Equivalent circuit for capacitive micromachined ultrasonic transducers to predict anti-resonances
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TECHNICAL PAPER
Equivalent circuit for capacitive micromachined ultrasonic transducers to predict anti-resonances Remzi Erkan Kemal1 • Ayhan Bozkurt2 • Goksen Goksenin Yaralıog˘lu1 Received: 25 February 2020 / Accepted: 9 April 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Equivalent circuit models have been long used to evaluate the dynamics of the capacitive micromachined ultrasonic transducer (CMUT). An important parameter in the characterization of a CMUT is the anti-resonance frequency, which limits the immersion bandwidth. However, there is no equivalent circuit model that can accurately determine the antiresonance frequency of a membrane. In this work, we present an improved lumped element parametric model for immersed CMUT. We demonstrate that the proposed equivalent circuit model accurately predicts anti-resonance and higher order mode frequencies, in addition to that of the fundamental mode. The proposed circuit model is in good agreement with device characteristics calculated using the finite element method and experimentally measured data.
1 Introduction Capacitive micro-machined ultrasonic transducers (CMUTs) which have been introduced more than two decades ago have been brought to a maturity level to find application in medical imaging. They provide superior features compared to their piezoelectric counterparts such as ease of fabrication and the possibility of obtaining broad frequency bandwidth. CMUTs with complex geometries, small device dimensions and optimized device properties can be fabricated using conventional micromachining techniques (Huang et al. 2004; Senlik et al. 2005; Yamaner et al. 2015). For a thorough analysis of the CMUT, numerous equivalent circuit and finite element method models have been proposed in the literature. Among these, the study by Warren P. Mason is the most widely applied model (Mason 1942). The equivalent circuit of Mason’s model comprises a two-port network: the electrical port & Remzi Erkan Kemal [email protected] Ayhan Bozkurt [email protected] Goksen Goksenin Yaralıog˘lu [email protected]
incorporates the clamped device capacitance, while the mechanical port is composed of the mass and stiffness of the membrane, and a negatively valued capacitor for the spring softening effect. The two ports are coupled through an electromechanical transformer. However, being designed for transduction in air, the model is inaccurate when there is medium loading (Haller and Khuri-Yakub 1996). Later, several equivalent circuit models have been developed to describe the device behavior in immersion (Lohfink and Eccardt 2005; Soh et al. 1996; Caronti et al. 2002; Yaralioglu et al. 2003; Oguz et al. 2013; Bozkurt 2008; Ko¨ymen et al. 2012), and in collapse mode (Olcum et al. 2011). Recently, an equivalent circuit model was developed to include higher modes of a plate (Mao et al. 2017), which was later improved for multiple CMUT cells (Mao et al. 2016). In this equivalent circuit model, three re
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