modelULine

Lossy RC Line

Information

As can be seen in the picture below, the lossy RC line ULine is a single conductor lossy transmission line which consists of segments of lumped series resistors and capacitors that are connected with the reference pin p3. The precision of the model depends on the number N of lumped segments.
To get a symmetrical line model, the first resistor is cut into two parts (R1 and R_Nplus1). These two new resistors have the half of the resistance of the original resistor.

ULine.png

The capacitances are calculated with: C=c*length/N.
The resistances are calculated with: R=r*length/(N+1).
For all capacitors and resistors the values of each segment are the same except for the first and last resistor, that only has the half of the above calculated value.

The user has the possibility to enable a conditional heatport. If so, the ULine can be connected to a thermal network. When the parameter alpha is set to a value greater than zero, the ULine becomes temperature sensitive due to their resistors which resistances are calculated by R_actual= R*(1 + alpha*(heatPort.T - T_ref)).

Note, this is different compared with the lumped line model of SPICE.

References: [Johnson1991]

Parameters

TypeNameDefaultDescription
RealrResistance per meter
RealcCapacitance per meter
SI.LengthlengthLength of line
IntegerNNumber of lumped segments
SI.LinearTemperatureCoefficientalpha0Temperature coefficient of resistance (R_actual = R*(1 + alpha*(heatPort.T - T_ref)))
BooleanuseHeatPortfalse= true, if heatPort is enabled
SI.TemperatureT293.15Fixed device temperature if useHeatPort = false
SI.TemperatureT_ref300.15Reference temperature

Connectors

TypeNameDefaultDescription
Modelica.Electrical.Analog.Interfaces.Pinp1
Modelica.Electrical.Analog.Interfaces.Pinp2
Modelica.Electrical.Analog.Interfaces.Pinp3
Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_aheatPort

Components

TypeNameDefaultDescription
SI.Voltagev13
SI.Voltagev23
SI.Currenti1
SI.Currenti2
Modelica.Electrical.Analog.Basic.Resistor[N + 1]R
Modelica.Electrical.Analog.Basic.Capacitor[N]C

Revisions

2016
by Christoph Clauss resistance calculation revised
1998
by Christoph Clauss initially implemented