Electrical Input Impedance Measurements

In air or vacuum, the medium loading on CMUT membranes is negligible, and the membranes show good resonance behavior. The input impedance measurements, in these cases, are helpful in determining the following parameters: resonant frequency, quality factor, device capacitance, static collapse voltage, leakage resistance and series resistance. These parameters, together with the membrane and gap dimension measurements, provide valuable insights to parameters that are more difficult to measure on finished devices, such as young’s modulus and residual stress in the membranes.

The input impedance can be directly measured using an impedance analyzer, or by measuring the scattering parameter (S11) using a network analyzer and converting to impedance. In either case, a bias T is needed to enable the superimposition of an AC voltage on top of a DC bias on the CMUT while protecting the measurement instrument from being exposed to the DC voltage (Fig. 1).

The real part of the input impedance peaks at the open circuit resonant frequency. This frequency decreases with increasing DC bias voltage in the conventional (pre-collapse) regime of operation. This phenomenon is due to the softening of the spring under electric field. The amplitude of the resonance peak will increase with increasing bias voltage due to the higher transduction efficiency. When the electrical attraction force surpasses mechanical restoring force from the membrane spring, the membrane will collapse. When this occurs, the resonant frequency increases significantly because of much stiffened membrane spring [ 1, 2]. The collapse voltage can therefore be determined experimentally by noticing this sudden change in the resonant frequency.

When the DC bias voltage is brought down to lower than the collapse voltage, the membrane will eventually “snap back”. However, the snap back voltage is not necessarily the same as the collapse voltage. If these two voltages differ, hysteresis exists.

 

FIGURE 1. Experimental setup for input impedance measurements.

 

 

FIGURE 2. Typical electrical input impedance of a CMUT element with a 250-um by 250-um size [3].

 

References

 

[1] Ö. Oralkan, B. Bayram, G. G. Yaralioglu, A. S. Ergun, M. Kupnik, D. T. Yeh, I. O. Wygant and B. T. Khuri-Yakub, “Experimental characterization of collapse-mode CMUT operation,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 53, no. 8, pp. 1513-1523, Aug. 2006.

[2] Y. Huang, et al, “Comparison of conventional and collapsed region operation of capacitive micromachined ultrasonic transducers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 53, no. 9, Sep. 2006.

[3] X. Zhuang, et al., “Two-dimensional capacitive micromachined ultrasonic transducer (CMUT) arrays for a miniature integrated volumetric ultrasonic imaging system,” presented at 2005 SPIE Medical Imaging Conference, San Diego, CA, Feb 12-17, 2005.