Power- and time-dependent equivalent circuit models for waveform-selective metasurfaces with varying electromagnetic responses to repeated pulses at the same frequency

TL;DR

This work tackles the challenge of predicting waveform-selective metasurface responses that depend on both pulse width and input power. It introduces an analytical equivalent-circuit model in which the diode bridge resistance becomes power- and time-dependent, expressed via the Maclaurin series and the Wright omega function to yield $R_j$, $I_L$, and transmittance $S_{21}$ with high fidelity. The approach is extended to repeated pulses, capacitor-based metasurfaces, and nonresonant frequencies using fitting parameters and a decomposition of the shunt admittance into $Y_{freq}$ and $Y_{time}$, enabling accurate near- or off-resonant predictions. Compared with conventional fixed-$R_d$ models, the new framework closely tracks numerical results and reduces design cycles from hours to minutes, offering practical benefits for dynamic wireless systems and real-time adaptation in smart radio environments. The analytical nature of the solution also facilitates integration with system-level simulators and optimization workflows.

Abstract

Waveform-selective metasurfaces offer unprecedented control over electromagnetic waves on the basis of pulse width. However, existing circuit models fail to capture the power-dependent behaviors of these metasurfaces, thereby limiting their use in practical applications. Here, for the first time, we present analytical equivalent circuit models that accurately predict both power- and time-dependent responses by incorporating voltage-dependent diode resistance through the Maclaurin series and Wright omega functions. As a result, the variations in the input power and time domain are effectively predicted theoretically. Moreover, our concept is successfully extended to different types of waveform-selective metasurfaces and increasingly complex scenarios, including repeated pulses and nonresonant frequencies. Thus, our equivalent circuit approach can readily explain and quantify the electromagnetic behaviors of waveform-selective metasurfaces. This strategy provides a high degree of control for addressing complex electromagnetic problems by leveraging pulse width as a tuning parameter, even at a fixed frequency.

Figures (11)

• Figure 1: Waveform-selective metasurface and simplified equivalent circuit models. (a) Periodic unit cell of an inductor-based waveform-selective metasurface. (b) Conventional simplified equivalent circuit model using $R_d$, which represents the effective resistive component of diodes only at their turn-on voltage $V_{on}$. (c) Current voltage characteristics of the diode. (d) Proposed simplified equivalent circuit model using $R_j$. Unlike the conventional model of (b), $R_j$ was used as a variable resistor whose resistance varied in accordance with the input power or the input voltage $E_L$ of (d).
• Figure 2: Transmission line model representing the waveform-selective metasurface shown in Fig. \ref{['fig:1']}a.
• Figure 3: Estimated power- and time-dependent $R_j$. The results with various (a) input powers, (b) $L$s, (c) $R_L$s, and (d) $I_s$s.
• Figure 4: Diode current. The results with various (a) input powers, (b) $L$s, (c) $R_L$s, and (d) $I_s$s.
• Figure 5: Transmittance. The results with various (a) input powers, (b) $L$s, (c) $R_L$s, and (d) $I_s$s.