Oscillator Stabilization Through Feedback With Slow Wave Structures

Abstract

This work presents a new formulation to predict the steady state, stability and phase-noise properties of oscillator circuits including either a self-injection network or a two-port feedback network for phase-noise reduction. The additional network contains a slow-wave structure that stabilizes the oscillation signal. Its long delay inherently gives rise to multivalued solutions in some parameter intervals, which should be avoided for a reliable operation. Under a two-port feedback network, the circuit is formulated extracting two outer-tier admittance functions, which depend on the node-voltage amplitudes, phase shift between the two nodes and excitation frequency. Then, the effect of the slow-wave structure is predicted through an analytical formulation of the augmented oscillator, which depends on the numerical oscillator model and the structure admittance matrix. The solution curves are obtained in a straightforward manner by tracing a zero-error contour in the plane defined by the analysis parameter and the oscillation frequency. The impact of the slow-wave structure on the oscillator stability and noise properties is analyzed through a perturbation method, applied to the augmented oscillator. The phase-noise dependence on the group delay is investigated calculating the modulation of the oscillation carrier. The various analysis and design methods have been applied to an oscillator at 2.73 GHz, which has been manufactured and measured, obtaining phase-noise reductions of 13 dB, under a one-port load network, and 18 dB, under a feedback network.

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

“…It can be reduced with the aid of a highquality factor element, such as a dielectric resonator, a delay line or a slow-wave structure. This can be placed in an external self-injection loop added to an existing oscillator [1]- [3] or be a constitutive part of the oscillator circuit [4]- [5]. In the selfinjection case [1]- [3], the external loop usually contains a circulator, a power divider, and an attenuator, so only a small fraction of the delayed signal is injected into the oscillator.…”

Analysis of a self-oscillating mixer based on a slow-wave structure

“…3(b), where it is compared with the experimental one, obtained with the R&S FSWP8 Phase Noise Analyzer. It is significantly lower than those obtained without the slow-wave structure in oscillators based on the same device (see the spectrum in [7] with -80 dBc at 100 kHz). Nevertheless, a higher spectra purity might be possible with other slow-wave structures.…”

“…In slowwave structures, a low phase velocity is achieved by increasing the effective capacitance and/or inductance of the line, implemented in practice through different strategies [5]- [6]. In prior works, slow-wave structures have been used in freerunning oscillators [6]- [7] but, to the best of our knowledge, they have not been considered yet for SOM design.…”

Double Functionality Concurrent Dual-Band Self-Oscillating Mixer

“…As in the single-frequency VCO of [15], two transistor devices are connected to two of the resonator ports. Our goal has been to obtain a demonstrator independent resonance modes at the incommensurate frequencies f1 = 2.4 GHz and f2 = 4.1 GHz; these values enable a comparison of the phase-noise spectral density with previous singlefrequency realizations [32]- [33] using similar components. The resonator design departs from the structure sketched in Fig.…”