modelTransmissionLineEquations
Information
In this model, a transmission line circuit is implemented by equations. Transmission line circuit is represented as in the figure below. The application is the same as the TransmissionLineModelica model.
Considering the nodes of the discrete transmission line(implemented in Electrical.Models.TransmissionLine), circuit equations are described. In the transmission line, there are N segments, therefore, there will be N+1 nodes and N+1 voltage and current variables.
where j= 2,..,N and Rx is the resistance per meter, Cx is the capacitance per meter and Lx is the inductance per meter.
output voltage is described as:
Moreover, considering the form of the second order low pass filter, equation of the filter to a step input can be defined in the following way:
where Vstep is the step voltage and v1is the output voltage of the filter. The parameters of the TransmissionLineEquations are:
| Parameters | Comment |
|---|---|
| N | number of segments |
| L | length of transmission line |
| l | length of each segment |
| res | resistor per meter |
| cap | capacitance per meter |
| ind | inductance per meter |
| RL | load resistance |
| w | angular frequency |
| TD | time delay of transmission line |
| v | velocity of signal |
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Integer | N | 2 | number of segments |
| SIunits.Length | L | length of the transmission line | |
| SIunits.Length | l | L/N | length of the each segment |
| SIunits.Resistance | res | resistance per meter | |
| SIunits.Capacitance | cap | capacitance per meter | |
| SIunits.Inductance | ind | inductance per meter | |
| SIunits.Resistance | RL | (ind/cap)^(1/2) | load resistance |
| SIunits.AngularFrequency | w | ||
| SIunits.Time | TD | L/v | time delay of the transmission line |
| SIunits.Velocity | v | 1/(ind*cap)^(1/2) | velocity of the signal |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| SIunits.Voltage | Vstep | if time > 0 then 1 else 0 | input step voltage |
| SIunits.Current[N] | cur | current values at the nodes of the transmission line | |
| SIunits.Current[N - 1] | cur_x | current state variables | |
| SIunits.Voltage[N] | vol | voltage values at the nodes of the transmission line | |
| Real | vvol | derivative of input voltage |