Passive Network Analysis Using Band-Extended S-Parameters
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Solution Overview
Problem
Existing methods for analyzing passive networks using band-limited S-parameters are inaccurate due to limitations in frequency band measurement, leading to causality errors in impulse response, particularly when low-frequency data is lacking or high-frequency data is limited.
Innovation Solution
A system that removes propagation delay time from band-limited S-parameters, extends the frequency band using interpolation and extrapolation functions, and performs Hilbert transform to derive an impulse response, thereby improving the accuracy of time response analysis without complex circuit conversions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If inverse Fourier transform is performed on band-limited S-parameters to obtain impulse response, then time response analysis can be conducted, but causality errors occur when low-frequency band data is missing or high-frequency band is limited
Solution Approach 1:
The patent applies preliminary action by performing band extension on S-parameters before conducting inverse Fourier transform. The system extends the frequency band of S-parameters using interpolation and extrapolation functions, and adjusts propagation delay time in advance, so that when IFT is performed, the impulse response is free from causality errors. This preliminary band extension and delay adjustment ensures that the necessary frequency information is available before the critical IFT operation.
Solution Approach 2:
The patent applies parameter changes by modifying the frequency band parameters of S-parameters. The system changes the frequency range from band-limited to extended band by adding low-frequency components through interpolation and high-frequency components through extrapolation. Additionally, the propagation delay time parameter is adjusted to optimize the impulse response accuracy, thereby transforming the input parameters to achieve reliable causality in the output.
2Ease of operation
If band-limited S-parameters are used directly for time response measurement, then measurement process is simple, but the impulse response contains causality errors and lacks accuracy
Solution Approach 1:
The patent applies preliminary action by performing band extension on S-parameters before conducting inverse Fourier transform. The system extends the frequency band of S-parameters using interpolation and extrapolation functions, and adjusts propagation delay time in advance, so that when IFT is performed, the impulse response is free from causality errors. This preliminary band extension and delay adjustment ensures that the necessary frequency information is available before the critical IFT operation.
Solution Approach 2:
The patent applies parameter changes by modifying the frequency band parameters of S-parameters. The system changes the frequency range from band-limited to extended band by adding low-frequency components through interpolation and high-frequency components through extrapolation. Additionally, the propagation delay time parameter is adjusted to optimize the impulse response accuracy, thereby transforming the input parameters to achieve reliable causality in the output.
3Measurement precision
If equivalent circuit conversion method is used for S-parameters, then time response can be obtained, but the process becomes complicated and accuracy decreases
Solution Approach 1:
The patent applies mechanics substitution by replacing the equivalent circuit conversion method with a direct signal processing approach. Instead of converting S-parameters to an equivalent circuit model and then analyzing time response, the system directly processes S-parameters through band extension and inverse Fourier transform to obtain impulse response. This substitution eliminates the intermediate circuit conversion step, reducing complexity while maintaining or improving accuracy.
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 enhances the accuracy of impulse response and time response performance of passive networks by adjusting propagation delay time, ensuring band extension errors remain within a predetermined reference value, thus improving the analysis without requiring complex circuit conversions.
Implementation Method 1
performing Hilbert transform on the imaginary part of the derived band-extended S-parameter to derive an impulse response
Data Source
AI summary
A system for analyzing a passive network is provided, the system being configured to extend the frequency band with the interpolation function of the low frequency band and the extrapolation function of the high frequency band for S-parameters with limited measurement band, adjust the propagation delay time for the band-extended S-parameter to derive the final band-extended S-parameter, and analyze the time response of the passive network on the basis of the output voltage waveform estimated by performing convolution on the impulse response to the derived final band-extended S-parameter and the input voltage waveform of the passive network, thereby improving the time response performance of the passive network without a complex circuit conversion process, and making it possible to be capable of lightweight structures. Furthermore, it is possible to improve the accuracy of the impulse response by adjusting the propagation delay time removed from the band-limited S-parameter.