State Space Model for Lossy Transmission Line Simulation
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Solution Overview
Problem
Traditional transmission line simulation methods are inadequate for accurately simulating the complex behaviors of smaller transmission lines in modern devices, such as mobile computing and portable fitness devices, due to increased electrical resistance and material reflections, leading to noticeable signal degradations.
Innovation Solution
A computer-implemented system constructs a physical transmission line system through simulation by building a model based on characteristic data, determining a characteristic admittance matrix, a propagation function matrix, and a linking matrix, and using a state space model to simulate physical characteristics, thereby eliminating errors in steady-state responses.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Volume of moving object
If transmission line size is reduced to enable smaller devices, then device size is reduced, but electrical resistance increases causing signal degradation
Solution Approach 1:
The patent transforms the transmission line simulation problem from the time domain to the frequency domain by applying Fourier transforms. This parameter transformation enables the use of frequency-dependent characteristic admittance and propagation functions that accurately model lossy transmission lines, thereby maintaining signal integrity in reduced-size devices.
Solution Approach 2:
The patent replaces traditional time-domain numerical simulation methods with a frequency-domain analytical approach using state-space models. This substitution provides more accurate results for lossy transmission lines by using closed-form frequency-domain solutions that can be efficiently transformed back to the time domain, ensuring reliable signal integrity analysis.
2Productivity
If traditional simulation methods are used for lossy transmission lines, then computational simplicity is maintained, but simulation accuracy deteriorates due to errors in steady-state responses
Solution Approach 1:
The patent changes the domain parameter from time to frequency, enabling the use of frequency-dependent characteristic admittance and propagation functions. This transformation allows accurate modeling of lossy transmission lines while maintaining computational efficiency through analytical frequency-domain solutions that avoid the inaccuracies of traditional time-domain methods.
Solution Approach 2:
The patent introduces frequency-dependent characteristic admittance and propagation functions as intermediary elements that bridge the input and output of the transmission line system. These intermediary functions enable accurate representation of signal behavior in lossy lines, allowing precise simulation results to be obtained through frequency-domain analysis and inverse Fourier transformation.
3Reliability
If frequency-dependent characteristic admittance and propagation functions are used, then transient behavior accuracy is improved, but model complexity increases
Solution Approach 1:
The patent replaces complex time-domain differential equations with frequency-domain algebraic equations using state-space models. This substitution simplifies the mathematical representation while maintaining accuracy in transient behavior prediction, as the frequency-domain models naturally capture the frequency-dependent characteristics of lossy transmission lines without requiring complex numerical integration.
Data Source
AI summary
Systems and methods are provided for constructing a physical transmission line system. Characteristic data associated with a transmission line system is received. A model of the transmission line system is built based on the characteristic data. Building a model of the transmission line system includes determining a characteristic admittance matrix based on the characteristic data, determining a propagation function matrix based on the characteristic data, calculating a linking matrix based on the characteristic admittance matrix and the propagation function matrix, and determining a state space model based on the characteristic admittance matrix and the linking matrix. A simulation is performed using the state space model to determine a physical characteristic, where the transmission line system is built or modified based on the simulation-determined physical characteristic.