Measurement setup for X-Parameter characterization of bulk acoustic wave resonators

Abstract

In this work a modern measurement method has been utilized in order to characterize nonlinear behavior of bulk acoustic wave (BAW) solidly mounted resonators (SMR). Unlike typical nonlinearity characterization methods, the method which was employed here not only records amplitudes, but also the phase of generated harmonics. Furthermore, the relations between the harmonics of different order are given. The modeling approach being used is the poly harmonic distortion (PHD) modeling approach, realized by the measurement of X-Parameters. For that purpose it was necessary to extend a nonlinear vector network analyzer (NVNA) by external components in order to enable high power measurements. Afterwards, several optimization steps were required to perform phase calibration. This difficulty arose due to the high power incident tones and steep resonator impedance curves on the one hand and the limited power provided by the phase calibration standard on the other hand.