Impedance Losses in Negative Capacitance Circuits for Semi‐Passive Vibration Control with Piezo‐Ceramics

Abstract

Damping or absorbing effect in vibration control applications with piezo elements may be customized by an external impedance shunt branch connected to the plates of the piezo element. The negative capacitance present in the shunt significantly improves the damping and absorbing performance of such systems. The circuit is built up of an electronic gyrator realized by the operational amplifier, which is in reality not the ideal element. Therefore the performance of the proposed systems is limited, concerning the maximum voltages and currents at which the operational amplifiers can operate. In the paper, the finite gain of the operational amplifier, together with the loss impedances and the feedback gain factor is studied. The influence of the certain imperfections in the design of the electronic gyrator is based on 1DOF mechanical oscillator, with a piezo stack. Vibration control with piezo elementsThe vibrating system consists of a 1DOF spring-mass-damper oscillator with a piezo stack placed between mass m and the base Fig.1a. The Piezo element influences the frequency response function (FRF) of the system according to the complex impedance of a shunt branch consisting of the inductance L, capacitance C, and the resistance R. Passive technique used in discussed system is supported by semi-active, negative capacitance elements. As the result, significantly improved damping or absorbing performance is observed with a drawback of the necessity of the inconspicuous external power supply, and possible instabilities. For the design of the negative capacitance, the maximum value of the voltage present at it's terminals has to be calculated. The appearing voltage U ZC (s) on the electrodes of the circuit in Laplace domain (s = jω) U ZC (s) = I p (s)Z C (s), where Z C (s) = 1 sC . For the proposed system, the piezo current I p (s), based on [1], reads:where: c 0 and d 0 is the external stiffness and damping in the mechanical system respectively; c 33 -the mechanical stiffness, d 33 -the charge density per unity stress under constant electric field and C ps -the capacitance of the piezo element; u pvoltage appearing on the electrodes of the piezo, and i p -the current flowing to the external shunt branch. Impedance converterNegative capacitance is realized by impedance converter build up of the operational amplifier, a passive capacitance element characterized by the complex impedance Z p (s) and the resistive voltage divider feedback loop gain c Z , where c Z ∈ (0, 1), cp. Fig.1b. The input voltage U in (s) at the terminals of the converter is summed with the portion of the output voltage of the operational amplifier. This voltage is delivered to the controlled voltage source of the amplifier, and present at the output of the amplifier. Due to the existence of the output impedance Z o , and the current loop in the circuit flowing via the positive

Voltage amplification transfer function analysis of the operational amplifier in the negative capacitance circuits for vibration control with piezoceramics

“…Assuming the ideal components in the shunt branch Fig.1a, the voltage U ZC (s) at the negative capacitance circuit in Laplace domain (s = jω): U ZC (s) = I p (s)Z C (s), where Z C (s) = 1 sC . For the proposed system, the piezo current I p (s) reads [1]:…”