Uniform Distributed RC Model (URC)

The URC model is derived from a model proposed by L. Gertzberg in 1974. The model is accomplished by a subcircuit type expansion of the URC line into a network of lumped RC segments with internally generated nodes. The RC segments are in a geometric progression, increasing toward the middle of the URC line, with (K) as a proportionality constant. The number of lumped segments used, if not specified for the URC line device, is determined by the following formula:

[\begin{array}{ll} {N = \frac{\log\left| {F_{\lbrack font\ rm\ \lbrack char\ m\ mathalpha\rbrack\lbrack char\ a\ mathalpha\rbrack\lbrack char\ x\ mathalpha\rbrack\rbrack}\frac{R}{L}\frac{C}{L}2\pi L^{2}\left| \frac{\left( {K - 1} \right)}{K} \right|^{2}} \right|}{\log K}} & \ \end{array}]The URC line is made up strictly of resistor and capacitor segments unless the ISPERL parameter is given a nonzero value, in which case the capacitors are replaced with reverse biased diodes with a zero-bias junction capacitance equivalent to the capacitance replaced, and with a saturation current of ISPERL amps per meter of transmission line and an optional series resistance equivalent to RSPERL ohms per meter.

Name
Parameter
Units
Default
Example
Area
K
Propagation Constant
-
2.0
1.2
-
FMAX
Maximum Frequency of interest
Hz
1.0 G
6.5 Meg
-
RPERL
Resistance per unit length
$\frac{\Omega}{m}$
1000
10
-
CPERL
Capacitance per unit length
$\frac{F}{m}$
10e-15
1 p
-
ISPERL
Saturation Current per unit length
$\frac{A}{m}$
0
-
-
RSPERL
Diode Resistance per unit length
$\frac{\Omega}{m}$
0
-
-