Abstract
This article 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.
Highlights
PHASE noise is an undesired characteristic of oscillator circuits, which degrades their spectral purity and can give rise to demodulation errors [1]-[3]
The recent work [11] uses the slow-wave structure as an external network, in a manner similar to what is done in [4]-[10] with long cables and delay lines. As in those previous works, the aim is to increase the oscillator quality factor, which is enabled by the high group delay of the slow-wave structure
The phase-noise reduction is achieved through a suitable synthesis of the slow-wave structure only, without having to redesign the oscillator circuit
Summary
PHASE noise is an undesired characteristic of oscillator circuits, which degrades their spectral purity and can give rise to demodulation errors [1]-[3]. The recent work [11] uses the slow-wave structure as an external network, in a manner similar to what is done in [4]-[10] with long cables and delay lines. Note that instability problems resulting from the use of long delay lines and high quality-factor resonators have been reported in previous works [4], [17] For this optimization, a new methodology is presented here, which departs from accurate numerical models of both the oscillator and the slow-wave structure. In comparison with the previous work [11], two different ways to introduce the slow-wave structure are considered: as a one-port configuration, connected to the oscillator output, and as an external two-port feedback network.
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