Microwave Filter Spectral Analysis with Green's Function Reduction
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Solution Overview
Problem
Conventional electronic circuit spectral analysis methods require extensive CPU time and resources due to linear scaling with the number of frequency points, particularly in designing and manufacturing microwave filter circuits, which slows down the manufacturing process.
Innovation Solution
The algebraic node transformation method shifts frequency-dependent features to later calculations, allowing for CPU time to scale sublinearly with the number of frequency points by transforming the admittance into a Green's function form, enabling efficient linear algebra methods to accelerate spectral analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional frequency-by-frequency spectral analysis is used, then spectral properties can be calculated, but CPU time scales linearly with the number of frequency points requiring extensive processing resources
Solution Approach 1:
The patent applies preliminary action by performing interior node elimination and constructing the exterior node admittance matrix at a single reference frequency before the frequency sweep. This preprocessing step eliminates repeated computational work across all frequency points, transforming the linear scaling problem into a more efficient computational structure where only the frequency-dependent diagonal terms need updating during the sweep.
Solution Approach 2:
The patent segments the computational process into distinct phases: (1) frequency-independent interior node elimination and matrix construction, and (2) frequency-dependent diagonal term updates during the sweep. This segmentation allows the computationally intensive parts to be performed once, while only the frequency-varying components are recalculated at each step, breaking the linear scaling bottleneck.
2Measurement precision
If the number of frequency points is increased for accurate spectral analysis, then spectral resolution improves, but processing time and computational resources increase linearly
Solution Approach 1:
By performing the computationally intensive interior node elimination and matrix construction once at a reference frequency, the patent enables high-resolution spectral analysis across many frequency points without proportionally increasing processing time. The preliminary setup creates a reusable computational framework that accelerates high-resolution sweeps.
Solution Approach 2:
The computational workflow is segmented into a one-time setup phase and a rapid frequency-sweep phase. This allows manufacturers to perform high-resolution spectral analysis with fine frequency spacing without linearly increasing total processing time, thereby improving spectral resolution while maintaining manufacturing throughput.
3Reliability
If conventional spectral analysis methods are used for microwave filter circuit design, then circuit performance can be verified, but extensive processor resources and time are consumed
Solution Approach 1:
The patent performs reliability-critical computations (interior node elimination, admittance matrix construction) once during preliminary setup, then reuses these results across all frequency points. This maintains circuit performance verification reliability while dramatically reducing the computational resource requirements during the actual spectral sweep and design iteration phases.
Solution Approach 2:
By segmenting the analysis into frequency-independent and frequency-dependent components, the patent reduces the computational burden of repeated analyses during design iterations. The complex matrix operations are performed once, while the simpler frequency-sweep phase maintains verification reliability with minimal additional resources.
Data Source
AI summary
A method of designing a filter to meet a set of specifications. The set of specifications is received, and a filter design is established. Analysis of the filter design is performed by: determining a part admittance matrix; determining a circuit admittance matrix based on the part admittance matrices; reducing interior nodes of the circuit admittance matrix; reducing algebraic nodes to transform the circuit admittance matrix into a Green's Function; evaluating the Green's Function to determine a circuit exterior node admittance matrix; and transforming the circuit exterior node admittance matrix to a circuit scattering matrix. The circuit scattering matrix is compared to the set of specifications to determine whether the filter design is satisfactory. When a determination is made that the design is not satisfactory, the filter design is modified and the process is repeated. When a determination is made that the design is satisfactory, a filter design description is output.