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

Abstract

This work investigates the capabilities of oscillators based on step-impedance and slow-wave structures to sense dielectric constants. The material under test (MUT) is placed over the structure and the objective is to achieve a high sensitivity of the oscillation frequency with the advantage of a low phase noise, enabled by the high-quality factor of the structure. With the aid of simplified analytical models, we will initially study the variation of the resonance frequency of a step-impedance transmission line with the dielectric constant of the MUT, paying attention to the influence of the number of line sections. The study includes the derivation of analytical expressions for the sensitivity of the resonance frequency. Next 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. The resulting semi-analytical formulation will provide insight into the variation of the oscillation frequency and amplitude with the dielectric constant of the MUT, as well as the variation of the phase-noise spectral density. It will also enable a versatile test and optimization of the various structures to achieve a high sensitivity with a low phase noise. The methods have been successfully applied to a FET-based oscillator at about 2 GHz.

Analysis of the Nonlinear Dynamics of an Injection-Locked Dual-Mode Oscillator

“…The comparison is carried out with an empty deposit and with a deposit full of water. In the two cases, the injection locking gives rise to a reduction of the spectral density, as theoretically demonstrated in [14]. This reduction is a significant advantage of the injection-locked regime.…”

“…In turn, the analyses of [9] rely on an empirical estimation of the oscillator quality factor from the locking bandwidth, so they are approximate. In fact, the locking band of a transistor-based oscillator has more complex dependences [10], [11], [12], [13], [14], [15], [16], [17], involving the device nonlinearities and the entire passive linear network. For a more realistic prediction, Sancho et al [18], devoted to a single-frequency injection-locked oscillator, make use of a semianalytical formulation, based on the linearization of the oscillator circuit about its free-running solution.…”

“…The sensing function (15) is calibrated by varying the percentage p of ethanol from 10 to 100 in tens. For each p, the parameters f and BW in(14) are obtained from measurements. The corresponding ε M and tanδ values (dots) are obtained from published values.…”