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This article presents a length-dependent deep neural network (LD-DNN) based channel modeling methodology to predict the frequency response of high-speed channels. The proposed method significantly enhances the model accuracy and design efficiency while considering the channel length dependence that was neglected in previous modeling approaches. We define the concept of the electrical length to model the length and frequency dependence, then further leverage the activation function to capture the multiple reflection effects to improve accuracy. Additionally, we model the insertion loss resonance induced by crosstalk that can seriously deteriorate signal integrity. As a result, by adopting the proposed model which can predict the S-parameters as a function of length, the need for performing additionally 3D electromagnetic simulations when adjusting the channel length can be eliminated. Various high-speed channel cases are tested to validate the accuracy of the proposed method. The modeling accuracy is less than 4% for different high-speed channel structures with run times of less than 1.4 second per design.

Length-Dependent Deep Neural Network Based Modeling for High-Speed Channels