Exploring the Parametric Energy Transfer in a Multi-Mode Piezoelectric Resonator with Nonlinear Harmonics

In this work, we investigate the parametric energy transfer phenomenon in a multi-mode nonlinear piezoelectric resonator over a wide frequency span through a simple, all-electrically interfaced setup. We propose a 4-port PZT-based parametric resonator with two lowest modes around 170 kHz ( fo) and 340 kHz ( 2 fo) designated for energy receiving and pumping, respectively. The mere 2 fo electrical excitation for the energy transfer into other tones is unique and more efficient as compared to the conventional nonlinear operation. By modulating the piezoelectric stress at 340 kHz with actuating signal of CMOS compatible threshold ( ), the energy up- and downconversion are recorded in real time by a spectrum analyzer (SA). The wide modulation bandwidths (MBW) of 25 kHz (7.3%) and 30 kHz (8.8%) at 2 fo are observed with vac of 500 mV and 1 V, respectively, where the signal bandwidth of transferred energy at fo is half of the MBW. Furthermore, the mechanical displacements of the resonator and the modes are also verified by a Laser Doppler Vibrometer (LDV) from DC to 800 kHz, showing a displacement amplification factor of 50X at fo as parametric effect is triggered. Compared to the conventional nonlinear harmonics operation under the same input signal (500 mV), the output signal of each mode has been significantly enhanced due to the proposed parametric excitation.