ULine

Lossy RC Line

    ULine

Library

Modelica/Electrical/Analog/Lines

Description

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 symmetric 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 an 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

Johnson, B.; Quarles, T.; Newton, A. R.; Pederson, D. O.; Sangiovanni-Vincentelli, A.
SPICE3 Version 3e User's Manual (April 1, 1991). Department of Electrical Engineering and Computer Sciences, University of California, Berkley p. 22, p. 124

Parameters

ULine_0

NameLabelDescriptionData TypeValid Values

mo_r

r

Resistance per meter

Scalar

mo_c

c

Capacitance per meter

Scalar

mo_length

length

Length of line

Scalar

mo_N

N

Number of lumped segments

Scalar

mo_alpha

alpha

Temperature coefficient of resistance (R_actual = R*(1 + alpha*(T_heatPort - T_ref))

Scalar

mo_useHeatPort

useHeatPort

=true, if HeatPort is enabled

Number

0
1

mo_T

T

Fixed device temperature if useHeatPort = false

Scalar

mo_T_ref

T_ref

Scalar

mo_rm

rm

Vector

ULine_1

NameLabelDescriptionData TypeValid Values

mo_v13

v13

v13

Structure

mo_v13/fixed

fixed

Cell of scalars

true
false

mo_v13/start

start

Cell of scalars

mo_v23

v23

v23

Structure

mo_v23/fixed

fixed

Cell of scalars

true
false

mo_v23/start

start

Cell of scalars

mo_i1

i1

i1

Structure

mo_i1/fixed

fixed

Cell of scalars

true
false

mo_i1/start

start

Cell of scalars

mo_i2

i2

i2

Structure

mo_i2/fixed

fixed

Cell of scalars

true
false

mo_i2/start

start

Cell of scalars

Ports

NameTypeDescriptionIO TypeNumber

p1

implicit

input

1

p2

implicit

input

2

p3

implicit

input

3

Port 4

implicit

input

mo_useHeatPort