RF Filters with Periodic Passbands for Sparse Fourier Transform-Based Spectrum Sensing

This paper demonstrates a passive low-insertionloss (IL) RF filter with periodic passbands and capable of sparsifying the spectrum from 238 to 526 MHz for sparse Fourier transform (SFT)-based spectrum sensing. The demonstrated periodic filter employs LiNbO
₃
lateral overtone bulk acoustic resonators (LOBARs) with high-quality factors (Qs), large electromechanical coupling (k
_t
²
), and multiple equally spaced resonances in a ladder topology. To demonstrate the periodic filter, the LOBARs is first modeled to predict k
_t
²
of various tones accurately. The fabricated LOBARs show k
_t
²
larger than 1.5% and figure of merits (Q · k
_t
²
) more than 30 for over 10 tones simultaneously, which agree with our modeled response, and are both among the highest demonstrated in overmoded resonators. The multi-band filter centered at 370 MHz has then been obtained with a passband span of 291 MHz, a spectral spacing of 22 MHz, an IL of 2 dB, FBWs around 0.6% and a sparsification ratio between 7 and 15. An out-of-band rejection around 25 dB has also been achieved for more than 14 bands. The great performance demonstrated by the RF filter with 14 useable periodic passbands will serve to enable future SFT-based spectrum sensing.