A Multirate Transient Simulation Technique for Circuits described by Integro-Differential Equations
Abstract
The multirate partial differential equation (PDE) technique is considered as one of the most powerful methods for the simulation of radio frequency (RF) circuits. The method reformulates the underlying ordinary differential algebraic equation (DAE) by a PDE. The DAE solution is obtained along a characteristic curve of the PDE. Numerical solution techniques comprise (envelope modulated) Harmonic Balance (HB), multistep finite difference (FD) and spline/wavelet techniques. All techniques have disadvantages when mixed lumped/distributed devices occur and the waveforms exhibit pulse shaped behavior. Furthermore, communication systems are modeled and simulated by the Equivalent Complex Baseband (ECB) approach. Signals and impulse responses are described by their baseband counterparts, employing the Hilbert transformation. A coupled system/circuit simulation requires therefore novel numerical techniques for the solution of integro-differential equations.
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BibTeX
@misc{brachtendorf2026multirate,
title = {{A Multirate Transient Simulation Technique for Circuits described by Integro-Differential Equations}},
author = {Hans Georg Brachtendorf and Kai Bittner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25854},
eprint = {2609.25854},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25854},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Multirate Transient Simulation Technique for Circuits described by Integro-Differential Equations
AU - Hans Georg Brachtendorf
AU - Kai Bittner
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25854
UR - https://arxiv.org/abs/2609.25854
AB - The multirate partial differential equation (PDE) technique is considered as one of the most powerful methods for the simulation of radio frequency (RF) circuits. The method reformulates the underlying ordinary differential algebraic equation (DAE) by a PDE. The DAE solution is obtained along a characteristic curve of the PDE. Numerical solution techniques comprise (envelope modulated) Harmonic Balance (HB), multistep finite difference (FD) and spline/wavelet techniques. All techniques have disadvantages when mixed lumped/distributed devices occur and the waveforms exhibit pulse shaped behavior. Furthermore, communication systems are modeled and simulated by the Equivalent Complex Baseband (ECB) approach. Signals and impulse responses are described by their baseband counterparts, employing the Hilbert transformation. A coupled system/circuit simulation requires therefore novel numerical techniques for the solution of integro-differential equations.
ER -