Causal and Passive Parameterization of S-Parameters Using Neural Networks

Torun H. M. , Durgun A. C. , Aygun K., Swaminathan M.

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, vol.68, no.10, pp.4290-4304, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 68 Issue: 10
  • Publication Date: 2020
  • Doi Number: 10.1109/tmtt.2020.3011449
  • Page Numbers: pp.4290-4304
  • Keywords: Scattering parameters, Artificial neural networks, Predictive models, Training, Computational modeling, Microwave theory and techniques, Data models, Causality, electromagnetic modeling, high-speed channels, microelectronic packaging, neural networks (NNs), passivity, MICROWAVE, ENFORCEMENT, MODELS, BOUNDS


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.