Isolating Bandpass Filters Using Time-Modulated Resonators

Abstract

In this paper, we demonstrate for the first time an isolating bandpass filter with low-loss forward transmission and high reverse isolation by modulating its constituent resonators. To understand the operating principle behind the device, we develop a spectral domain analysis method and show that same-frequency non-reciprocity is a result of non-reciprocal frequency conversion to the intermodulation (IM) frequencies by the time-varying resonators. With appropriate modulation frequency, modulation depth, and phase delay, the signal power at the IM frequencies is converted back to the RF frequency and add up constructively to form a low-loss forward passband, whereas they add up destructively in the reverse direction to create the isolation. To validate the theory, a lumped-element 3-pole 0.04-dB ripple isolating filter with a center frequency of 200 MHz, a ripple bandwidth of 30 MHz, is designed, simulated, and measured. When modulated with a sinusoidal frequency of 30 MHz, a modulation index of 0.25, and an incremental phase difference of 45 • , the filter achieves a forward insertion loss of 1.5 dB and a reverse isolation of 20 dB. The measured non-modulated and modulated results agree very well with the simulations. Such nonreciprocal filters may find applications in wide-band simultaneous transmit and receive radio front-ends.

Nonreciprocal Yagi–Uda Filtering Antennas

“…To break time-reversal symmetry, a sinusoidal modulating signal of frequency is applied to the different varactors. This modulation signal imparts different phases ( 1 , 2 , 3 ) to the resonators and transform the filtering antenna into a non-linear component [31,32]. Strong nonreciprocity appears due to nonreciprocal couplings and phase cancellation effects among the nonlinear harmonics that are generated in the time-modulated resonators, as detailed in [32].…”

“…To design the proposed nonreciprocal devices, we first independently consider its radiation [34] and filtering parts [31], [32]. For the latter, we assume that the nonreciprocal filter is loaded with the input impedance of the Yagi-Uda antenna.…”

“…We remark that we have not considered yet the presence of the modulation signals that will time-modulate the resonators. As detailed in the following, the filtering part of the device will become nonreciprocal by properly adjusting the relevant parameters of the modulating signals, namely the frequency ( ), the static capacitance ( 0 ), the modulation index (Δ ) and the phase shift between resonators (Δ ) [31], [32].…”

“…Strong nonreciprocity between transmission and reception operation can be obtained by properly optimizing the parameters of the modulating signals. After following the procedure detailed in [31], [32], we find the following quasioptimized values for our proposed configuration: =75 MHz, 0 =0.86 pF, ∆ =0.09, and Δ =56°. It can be observed that the design leads to weak modulation signals (small modulation frequency and index) that are common in other implementations [28], [29] and permit to operate the varactors in their linear regime.…”

“…Besides, time-modulated metasurfaces can provide exotic functionalities such as nonreciprocal beam scanning and/or focusing [29] and serrodyne frequency translation [30]. Very recently, nonreciprocal microstrip filters based on time modulated resonators have been proposed and experimentally demonstrated [31,32]. Several prototypes based on both lumped elements and on distributed resonators were fabricated and successfully measured, showing isolation levels higher than 15 dB over 2% fractional bandwidths.…”