Causal and Passive Parameterization of S-Parameters Using Neural Networks

Torun, Hakki Mert
Durgun, Ahmet Cemal
Aygun, Kemal
Swaminathan, Madhavan
Neural networks (NNs) are widely used to create parametric models of S-parameters for various components in electronic systems. The focus of deriving these models has so far been numerical error reduction between the NN-generated S-parameters and the data source. However, this is not sufficient when creating such NNs since it does not guarantee predicted S-parameters to be physically consistent, i.e., passive and causal, which restricts their use cases. This article, therefore, proposes a causality enforcement layer (CEL) and passivity enforcement layer (PEL) that can be used in NNs, which ensures that NN-predicted S-parameters are of a passive and causal system. To achieve this, we utilize Kramers-Kronig relations and singular value properties of S-parameters during the training stage with the purpose of learning a physically consistent representation. This enables end-to-end training where no postprocessing is required to ensure physical consistency. We demonstrate the effectiveness of the presented approach for three different design applications, where the goal is to predict S-parameters from dc to 100 GHz. The results show that when NNs are trained using CEL and PEL, the predicted S-parameters are characterized as 100.0% causal and passive while having the same level of accuracy as NNs that solely focus on error minimization.
Citation Formats
H. M. Torun, A. C. Durgun, K. Aygun, and M. Swaminathan, “Causal and Passive Parameterization of S-Parameters Using Neural Networks,” pp. 4290–4304, 2020, Accessed: 00, 2021. [Online]. Available: