iDARE, ECE, IISc

We demonstrate the analysis and synthesis of time-modulated electromagnetic systems using Finite-difference time-domain (FDTD) methods. First, we establish the computational foundation by developing FDTD update equations for transmission lines loaded with time-varying series capacitors. Starting from classical Telegrapher's equations, the formulation incorporates lumped series capacitors switching sinusoidally between two states at modulation frequency f_s, generating new spectral components at f_op ± qf_s in the propagating wave. A complementary Simulink-based approach using MATLAB's RF Blockset Library is introduced and validated against FDTD results. Parametric studies demonstrate how source frequency, switching frequency, capacitance contrast, number of capacitors, and inter-capacitor spacing govern mixing efficiency, establishing the core FDTD machinery for time-modulated lumped elements.

After experimental demonstration of time-varying transmission lines loaded with PIN diodes, we further translate these ideas into a physically realizable multifunctional metasurface using PIN-diode-loaded metallic loop unit cells on FR4 substrate. Under reverse bias it operates as a narrowband reflective FSS with over 30 dB attenuation at 2 GHz; under forward bias it becomes transmissive. When bias is periodically modulated at f_m, on-air frequency mixing produces components at f_i ± nf_m. Finally, we generalize the framework to multiport nonreciprocal RF circuits with spatiotemporally modulated resonators and complex junction topologies. Novel boundary conditions enable arbitrary multiport interconnections previously inaccessible to FDTD. The framework is validated across nonreciprocal bandpass filters, power dividers, and couplers, confirmed by harmonic balance simulations and three fabricated UHF prototypes. QPSK constellation diagrams demonstrate direction-dependent signal integrity, while memory and runtime comparisons establish clear advantages over harmonic balance methods.