WOLFRAM SYSTEM MODELER
SmoothStepCompares oLine and tLine behaviour |
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Diagram
Wolfram Language
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SystemModel["Modelica.Electrical.Analog.Examples.Lines.SmoothStep"]
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Information
This information is part of the Modelica Standard Library maintained by the Modelica Association.
This example shows a comparison of a multi-segment OLine model with the distributed-parameter line model TLine.
If resistances and conductances are negligible, with OLine the results should become closer and closer as the number of segments increases.
Suggested tests:
Steep step
Use the model as it is (it has firstOrder.T=1e-9 s) and compare R1.v, R5.v, R50.v, Rdistr.v: Rdistr.v is the ideal voltage of the receiving-end resistor for a lossless line, while the others are approximations with 1, 5, 50 cascaded segment models.
The step in this case is nearly ideal, and therefore is a very tough test for cascaded segments, and in fact they are not very good in approximating the real line behaviour.
Smoother step
Repeat the simulation using firstOrder.T=20e-6 s. You will see that the OLine compliance with the reference result given by TLine is much better, and 50 segments are probably adequate for several applications; in comparison with, they add the option of evaluating losses.
Parameters (12)
| Rload |
Value: 1000 Type: Resistance (Ω) Description: Load resistance |
|---|---|
| r1 |
Value: 1e-6 Type: Real (Ω/m) Description: Resistance per meter |
| g1 |
Value: 1e-12 Type: Real (S/m) Description: Conductance per meter |
| l1 |
Value: 1e-6 Type: Real (H/m) Description: Inductance per meter |
| c1 |
Value: 1e-11 Type: Real (F/m) Description: Capacitance per meter |
| len |
Value: 100e3 Type: Length (m) Description: Length of line |
| N1 |
Value: 1 Type: Integer Description: Number of lumped segments of oline1 |
| N5 |
Value: 5 Type: Integer Description: Number of lumped segments of oline5 |
| N50 |
Value: 50 Type: Integer Description: Number of lumped segments of oline50 |
| c |
Value: 1 / sqrt(l1 * c1) Type: Velocity (m/s) Description: Speed of EM wave |
| td |
Value: len / c Type: Time (s) Description: Transmission delay |
| z0 |
Value: sqrt(l1 / c1) Type: Impedance (Ω) Description: Characteristic impedance for very high frequency |
Components (14)
 |
step |
Type: Step Description: Generate step signal of type Real |
|---|---|---|
 |
firstOrder |
Type: FirstOrder Description: First order transfer function block (= 1 pole) |
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sourceV |
Type: SignalVoltage Description: Generic voltage source using the input signal as source voltage |
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groundS |
Type: Ground Description: Ground node |
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oLine1 |
Type: OLine Description: Lossy Transmission Line |
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R1 |
Type: Resistor Description: Ideal linear electrical resistor |
|
oLine5 |
Type: OLine Description: Lossy Transmission Line |
|
R5 |
Type: Resistor Description: Ideal linear electrical resistor |
|
oLine50 |
Type: OLine Description: Lossy Transmission Line |
|
R50 |
Type: Resistor Description: Ideal linear electrical resistor |
|
groundO |
Type: Ground Description: Ground node |
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tLine |
Type: TLine Description: Lossless transmission line with characteristic impedance Z0 and transmission delay TD |
|
Rdistr |
Type: Resistor Description: Ideal linear electrical resistor |
|
groundT |
Type: Ground Description: Ground node |
Revisions
- May, 2021 implemented by Massimo Ceraolo, University of Pisa