Two-stage radio-frequency interferometer sensors

Abstract

We show that simple radio-frequency (RF) interferometers can have slow-wave positive group delay (PGD) or negative group delay (NGD), as well as superluminal propagation (SP) regions, due to a destructive interference process. These properties are easily tunable, which makes RF interferometers unique among systems that have NGD and SP regimes. A two-stage interferometer arrangement, which includes a first stage interferometer in the material-under-test path of a second stage, has significantly improved sensitivity in comparison with a one-stage reference interferometer. With a power divider based first stage and at its maximum NGD frequency, the frequency sensitivity improvement is as high as 7 times. With a quadrature based first stage, the sensitivity is increased by as much as 20 times. Sensitivity improvements are also observed at PGD and SP frequency regions. [5][6][7] in solution. Their design flexibility, tunable sensitivity, and frequency coverage are attractive properties for various sensing applications. Nevertheless, for high sensitivity measurements, the required system dynamic range is exceptionally large, e.g., $120 dB for an effective quality factor of $3 Â 10 6 . 7 As a result, such systems are difficult to use in rugged environments. To help address this problem, different filters and resonators 8-10 are proposed and demonstrated to improve sensitivity for a given dynamic range. With engineered spectrum and dispersion relationship, the probing RF waves in these devices are slowed down with enhanced field intensities, which lead to longer and stronger interactions between RF fields and material-under-test (MUT). The group delays, which are defined as t g ¼ Àdu/ dxj x0 with u is the frequency dependent phase shift and x 0 is the operating frequency, of these filters and resonators are positive. Corresponding group velocities, v g , are lower than the speed of light, c, in the medium, i.e., v g < c.In this work, we show that an RF interferometer can be incorporated into a second one to form a two-stage interferometer to achieve up to 20-times higher frequency sensitivity, compared with one-stage interferometers. The improvements are better than that with filters and resonators. [8][9][10] We also show that a single stage interferometer has negative group delays (NGDs), i.e., negative group velocities (NGVs), and superluminal propagation (SP) regimes. Such abnormal electromagnetic properties have been reported in a few other structures and circuits. [11][12][13][14] In RF interferometers, these properties occur around the operating frequency points and are caused by destructive interference of two traveling waves at the output port. The process is similar to that at the dark port of a Mach-Zehnder interferometer. 13 A simple model shows that loss or reflection is not necessary for the RF interferometer to exhibit those properties. At the same time, large positive group delays (PGDs) can be easily obtained. The achievable NGD, slow wave PGD, and SP levels can be easily tuned. Such tunability is not ...

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