Large signal design of broadband monolithic microwave frequency dividers and phase-locked oscillators

Abstract

International audienceThis paper presents a design method for phaselocked devices such as frequency dividers or injection-locked oscillators. The method requires a full nonlinear analysis of the circuit. This analysis relies upon harmonic balance techniques and is suitable for monolithic circuits simulation. First, a modified formulation of the general harmonic balance equation is proposed which includes the presence of probes. These probes allow us to suppress the degenerated solution of the HB equation in autonomous cases. Moreover, a global stability analysis of phaselocked regimes is carried out. It provides invaluable information on the nonlinear behavior of the device. In particular, synchronization bandwidths as well as power ranges for which the circuit can be synchronized are obtained from the stability loci drawn in the parameter space. All these features have been used to design a broadband monolithic frequency divider, and the simulated and experimental results have been compared with very good accuracy. Therefore, the method proposed is a very useful tool for the design of potentially unstable circuit

A Novel Substitution Algorithm for the Efficient Analysis and Optimisation of Microwave Oscillators

“…This problem may be tackled by continuation with artificial embedding [1], [2], inclIusion of the Kurokawa condition in the HB system [5], and optimisation [6]. In this paper we propose a method based on the substitution algorithm and on the principles of bifurcation theory.…”

“…Convergence of the HB analysis to a degenerate solution may cause startup difficulties and seriously degrade the efficiency of the design process. Several attempts to circumvent this problem have been proposed, including continuation methods with artificial embedding [ 1], [2], and backup algorithms for the generation of an initial oscillatory regime from which the Newton iteration-based optimisation may be started [3]. In this paper we propose a much more efficient method based on a new algorithmic concept that will be conventionally referred to as a substitution algorithm.…”

“…All the difficulties related to the existence of degenerate solutions are effectively suppressed in this way, and the performance of the optimisation algorithm is very significantly improved. The new oscillator topology defined by the updated Q at a generic step of the optimisation must satisfy two constraints: it must oscillate at the prescribed fundamental frequency, wo, with a power level defined by the magnitude of the reference harmonic, M. The solution of (2) for the given Q, M provides the values of U, T that allow these conditions to be met. Thus U, T have the meaning of power and frequency tuning parameters.…”

A novel approach to the analysis of microwave regenerative analog frequency dividers

“…Based upon Volterra series analysis, the determining equation for an analog 1/3 frequency divider may be derived as (4) where is the Volterra kernel of th order [5]. Note that is simply the input impedance of the nonlinear subcircuit in the absence of nonlinearities.…”

“…These components include injection-locked oscillators and frequency dividers. A number of reports have been published on the analysis of injection-locked oscillators including time-domain methods [2], frequency-domain methods [3], and harmonic balance algorithms [4]. In this letter, a simple, fast, and general approach to the analysis of regenerative analog frequency dividers based upon the Volterra series method is presented.…”