A Pigeonhole Principle-Based Method for Estimating the Resonant Frequency of SAWR Sensors

Abstract

Surface acoustic wave resonator (SAWR) sensors are passive and wireless devices whose resonant frequency is dependent to a measurand. The nominal value of the resonant frequency is about several hundred megahertz which slightly varies with the measurand to about several hundred megahertz. Due to the passive structure of an SAWR sensor, it is stimulated using a relevant signal. In response, the SAWR sensor resends a decaying signal toward the interrogation unit whose carrier frequency is equal to the sensor’s resonant frequency. In order to determine the value of the measurand, the carrier frequency of the response signal should be extracted. In this paper, a pigeonhole principle-based method is proposed which is used for accurate estimation of the carrier frequency of the short decaying response signal of the SAWR device. This method employs two signal paths of dc output voltages which are strongly related to the response signal frequency. The combination of these two voltages for each values of the input signal frequency is unique. So by accurate measuring these dc voltages and comparing their combination with the values stored in a lookup table, the signal carrier frequency is detected. We have designed and implemented a case study of the proposed scheme which can measure about 250-kHz variations of the carrier frequency around 434 MHz in less than some microseconds. The best and worst average resolutions of the implemented scheme are 216 Hz and 6.5 kHz, respectively.