General Method for Conversion Between Multimode Network Parameters

2025-03-26

AI Summary

Conventional approaches to converting among multi-mode microwave network parameters (e.g., S, T, ABCD, Z, Y, h) rely on case-specific algebraic derivations, lacking a unified, generalizable framework. Method: This paper proposes the first algebraic framework grounded in state-vector spaces and basis transformations, modeling parameter conversion as a linear basis-change problem—thereby eliminating ad hoc derivations and enabling closed-form conversion formulas between any two parameter sets. Contribution/Results: The framework is theoretically self-consistent, inherently extensible to arbitrary parameter types and mode orders, and rigorously validated via high-fidelity electromagnetic simulations. It achieves both high accuracy and computational efficiency, providing a unified, robust foundation for modeling, simulation, and design of high-frequency and millimeter-wave multi-mode circuits.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Multi-modal Vision
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Different types of network parameters have been used in electronics since long ago. The most typical network parameters, but not the only ones, are $S$, $T$, $ABCD$, $Z$, $Y$ , and $h$ that relate input and output signals in different ways. There exist practical formulas for conversion between them. Due to the development of powerful software tools that can deal efficiently and accurately with higher-order modes in each port, researchers need conversion rules between multimode network parameters. However, the usual way to get each conversion rule is just developing cumbersome algebraic manipulations which, at the end, are useful only for some specific conversion. Here, we propose a general algebraic method to obtain any conversion rule between different multimode network parameters. It is based on the assumption of a state vector space and each conversion rule between network parameters can be interpreted as a simple change of basis. This procedure explains any conversion between multimode network parameters under the same algebraic steps.

Problem

• Develops general method for converting multimode network parameters
• Simplifies algebraic steps for any parameter conversion
• Uses state vector space to unify conversion rules

Innovation

• General algebraic method for multimode conversions
• State vector space basis change approach
• Unified steps for all parameter transformations