Stability Analysis of Oscillation Modes in Quadruple-Push and Rucker's Oscillators

Abstract

Oscillator systems composed by sub-oscillators coupled through a symmetric linear network enable the combination of output power at the first or th harmonic component of the oscillation frequency of each sub-oscillator. However, they have the drawback of a possible coexistence of different oscillation modes, which limits their practical application. This paper presents an in-depth stability analysis of coexisting steady-state solutions in Rucker's oscillator and -push oscillators. Criteria are provided to avoid undesired oscillation modes. The coupled system is described by means of a semianalytical formulation based on numerical models of the active subcircuits, extracted from harmonic-balance (HB) simulations. Each active subcircuit is composed by the transistor(s), feedback elements, and termination load. The use of the HB numerical models allows a realistic prediction of the behavior of the globally coupled oscillator. Alternatively, a graphical technique is provided to obtain the different oscillation modes using full HB simulations. The perturbation of the reduced-order nonlinear system enables the stability and phase-noise analysis of the steady-state oscillatory solutions. In the derived formulation for phase-noise analysis, both flicker-and white-noise perturbations are considered. The different techniques have been applied to a Rucker's oscillator at 3.9 GHz and a quadruple-push oscillator at 15.6 GHz.

Harmonic-balance design and analysis of an injection-locked push-push oscillator

“…However, as was demonstrated in [3], oscillation modes that are different to the adequate one for an N-push oscillator (push-push oscillator is the case for 2 N = ) can coexist for the same values of the circuit parameters. The coexistence of these solutions will require the identification and further stabilization of the desired oscillation mode [4]. Therefore, despite the mentioned advantages of N-push topologies and due to the complexity of the required design procedure, that is necessary to ensure the proper operation mode, the utilization of these oscillators has not been investigated for other applications.…”

“…Here, and following the design procedures presented in [2] and [4], the application of push-push oscillators is extended to the synchronized case. In this particular circuit, and taking into account that the output frequency of the push-push oscillator is twice the original oscillation frequency, a frequency doubler is proposed by appropriately synchronizing the oscillator with an external signal.…”

“…The behavior of the circuit is analyzed using harmonic balance (HB) techniques and the results are compared for validation with time-domain simulations. The stability of the desired oscillation mode is verified using the technique proposed in [4] and through pole-zero identification [10]. The phase noise of the frequency doubler, based on the push-push oscillator, will be also analyzed.…”

A Low Power Push-Push Differential Vco Using Current-Reuse Circuit Design Technique

“…It has been shown [13] that the near-carrier phase noise is reduced to 1/2 that of a single oscillator for two oscillators coupled by a reciprocal coupling network. An improvement of the phase noise of both the Rucker and quadruplepush oscillators, using four sub-oscillators coupling by a star and a ring coupler respectively with respect to a single oscillator, obtained by replacing the coupling network with a short-circuit termination, has been observed [14]. The differential cross-coupled VCO has a medium phase noise performance.…”

“…The QVCO in the proposed circuit uses both the quadruple-push coupling technique and BJT coupling methods to minimize the phase noise of QVCO and improve the phase accuracy. The quadruple-push coupling technique is a passive low phase noise coupling technique similar to the method in [14], and the BJT coupling is also a low-phase noise approach similar to the method in [13]. Because the BJT is a bulk device, the parasitic BJT coupling technique is better than the parallel nMOSFET coupling and has lower flicker noise than the surface-channel nMOSFET.…”