Fast real‐time convolution algorithm for transients of nonlinearly‐terminated microwave multiport circuits

Abstract

In this work, a fast real‐time convolution algorithm is proposed. By using this approach, the cost for real‐time convolution in the presence of nonlinear terminations is reduced from O(N2) to O(N log2N). It is important to reduce the cost for the convolution operation because it usually dominates the computation time in a nonlinear circuit simulation. A nonlinearly‐terminated microwave 3‐port circuit, characterized by S parameters, is employed to demonstrate the efficiency of this fast algorithm. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 39: 280–282, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11190

Time‐domain finite‐element modeling of electrically and magnetically dispersive medium via recursive FFT

“…The second convolution is embedded in the evaluation of Q(t) in (6). By taking the time derivative of (2) and then substituting it into (3), we obtain…”

“…However, this approach is restricted to the cases when the susceptibility functions can be represented by a pole expansion. To remove this restriction, we propose to employ the recursive FFT algorithm [6,7] to evaluate (10). The basic idea of the recursive FFT algorithm can be understood by splitting (10) into two parts as follows:…”

“…To use this recursive convolution, the electric and magnetic susceptibility functions must be first expressed as a pole expansion, which imposes a restriction on the type of medium that can be modeled. In this article, we present an approach to model a more general dispersive medium via the recursive fast Fourier transform (FFT) [6,7]. The proposed approach only requires the values of the susceptibility functions instead of their explicit mathematical form in pole expansion.…”

Influence of Measured Scattering Parameters on the Convolution Simulation of Nonlinear Loaded High-Speed Microstrip Interconnects

“…By the same time, Djordjevic et al [5,6] analyzed time-domain responses of multiconductor transmission lines by means also of convolution. Afterward, a plethora of researchers [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] presented different applications of the convolution concept to simulate linearly and nonlinearly terminated transmission lines and high-speed microstrip interconnects. A more complete representation for the microstrip interconnects, based on a time-domain RLCG-model instead of the classic frequency-domain S-parameter-model was introduced in [23].…”

A Fast Approach for Simulating Long-Time Response of High-Speed Dispersive and Lossy Interconnects Terminated With Nonlinear Loads

“…An efficient approach is proposed to resolve this problem based on the wideband closed-form formulas for expressing the Sparameters of interconnects and the fast real-time convolution (FRTC) algorithm [18,19], which originates from the idea in [20]. The computation time of the S-parameters by the formulas is in a flash.…”