Coupling Matrix Representation of Nonreciprocal Filters Based on Time-Modulated Resonators

This article addresses the analysis and design of nonreciprocal filters based on time-modulated resonators. We analytically show that time modulating a resonator leads to a set of harmonic resonators composed of the unmodulated lumped elements plus a frequency-invariant element that accounts for differences in the resonant frequencies. We then demonstrate that harmonic resonators of different orders are coupled through nonreciprocal admittance inverters, whereas harmonic resonators of the same order couple with the admittance inverter coming from the unmodulated filter network. This coupling topology provides useful insights to understand and quickly design nonreciprocal filters and permits their characterization using an asynchronously tuned coupled resonators network together with the coupling matrix formalism. Two designed filters, of orders three and four, are experimentally demonstrated using quarter wavelength resonators implemented in microstrip technology and terminated by a varactor on one side. The varactors are biased using coplanar waveguides integrated into the ground plane of the device. Measured results are found to be in good agreement with numerical results, validating the proposed theory.

[1]  Zongfu Yu,et al.  Complete optical isolation created by indirect interband photonic transitions , 2008, OPTO.

[2]  Andrea Alù,et al.  Broadband passive isolators based on coupled nonlinear resonances , 2018 .

[3]  D. Pozar.  Microwave Engineering , 1990 .

[4]  Louis A. Pipes,et al.  Matrix Analysis of Linear Time‐Varying Circuits , 1954 .

[5]  R. Cameron.  Advanced coupling matrix synthesis techniques for microwave filters , 2003 .

[6]  Pablo Soto,et al.  Accurate Synthesis and Design of Wideband and Inhomogeneous Inductive Waveguide Filters , 2010, IEEE Transactions on Microwave Theory and Techniques.

[7]  K. D. Dikshit.  An analysis of time-varying circuits , 1973 .

[8]  C. Caloz,et al.  Magnetless Nonreciprocal Metamaterial (MNM) Technology: Application to Microwave Components , 2013, IEEE Transactions on Microwave Theory and Techniques.

[9]  Harish Krishnaswamy,et al.  Magnetic-free non-reciprocity based on staggered commutation , 2016, Nature Communications.

[10]  C. F. Kurth,et al.  Steady-state analysis of sinusoidal time-variant networks applied to equivalent circuits for transmission networks , 1977 .

[11]  Andrea Alù,et al.  Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops , 2014, Nature Physics.

[12]  Yuanxun Ethan Wang,et al.  Nonreciprocal Components With Distributedly Modulated Capacitors , 2014, IEEE Transactions on Microwave Theory and Techniques.

[13]  Yuanxun Ethan Wang,et al.  Ultra-Wide Band Non-reciprocity through Sequentially-Switched Delay Lines , 2017, Scientific Reports.

[14]  Jian-Xin Chen,et al.  A Novel Dielectric Strip Resonator Filter , 2018, IEEE Microwave and Wireless Components Letters.

[15]  C. Caloz,et al.  Mixer-Duplexer-Antenna Leaky-Wave System Based on Periodic Space-Time Modulation , 2016, IEEE Transactions on Antennas and Propagation.

[16]  F.M. Vanin,et al.  Dimensional synthesis for wide-band waveguide filters and diplexers , 2004, IEEE Transactions on Microwave Theory and Techniques.

[17]  Xi-Lang Zhou,et al.  Characterization of Average Power Handling Capability of Bandpass Filters Using Planar Half-Wavelength Microstrip Resonators , 2009, IEEE Microwave and Wireless Components Letters.

[18]  Raafat R. Mansour,et al.  Microwave Filters for Communication Systems: Fundamentals, Design and Applications , 2007 .

[19]  Harish Krishnaswamy,et al.  Synchronized conductivity modulation to realize broadband lossless magnetic-free non-reciprocity , 2017, Nature Communications.

[20]  Ahmed Kord,et al.  Magnetic-free radio frequency circulator based on spatiotemporal commutation of MEMS resonators , 2018, 2018 IEEE Micro Electro Mechanical Systems (MEMS).

[21]  Harish Krishnaswamy,et al.  A CMOS Passive LPTV Nonmagnetic Circulator and Its Application in a Full-Duplex Receiver , 2017, IEEE Journal of Solid-State Circuits.

[22]  Dimitrios Peroulis,et al.  Isolating Bandpass Filters Using Time-Modulated Resonators , 2019, IEEE Transactions on Microwave Theory and Techniques.

[23]  M. Lipson,et al.  Subject Areas : Optics A Viewpoint on : Electrically Driven Nonreciprocity Induced by Interband Photonic Transition on a Silicon Chip , 2012 .

[24]  Jason Soric,et al.  Breaking temporal symmetries for emission and absorption , 2016, Proceedings of the National Academy of Sciences.

[25]  R. Fleury,et al.  Sound Isolation and Giant Linear Nonreciprocity in a Compact Acoustic Circulator , 2014, Science.

[26]  Andrea Alù,et al.  Achieving Full-Duplex Communication: Magnetless Parametric Circulators for Full-Duplex Communication Systems , 2018, IEEE Microwave Magazine.

[27]  Andrea Alù,et al.  Magnetic-free nonreciprocal photonic platform based on time-modulated graphene capacitors , 2018, Physical Review B.

[28]  A. Alvarez-Melcon,et al.  Nonreciprocal Graphene Devices and Antennas Based on Spatiotemporal Modulation , 2016, IEEE Antennas and Wireless Propagation Letters.

[29]  S. Tretyakov,et al.  Electromagnetic Nonreciprocity , 2018, Physical Review Applied.

[30]  Huei Wang,et al.  Design and Analysis of 24-GHz Active Isolator and Quasi-Circulator , 2015, IEEE Transactions on Microwave Theory and Techniques.

[31]  Andrea Alù,et al.  Magnet-Less Circulators Based on Spatiotemporal Modulation of Bandstop Filters in a Delta Topology , 2017, IEEE Transactions on Microwave Theory and Techniques.

[32]  Sidney Darlington.  Linear time-varying circuits — Matrix manipulations, power relations, and some bounds on stability , 1963 .

[33]  Andrea Alù,et al.  Pseudo-Linear Time-Invariant Magnetless Circulators Based on Differential Spatiotemporal Modulation of Resonant Junctions , 2017, IEEE Transactions on Microwave Theory and Techniques.

[34]  Dimitrios L. Sounas,et al.  Magnetless Microwave Circulators Based on Spatiotemporally Modulated Rings of Coupled Resonators , 2016, IEEE Transactions on Microwave Theory and Techniques.