Electromechanical equivalent circuit

Fig. 6.16. Piezoelectric stack translator, a Structure, b electromechanical equivalent circuit and amplitude responses of the actuator and sensor transfer behaviour in small signal operation (derived from [5])...

Fig. 6.130. Electromechanical equivalent circuit diagram and amplitude responses of actuator and sensor transfer characteristic in small signal operation...

The interpretation of (6.44), (6.45), (6.46) and (6.47) is illustrated in Fig. 6.130, showing an electromechanical equivalent circuit diagram. Accordingly, the input of a piezoelectric transducer can be considered as an electrical capacitor with the capacitance C and its output as a mechanical spring with the stiffness cp. As in reality C is always lossy and cp has always a mass and a structural damping behaviour, the amplitude response IV /Fgl of the piezoelectric transducer has a definite lower cut-off frequency /u and a mechanically determined natural frequency /o for an open electrical port (Jg = 0), and the amplitude response s/V has a mechanically determined natural frequency /o for an open mechanical port F = 0). 

The description of the transfer characteristic of solid-state actuators can be generalised if the system equations which have been introduced in Sect. 6.9.2 are not interpreted as electromechanical equivalent circuit diagrams but as signal flow charts [335]. The result is shown in Fig. 6.134. 

In the schematic shown in Figure 4.2.10, the RF path is visible between the two signal sources (RF ports) used for extracting the S parameters, and is composed of a length of microstrip transmission line from each port connected to a model for a series-switch plate . Driven by the 6 mechanical wires at each side, which control its position, the switch plate is internally modeled as an equivalent circuit including transmission line, frequency-dependent resistance, and variable capacitance between the conductor on the plate and the underlap of the ends of the microstrip lines separated by the gap for the switch isolation. As with the beams, this model is defined by a complete set of parameters, such as the dimensions and material properties. Parameters can be adjusted quickly to achieve the desired RF performance for different closing states of the electromechanical structure. 

Costa Branco, P. J. and Dente, J. A. (2006). Derivation of a continuum model and its electric equivalent-circuit representation for ionic polymer-metal composite (IPMC) electromechanics. Smart Materials and Structures 15, pp. 378-392. 

Physieal models and equivalent circuit representations for conducting polymer actuators and sensors are presented, including mechanical, electrical, and electromechanical descriptions. The underlying concept of most models is that strain is proportional to charge density, and sense voltage is proportional to stress. Dynamics are determined by the rate of charge transfer, as well as the mechanical properties of... 

Electrostatic speaker and earphone did not become popular because they need special driving circuits for the capacitive load. The equivalent circuits for the electret-based device and the device with external bias are the same, but the electromechanical force factor is different. For the electret speakers, the induced charge becomes unstable for a large gap as can be seen in microphones. Based on optimization studies of the acoustic parameters from an equivalent-circuit analysis, nonlinear distortion in a push-pull structure derived from a single-ended structure... 

Since the unloaded QCM is an electromechanical transducer, it can be described by the Butterworth-Van Dyke (BVD) equivalent electrical circuit represented in Fig. 12.3 (box) which is formed by a series RLC circuit in parallel with a static capacitance C0. The electrical equivalence to the mechanical model (mass, elastic response and friction losses of the quartz crystal) are represented by the inductance L, the capacitance C and the resistance, R connected in series. The static capacitance in parallel with the series motional RLC arm represents the electrical capacitance of the parallel plate capacitor formed by both metal electrodes that sandwich the thin quartz crystal plus the stray capacitance due to the connectors. However, it is not related with the piezoelectric effect but it influences the QCM resonant frequency. 

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