method and the numerical implementation for the proposed analysis are described. Several examples demonstrate that the new analysis accurately and efficiently tunes circuit parameters that conform to a wide range of design specifications.

A new oscillator sensitivity analysis that predicts the impact of parameter variations of a VCO in a PLL is presented in this paper. Sensitivities of an oscillator's steady-state performance to design, process, or environmental parameter variations can be accurately and efficiently computed with the proposed analysis.

This paper presents an analysis for calculating sensitivities of an oscillator's periodic steady state and perturbation projection vector to design, process, or environmental parameters. A general continuous-time formulation and time-domain numerical methods are described. The applications of the oscillator sensitivity analysis in design optimization, macromodeling, as well as in analyzing the impact of process variations are demonstrated through examples.

This paper presents a generalized formulation of the periodic steady-state analysis for oscillators. The new formulation finds the value of a circuit parameter that results in a desired oscillation frequency for the circuit. Numerical methods based on the time-domain finite difference and shooting methods, and the frequency-domain harmonic balance method are described. Comparisons with search-based methods demonstrate the efficacy of the new approach.

This paper presents an analysis for calculating sensitivities of an oscillator’s periodic steady-state and perturbation projection vector to design, process, or environmental parameters. A general continuous- time formulation is described. Applications of the oscillator sensitivity analysis in design optimization and macromodeling are demonstrated through examples.

In this paper a modification of the time-domain periodic steady-state analysis for oscillators is presented. The proposed analysis finds the value of a circuit parameter that results in the circuit oscillating at a desired frequency. This analysis is based on the steady-state analysis for voltage and current controlled oscillators, i.e., replacing the oscillation period by a circuit parameter in the list of unknowns. A generalized formulation that can handle a control voltage or current, as well as any frequency-tuning circuit parameter, such as a tank capacitor or device geometry is developed in this paper.