A highly accurate measurement of resonator Q-factor and resonance frequency

Abstract

The microwave cavity perturbation method is often used to determine material parameters (electric permittivity and magnetic permeability) at high frequencies and it relies on measurement of the resonator parameters. We present a method to determine the Q-factor and resonance frequency of microwave resonators which is conceptually simple but provides a sensitivity for these parameters which overcomes those of existing methods by an order of magnitude. The microwave resonator is placed in a feedback resonator setup, where the output of an amplifier is connected to its own input with the resonator as a band pass filter. After reaching steady-state oscillation, the feedback circuit is disrupted by a fast microwave switch and the transient signal, which emanates from the resonator, is detected using down-conversion. The Fourier transform of the resulting time-dependent signal yields directly the resonance profile of the resonator. Albeit the method is highly accurate, this comes with a conceptual simplicity, ease of implementation and lower circuit cost. We compare existing methods for this type of measurement to explain the sensitivity of the present technique and we also make a prediction for the ultimate accuracy for the resonator Q and f 0 determination.

Heating Causes Nonlinear Microwave Absorption Anomaly in Single‐Walled Carbon Nanotubes

“…It is based on irradiating the cavity on resonance with microwaves for about 5 À 10 Â τ in a pulsed manner. [28,29] During this time, the cavity accumulates a sizeable energy from the microwave irradiation and stores it. The cavity starts to emit the stored energy immediately following the switch off, whose time decay envelope is an exponential function with the time constant τ.…”

Review of Resonator’s Q-Factor Measurement With Focus on Design of Analog and Mixed Circuits for In-Situ Measurement

“…A single frequency excitation is used to put the resonator into vibration, which can be done either by an external pulsed source in an open loop [21] (Fig. 9) or by a feedback system in a closed loop [14] (Fig. 10) by using a signal amplifier to ensure certain phase shift requirement.…”

“…To simplify the frequency-domain measurement, the mixed approach is proposed [7], [13]- [14]. A single frequency operation is used instead of a frequency sweeping.…”

Ultrafast sensing of photoconductivity decay using microwave resonators

“…The cavity is undercoupled for both the input and output (β input ≈ β output ≈ 1/3) which represents a compromise between the resonator bandwidth and transmitted signal 20 . The parameters of the resonator are measured with the transient method 31,32 : the exciting microwaves are pulsed, which forces the cavity to transmit microwaves in a transient state. Although the exciting carrier frequency, f LO , does not necessarily match the resonator eigenfrequency, still the transient signal oscillates on the resonant frequency of the cavity, f 0 .…”