De-embedding S-parameters Using Closed-Form Matrix Inversion
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Solution Overview
Problem
Current methods for de-embedding measurements in electronic networks are limited, as they often require iterative processes, are difficult to automate, and cannot handle multiple unknown devices or systems with an arbitrary number of ports, leading to incomplete or inaccurate behavioral models of devices.
Innovation Solution
A method that uses a net-list description and known S-parameters to directly calculate the S-parameters of unknown elements in a system, providing a closed-form solution that can handle any number of ports and multiple unknown devices, without requiring reexamination of the topology on each application.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If iterative processes are used for de-embedding measurements, then measurement precision can be improved, but productivity decreases due to time-consuming calculations
Solution Approach 1:
The patent replaces iterative numerical methods with a closed-form mathematical solution using matrix operations. The de-embedding process uses direct matrix inversion and multiplication formulas instead of iterative approximation, achieving both high precision and fast computation suitable for real-time applications.
Solution Approach 2:
The patent transforms the measurement parameters from S-parameters to T-parameters (transfer matrices), enabling a direct algebraic solution. By changing the parameter representation and using matrix algebra relationships, the system achieves exact solutions without iteration, improving both accuracy and computational efficiency.
2Adaptability or versatility
If conventional de-embedding methods are used, then simple two-port devices can be characterized, but adaptability decreases when handling multiple unknown devices or systems with arbitrary number of ports
Solution Approach 1:
The patent creates a universal de-embedding framework that can handle any number of ports and multiple unknown devices simultaneously. The matrix-based approach generalizes the two-port case to N-port systems, allowing a single methodology to address diverse measurement scenarios without requiring specialized procedures for each configuration.
Solution Approach 2:
The patent segments the measurement system into known and unknown components, representing each device as an independent matrix block. This segmentation allows the overall system matrix to be decomposed and solved for individual unknown devices, enabling modular characterization of complex multi-device systems.
3Ease of operation
If time gating is used to move the reference plane, then some S-parameter measurements can be obtained, but measurement precision decreases because complete de-embedding is not achieved
Solution Approach 1:
The patent introduces T-parameters (transfer matrices) as an intermediary representation that connects the known S-parameters of the overall system with the unknown S-parameters of individual devices. This intermediary mathematical framework enables complete de-embedding by providing the necessary relationships to solve for all unknown parameters simultaneously, rather than partially moving the reference plane.
Data Source
AI summary
A method is provided for de-embedding measurements from a given network containing mixtures of devices with known and unknown S-parameters given a description of the network and the known S-parameters of the overall system.