Frequency Scaling of Passive Voltage Gain in 1-Port VHF Quartz Resonators

Abstract

This paper examines 1-port thickness-shear mode quartz resonators for use in RF wake-up receiver (WUR) front-ends within the very high frequency (VHF) range up to 200 MHz. Although RF voltage gain has been demonstrated in these devices only at frequencies ≤ 76 MHz to date, models and measurements in this work indicate that they provide high voltage gain and interference rejection over a broad frequency range. To assess performance, this work examines devices with varying frequency (50-200 MHz), geometry, and shunt capacitance, focusing on designs with moderate gain or higher (≥ 10 V/V) at load impedances around the input impedance of a near-zero-power envelope detector (around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{\mathrm {L}} =10\,\,\text{M}\Omega \vert \vert C_{\mathrm {L}} =120$ </tex-math></inline-formula> fF). An active probe presents these load impedances while precisely measuring voltage gain and quality factor ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q_{\mathrm {m}}$ </tex-math></inline-formula> ). Overall, loaded gain, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q_{\mathrm {m}}$ </tex-math></inline-formula> , and figure of merit (FoM) measurements validate model predictions. Furthermore, devices around 200 MHz demonstrate higher <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q_{\mathrm {m}}$ </tex-math></inline-formula> than previously predicted. Voltage gain 140 V/V is demonstrated at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{\mathrm {r}} \approx ~184.5$ </tex-math></inline-formula> MHz, the highest gain directly measured in a piezoelectric microresonator in this frequency range. Subject to post-fabrication variation, these results are repeatable within a commercial quartz process, enabling widespread utility of this technology. [2021-0133]