Perturbation Analysis of Nonlinearity in Radio-Frequency Bulk Acoustic Wave Resonators Using the Mass-Spring Model.

This article describes derivation of an equivalent circuit for nonlinear responses in film bulk acoustic resonators from the first-order perturbation analysis using the piezoelectric constitutive equations with the h -form. For simplicity, electrodes and piezoelectric layers are considered as mass and spring, respectively, in the derivation. Then, it is demonstrated that the second- and third-order harmonic responses can be simulated well by the circuit. In addition, nonlinearity in the Si substrate is also taken into account and its impact is discussed. It is also discussed how the frequency dependences vary with the nonlinearity mechanisms as a finding from the derived equivalent circuit.

Use of fluorine-doped silicon oxide for temperature compensation of radio frequency surface acoustic wave devices.

This paper investigates acoustic properties, including the temperature coefficient of elasticity (TCE), of fluorine-doped silicon oxide (SiOF) films and proposes the application of the films to the temperature compensation of RF SAW devices. From Fourier transform infrared spectroscopy (FT-IR), SiOF films were expected to possess good TCE properties. We fabricated a series of SAW devices using the SiOF-overlay/Cu-grating/LiNbO(3)-substrate structure, and evaluated their performance. The experiments showed that the temperature coefficient of frequency (TCF) increases with the fluorine content r, as we expected from the FT-IR measurement. This means that the Si-O-Si atomic structure measurable by the FT-IR governs the TCE behavior of SiO(2)-based films even when the dopant is added. In comparison with pure SiO(2) with the film thickness h of 0.3 wavelengths (λ), TCF was improved by 7.7 ppm/°C without deterioration of the effective electromechanical coupling factor K2 when r = 3.8 atomic % and h = 0.28λ. Fluorine inclusion did not obviously influence the resonators' Q factors when r < 8.8 atomic %.

Theoretical considerations on influence of circuit impedance on IMD2 measurement of radio-frequency bulk acoustic wave duplexers.

This paper discusses theoretically how the impedance of peripheral circuits influences the measurement of second-order inter-modulation distortion (IMD2) generated in RF BAW duplexers. First, IMD2 properties of RF BAW duplexers are expressed by a rank three tensor. Then, the tensor expression is used to evaluate how the port termination affects the IMD2 output. It is shown that variation of IMD2 output is caused mainly by five mechanisms: 1) variation of the transmit (Tx) signal intensity caused by impedance mismatching at the Tx port; 2) variation of the jammer signal intensity caused by impedance mismatching at the antenna (ANT) port; 3) variation of detector read caused by impedance mismatching at the receive (Rx) port; 4) reentry of the IMD2 signal to the ANT port caused by impedance mismatching at the ANT port; and 5) reentry of the Tx signal to the ANT port caused by impedance mismatching at the ANT port. Because input impedance of the ANT port is usually not defined for jammer signals, a large attenuator must be added to the ANT port to suppress the impedance mismatching. This result is consistent with experiments reported previously.

Considerations for measurement setup for second-order nonlinearity in radio-frequency bulk acoustic wave duplexers.

This paper discusses the influence of the setup on the measurement reliability and reproducibility for the secondorder inter-modulation distortion (IMD2) generated in RF BAW duplexers. Our measurement results show that the IMD2 level can be reliably and reproducibly measured when the port terminations are properly applied. For example, a filter and a relatively large (>20 dB) attenuator are necessary between an oscillator and the antenna port of the duplexer to suppress the nonlinear mixing and the impedance mismatching. If the order of these two devices were reversed, the IMD2 level would change significantly. Although an isolator is commonly used to stabilize the power amplifier output, our research results show that not using an ISO produced more accurate results.

A circuit model for nonlinear simulation of radio-frequency filters using bulk acoustic wave resonators.

This paper describes a circuit model for the analysis of nonlinearity in the filters based on radiofrequency (RF) bulk acoustic wave (BAW) resonators. The nonlinear output is expressed by a current source connected parallel to the linear resonator. Amplitude of the nonlinear current source is programmed proportional to the product of linear currents flowing in the resonator. Thus, the nonlinear analysis is performed by the common linear analysis, even for complex device structures. The analysis is applied to a ladder-type RF BAW filter, and frequency dependence of the nonlinear output is discussed. Furthermore, this analysis is verified through comparison with experiments.