Voltage divider transfer function method

Fig. 12.5. Flowchart describing the voltage divider transfer function method (TFM) Real time measurement and nonlinear fit to the BVD equivalent electrical circuit.

Another passive method is the transference function method (TFM) introduced by Muramatsu [6]. The method consists of an oscillator that drives a crystal through a known measuring impedance and a radiofrequency voltmeter which measures the transference modulus of the system. Muramatsu [6] neglected the effect of the parasitic capacitance and his expression for the quartz impedance resulted in a nonlinear relationship between the measured resistance R with the ac voltage divider and the value of R measured by an impedance analyser. Calvo and Etchenique [74] improved the method and introduced an analytical expression to fit the entire transfer function around resonance in order to obtain the same values of R, L and C as measured by a frequency response analyser. 

V0/V/ (fti), to the analytical expression with recovery of the complete quartz impedance near resonance (admittance, conductance and impedance). Although the voltage divider method does not measure the transfer function phase and hence it is not possible to demonstrate the validity of BVD circuit, it has the advantage of speed. Also passive methods like TFM can be applied under high viscous damping so that the shear wave phase never crosses zero and the EQCM no longer resonates. 

Methods for measuring the impedance can be divided into controlled current and controlled potential [2, 4, 81]. Under controlled potential conditions, the potential of the electrode is sinusoidal at a given frequency with the amplitude being chosen to be sufficiently small to assure that the response of the system can be considered linear. The ratio of the response to the perturbation is the transfer function, or impedance, Z, when considering the response of an AC current to an AC voltage imposition and is defined asE = IZ, where E and I are the waveform amplitudes for the potential and the current respectively. Impedance may also be envisaged as the resistance to the flow of an alternating current. 

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