Conduction Mode Decomposition for High-Frequency Impedance Extraction
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Solution Overview
Problem
Current methods for extracting high-frequency electrical parameters in circuit designs become computationally expensive and inefficient above the skin effect threshold, particularly in high-frequency applications like RFICs and advanced telecommunication packages, due to the need to handle large linear systems and non-uniform current distribution.
Innovation Solution
The method decomposes current density into conduction modes, which are eigenmodes of the Helmholtz equation, reducing the size of the linear system and using domain-specific knowledge to compute matrix elements, thereby reducing the computational cost by over two orders of magnitude compared to standard approaches.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If filament decomposition is used to account for nonuniform current distribution above skin effect threshold, then measurement precision of impedance extraction is improved, but device complexity and computational cost increase significantly
Solution Approach 1:
The patent segments the current distribution into a small number of conduction modes (typically 1-3 modes per wire) rather than using fine filament decomposition. Each conduction mode represents a dominant current distribution pattern, allowing accurate impedance extraction with much fewer variables than traditional filament methods while maintaining precision above skin effect threshold
Solution Approach 2:
The patent changes the mathematical representation from spatial filament decomposition to modal decomposition using conduction modes. This parameter transformation reduces the problem from tracking current at many discrete filament locations to determining coefficients for a few dominant current distribution patterns, dramatically reducing linear system size while preserving accuracy
2Measurement precision
If standard direct solvers are used for computing impedance at high frequencies, then measurement precision is maintained, but productivity drops to 1 wire per second
Solution Approach 1:
By segmenting the current into conduction modes, the patent reduces the number of variables in the linear system from O(mN) in filament methods to O(n) in conduction mode methods. This enables the use of efficient direct solvers that can process many more wires per second while maintaining the same measurement precision for impedance extraction
Solution Approach 2:
The patent transforms the computational parameters from fine-grained filament current distributions to coarse-grained conduction mode coefficients. This parameter change reduces computational complexity from cubic to quadratic or linear scaling, enabling processing of 1000+ wires per second at high frequencies while preserving impedance accuracy
3Productivity
If conduction modes are used to reduce linear system size, then productivity is improved, but ease of manufacture and implementation becomes more challenging
Solution Approach 1:
The patent changes the mathematical basis from simple filament currents to conduction modes that are eigenmodes of the Helmholtz equation. While this improves productivity by reducing linear system size, it increases implementation complexity because conduction modes require solving differential equations and computing eigenmodes, which is more mathematically involved than simple filament decomposition
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach allows for accurate impedance extraction with improved computational efficiency, enabling processing of multiple wires per second even at high frequencies, maintaining better than 1% accuracy across a broad frequency domain.
Implementation Method 1
Conduction modes capture the characteristic order δ exponential decay of currents and fields from the surface of conductors inward
Data Source
AI summary
Described herein are embodiments of methods for extracting various high frequency parameters for a circuit design. In one exemplary embodiment, circuit design information indicating at least a geometric layout of conductors in the circuit design and a desired frequency of operation for the circuit design is received. Conduction modes representing distribution functions for currents in the conductors at the desired frequency of operation are defined. A conduction mode matrix including matrix elements based on the defined conduction modes is generated. Values for one or more matrix elements are computed by decomposing integrands for calculating the matrix elements into simplified terms that are less computationally intensive than the integrands and computing the values of the simplified terms. The values for the one or more matrix elements can be stored (e.g., on one or more computer-readable media).