Nonlinear analysis of oscillators based on a slow-wave structure for phase-noise reduction

Abstract

An in-depth investigation of oscillators containing a slow-wave structure for phase-noise reduction is presented. The analysis is carried out by extracting a nonlinear admittance function from a harmonic-balance simulator, which is combined with the passive linear admittance of the delay network. As will be shown, a sequence of distinct oscillation curves is obtained when varying the time delay, which are generated and extinguished at Hopf bifurcations. The formulation provides insight into this complex pattern, resulting from the strong impact of the delaynetwork parameters on the steady-state oscillation. The mechanism for phase-noise reduction is understood with the aid of an analytical expression that enables an estimation of the delay required for a given phase-noise improvement. The methods have been successfully applied to a FET-based oscillator at 2.3 GHz.

Oscillators Based on Step-Impedance and Slow Wave Transmission Lines for Sensing Applications

“…which agrees with the sensitivity of the resonance frequency to  mut calculated in (13). For comparison, the variation of the resonance frequency  r versus  mut obtained with the standalone passive structures under n = 3 and n = 4 has been superimposed in Fig.…”

“…Using a passive structure with a high frequency selectivity, the oscillator will both exhibit a low phase noise and be able to track the variation of the structure resonance frequency with the MUT dielectric constant. Thus, this work extends [13] with the investigation of the possible use of oscillators based on step-impedance transmission lines [6]- [7] or on slow-wave structures [8]- [9], [14]- [18] to implement lowcost dielectric sensors. Emphasis will be placed on the standalone oscillator operation since, as stated, frequency and amplitude detection methods have been established in the literature.…”

“…6(a)]. In the oscillator based on a slow-wave structure of [13], a lower phase noise was achieved when connecting this structure to the gate node, so this is the node where the sensing structure will be introduced here [Fig. 6(b)].…”

“…The dielectric covers at least a part of these structures and very good results are obtained in transmission mode, for slow-wave structures [8]- [9], and reflection mode, for open-ended step impedance lines [6]- [7]. On the other hand, the work [13] presents a detailed analysis of oscillators containing a slowwave structure [14]- [18], which enables a low phase-noise spectral density. In fact, oscillator-based sensors [19]- [29] have the advantage of a self-sustained operation, in which the MUT variations give rise to a change in the oscillation amplitude and frequency [21]- [22], easily measured with the aid of amplitude or frequency detection interfaces; for instance, frequency variations can be detected from the control voltage of a synthesizer and amplitude variations by means of a power detector or through the control voltage of a feedback loop [10], [21], [25]- [28].…”

“…M 2 TMTT-2022-07-0982.R1 here as the derivative of this resonance frequency with respect to the dielectric constant. Then the structure will be connected to the oscillator active core, which will be modeled with a numerical nonlinear admittance function extracted from harmonic-balance (HB) simulations [13], [30]. This nonlinear admittance will be combined with the passive linear one of each sensing structure, initially described in an analytical manner.…”