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Error Analysis on the TICER Approximation

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Abstract

Time constant equilibration reduction (TICER) is a local model reduction method based on Gaussian elimination for RC networks which was introduced in Sheehan (1999 IEEE/ACM international conference on computer-aided design. Digest of technical papers (Cat. No.99CH37051), pp 200–203, 1999). The main idea of TICER is selectively removing the non-port nodes of the circuits to produce a smaller RC circuit. Since proposed, TICER has been widely used in the electronic engineering, and lots of practices validate its reliability and robustness. It is a practical method to meet the needs of reduction and can produce a realizable RC circuit with good accuracy, and this is the reason why TICER has been used until now. Later, many scholars proposed RC-realizable reduction methods based on TICER. Quite surprisingly, as far as the authors know, there exists no rigorous analysis on this simple but wonderful method in the literature. In this short communication, we prove the optimal first-order asymptotic accuracy of TICER and present numerical evidences to validate our theoretical results.

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Acknowledgements

This work was supported by National Key R &D Program of China 2019YFA0709600, 2019YFA0709602, and National Natural Science Foundation of China 12171274.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Shuangqing Road, Haidian District, Beijing, 100084, People’s Republic of China

    Wenhui Yao & Chunxiong Zheng

  2. Empyrean Technology Co., Ltd., Lize Road, Chaoyang District, Beijing, 100102, People’s Republic of China

    Zhenya Zhou

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  1. Wenhui Yao
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  2. Chunxiong Zheng
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Correspondence to Wenhui Yao.

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The data and the program that support the findings of this study are available from the corresponding author upon reasonable request.

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Yao, W., Zheng, C. & Zhou, Z. Error Analysis on the TICER Approximation. Circuits Syst Signal Process 42, 4390–4400 (2023). https://doi.org/10.1007/s00034-023-02306-5

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