Filter Spectral Analysis Using Node Reduction and Green's Functions
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Solution Overview
Problem
Conventional electronic circuit spectral analysis methods require extensive CPU resources and time due to their linear scaling with the number of frequency points, particularly in designing and manufacturing microwave filter circuits, which slows down and increases the expense of the manufacturing process.
Innovation Solution
The proposed method employs algebraic node transformation and matrix transformations, such as successive nodal expansions and interior node reductions, to isolate frequency dependence, allowing most calculations to be performed once for all frequencies, thereby reducing CPU time dependence on the number of frequency points and accelerating the design process.
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 performs preliminary calculations of frequency-independent circuit properties (such as nodal admittance matrices and interior node elimination) before the frequency sweep. This allows the frequency-dependent calculations to be performed more efficiently at each frequency point, reducing the overall CPU time required for spectral analysis while maintaining accuracy.
Solution Approach 2:
The patent segments the spectral analysis process into distinct stages: (1) frequency-independent circuit reduction and matrix formation, and (2) frequency-dependent admittance calculation. This segmentation allows independent optimization of each stage, with the first stage performed once and the second stage efficiently repeated across frequency points.
2Reliability
If conventional spectral analysis methods are used, then circuit behavior can be predicted, but extensive processor resources and expense are required, slowing down the design and manufacturing process
Solution Approach 1:
The patent changes the mathematical parameters and representation of circuit properties by using nodal analysis and interior node elimination to transform the circuit into a form where frequency-independent and frequency-dependent components are separated. This parameter transformation enables more efficient computation across frequency points while maintaining prediction accuracy.
Solution Approach 2:
The patent replaces the conventional mechanical iterative frequency-by-frequency analysis approach with a more efficient mathematical methodology based on nodal admittance matrices and algebraic manipulations. This substitution of the analytical mechanism dramatically reduces CPU time requirements while maintaining the ability to predict circuit behavior accurately.
3Measurement precision
If interior node elimination is performed at each frequency point, then exterior node admittance spectrum can be calculated, but the process repeats extensively over frequency points, increasing CPU time
Solution Approach 1:
The patent performs interior node elimination as a preliminary action before the frequency sweep, calculating the frequency-independent reduced admittance matrix once. This eliminates the need to repeat the computationally intensive interior node elimination process at each frequency point, reducing computational complexity while maintaining accuracy.
Solution Approach 2:
The patent extracts and separates the frequency-independent components of the circuit analysis (such as the structure of nodal equations and interior node relationships) from the frequency-dependent components. This extraction allows the complex interior node elimination to be performed once on the frequency-independent part, with only simpler frequency-dependent calculations repeated across frequency points.
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.