Oscillation Modes in Multiresonant Oscillator Circuits

Abstract

An in-depth analysis of the oscillation modes in freerunning oscillators loaded with multi-resonance networks is presented. The analysis illustrates the mechanisms for the generation and stabilization of the various periodic modes and establishes the conditions for existence of a single stable periodic mode in distinct regions of the parameter plane. The mechanisms for the generation and stabilization of quasi-periodic regimes, with two concurrent oscillations, are also analyzed, considering different situations in terms of two relevant poles. The stability analysis of quasi-periodic solutions, derived in terms of admittance functions, can be applied to circuits simulated with harmonic balance, under the assumption of high quality factor resonators. The impact of the transistor biasing on the stability properties of the quasi-periodic regimes has been analyzed, demonstrating that it can be used to isolate the quasi-periodic solution from the periodic ones. The analysis procedures have been applied to a practical oscillator based on two cross-coupled transistors at the two frequencies 900 MHz and 2.5 GHz. The case of two independent oscillations operating in a synchronized regime is also analysed, as well as its impact on the phase-noise behavior.

Double Functionality Concurrent Dual-Band Self-Oscillating Mixer

“…2(a) where the results of system (2) have been validated with a harmonic-balance (HB) simulation of the circuit in Fig. 1, with the aid of an AG [8], [23]…”

“…In the concurrent dualfrequency zero-IF SOM, each oscillation gets locked to its corresponding RF signal [4], so the circuit behaves as a concurrent dual-frequency injection-locked oscillator. A major challenge in the design of concurrent dual-frequency oscillators is the robustness of this concurrent operation mode [8], which mathematically coexists with two periodic solutions, at ω1 and ω2, respectively, and with the DC solution. For a reliable concurrent operation, the quasiperiodic solution at ω1 and ω2 must be the only stable one.…”

Pole-Zero Identification: Unveiling the Critical Dynamics of Microwave Circuits Beyond Stability Analysis

“…A comprehensive description of most relevant local bifurcations in microwave circuits and their link to the crossing of the poles through the imaginary axis on the complex plane is given in [41]. Bifurcation-detection techniques (such as those based on the Auxiliary Generator technique [34]) through harmonic-balance simulations are often combined with the tracing of pole trajectories on the complex plane to study the stability of solution curves [42]- [47], which provides an insightful knowledge of the dynamic behavior of the autonomous circuit. As an example, in [43], a closed-form formulation for the optimized design of coupled oscillators has been presented.…”

“…Bifurcation analysis combined to pole-zero identification can be found in many other papers that carry out detailed investigations of the dynamic behavior of non-linear autonomous circuits, such as multi-resonant free-running oscillators [42]; varactor-based frequency dividers and multipliers [44], ring oscillators [46], and non-linear transmission line based oscillators [47]. Fig.…”

“…Thus, it is perfectly fitted for use in combination with conventional microwave simulators as Advanced Design System (ADS) or Microwave Office (MWO). Pole-zero identification has been increasingly used ever since to analyze the stability of active microwave circuits, mainly amplifiers [10]- [16], but also oscillators [17]- [18], frequency dividers [19]- [20] or even non-Foster circuits [21]. Perhaps the most attractive features of pole-zero identification for stability are its simplicity (it is actually a probe-based method) and the graphical and intuitive nature of the results: whenever a pair of complex conjugate poles is found lying on the Right-Half Plane (RHP), i.e.…”