Processor-implemented systems and methods for multi-conductor transmission line simulation
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.
1. A processor-implemented method of constructing a physical transmission line system, comprising:
receiving characteristic data associated with a physical transmission line system;
building a model of the physical transmission line system based on the characteristic data, wherein building a model of the physical transmission line system comprises:
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;
determining a state space model based on the characteristic admittance matrix and the linking matrix;
performing a simulation using the state space model to determine a physical characteristic;
wherein the physical transmission line system is (i) built based on the simulation predicting the physical transmission line system will behave as desired or (ii) modified based on the simulation predicting the physical transmission line system will not behave as desired.
2. The method of claim 1 , wherein the propagation function matrix represents delay, distortion, or attenuation in the physical transmission line system.
3. The method of claim 1 , wherein the linking matrix is determined according to:
Ψ= Y −1 ( I− Θ),
where Ψ is the linking matrix, Y is the characteristic admittance matrix, and Θ is the propagation function matrix.
4. The method of claim 1 , wherein the state space model is configured to simulate transmission of an impulse signal in a transmission line and a plurality of reflections in that transmission line.
5. The method of claim 4 , wherein the state space model is configured to determine an effect of transmission of the impulse signal in the transmission line in a second transmission line.
6. The method of claim 5 , wherein the transmission line and the second transmission line are in close proximity.
7. The method of claim 5 , wherein the transmission line and the second transmission line are parallel transmission lines.
8. The method of claim 1 , wherein the physical characteristic includes a constant voltage and current level associated with a steady state time after the plurality of reflections have dissipated.
9. The method of claim 1 , wherein the physical characteristic is a time-domain voltage and current response of a transmission line to an impulse signal.
10. The method of claim 1 , wherein a transmission line simulated by the state space model is a transmission line in a consumer electronics device.
11. The method of claim 10 , wherein the consumer electronics device is a mobile computing device or a mobile fitness device.
12. A processor-implemented system for constructing a physical transmission line system, comprising:
one or more data processors;
a computer-readable medium encoded with instructions for commanding the one or more data processors to execute steps of a method, comprising:
receiving characteristic data associated with a physical transmission line system;
building a model of the physical transmission line system based on the characteristic data, wherein building a model of the physical transmission line system comprises:
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;
determining a state space model based on the characteristic admittance matrix and the linking matrix;
performing a simulation using the state space model to determine a physical characteristic;
wherein the physical transmission line system is (i) built based on the simulation predicting the physical transmission line system will behave as desired or (ii) modified based on the simulation predicting the physical transmission line system will not behave as desired.
13. The system of claim 12 , wherein the propagation function matrix represents delay, distortion, or attenuation in the physical transmission line system.
14. The system of claim 12 , wherein the linking matrix is determined according to:
Ψ= Y −1 ( I −Θ),
where Ψ is the linking matrix, Y is the characteristic admittance matrix, and Θ is the propagation function matrix.
15. The system of claim 12 , wherein the state space model is configured to simulate transmission of an impulse signal in a transmission line and a plurality of reflections in that transmission line.
16. The system of claim 15 , wherein the state space model is configured to determine an effect of transmission of the impulse signal in the transmission line in a second transmission line.
17. The system of claim 16 , wherein the transmission line and the second transmission line are in close proximity.
18. The system of claim 16 , wherein the transmission line and the second transmission line are parallel transmission lines.
19. The system of claim 12 , wherein the physical characteristic includes a constant voltage and current level associated with a steady state time after the plurality of reflections have dissipated.
20. A non-transitory computer-readable medium encoded with instructions for commanding a processing system to execute steps of a method for constructing a physical transmission line system, the method comprising:
receiving characteristic data associated with a physical transmission line system;
building a model of the physical transmission line system based on the characteristic data, wherein building a model of the physical transmission line system comprises:
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;
determining a state space model based on the characteristic admittance matrix and the linking matrix;
performing a simulation using the state space model to determine a physical characteristic;
wherein the physical transmission line system is (i) built based on the simulation predicting the physical transmission line system will behave as desired or (ii) modified based on the simulation predicting the physical transmission line system will not behave as desired.