The W Element, multiconductor lossy frequencydependent transmission line, provides advanced modeling capabilities for transmission lines.
The W Element supports the analyses:
The W Element provides accurate results with just 12 time steps per excitation transient (0.1 ns in the above example). It supports StarHspice's iteration count (the option
LVLTIM
=0) and
DVDT
(
LVLTIM
=1 or 3) time step control algorithms. It does not support the LTE (
LVLTIM
=2) algorithm yet. StarHspice's default timestep control algorithm is
DVDT
.
The W Element limits the maximum time step by the smallest transmission line delay in the circuit.
The W Element supports the
TLINLIMIT
option like the T Element. The default value of
TLINLIMIT
=0 enables special breakpoint building that improves transient accuracy for short lines, but reduces efficiency. To disable this special breakpoint building, set
TLINLIMIT
=1.
For longer transmission lines, there could be prolonged time intervals when nothing happens at the terminals when the wave propagates along the line. StarHspice increases the time step, and when the wave finally reaches the terminal, it decreases the accuracy of simulation. To prevent this, for longer lines excited with short pulses, set the .option
DELMAX
to limit the time step to 0.51 of the excitation transient.
The .
OPTION
RISETIME
used by U Elements to compute the number of lumped segments, also affects the transient simulation of W Elements with frequencydependent parameters. It has no effect on AC analysis and W Elements with constant parameters (R
The option overrides W Element's internal frequencyrange control, and should only be used for longer (over 10 m) cables. Setting
RISETIME
to a smaller value than the actual value of the excitation transient, decreases simulation accuracy.
Accuracy has been improved for:
A slight accuracy problem with the StarHspice internal field solver for the case with both top and bottom ground planes has been discovered and fixed.
New modeling equations have been implemented to address two issues:
1. Inaccurate dielectric loss.
2. The linear dependency at the high frequency region, causing undesirable effects.
To remedy these issues a new cutoff frequency for the Gd term is introduced as follows:
The default value of fgd is 0. You can specify an alternate value in the W Element statement:
Wxxx i1 i2 ... iN iR o1 o2 ... oN oR N=val L=val fgd=val
If you prefer to use the previous linear dependency, set fgd to 0.
The RISETIME parameter is used to compute the maximum frequency range for the transient analysis of W Element. Depending on its value, the following scheme is employed to determine the maximum frequency of interest:
As of the 1999.4 release of StarHspice, to depict the correct frequency response at high frequency, the imaginary term of the skineffect has been added, and the resulting modeling equation for the frequency dependent resistance is given by:
However, for low frequency applications, this may cause significant errors and this imaginary term can optionally be excluded from the W Element statement:
Wxxx i1 i2 ... iN iR o1 o2 ... oN oR N=val L=val INCLUDERSIMAG=NO
The W Element supports four different formats to input transmission line properties:
The syntax of the W Element statement is:
Wxxx i1 i2 ... iN iR o1 o2 ... oN oR N=val L=val + <FSMODEL=name or RLGCMODEL=name or RLGCFILE=name or + UMODEL=name> + <INCLUDERSIMAG=YESNO> <FGD=val>
Number of signal conductors (excluding the reference conductor) 

Nodes for the nearend signalconductor terminal (see Terminal Node Numbering) 

Nodes for the nearend referenceconductor terminal (should be the same node as 

Name of the external file with RLGC parameters (see Input Model 4: W Element RLGC File) 

Name of U .MODEL (see Input Model 2: U Model). 

Specifies the imaginary term of the skin effect to be considered. The default value is YES. (see Using FrequencyDependent Resistance and Conductance Matrices). 

Specifies the cutoff frequency of dielectric loss. (see Dielectric Loss Modeling). 
You can specify parameters in the W Element card in any order. Specify the number of signal conductors, N, after the list of nodes. You can intermix the nodes and parameters in the W Element card.
You can specify only one
RLGCmodel
,
FSmodel
,
Umodel
, or
RLGCfile
in a single W Element card.
The section, Using Transmission Line Equations and Parameters describes the W Element inputs R, L, G, C, R
The W Element also handles frequencyindependent (RLGC) and lossless (LC) lines. It does not support RC lines.
Since RLGC matrices are symmetric, only the lowertriangular parts of the matrices are specified in the RLGC model. The syntax of W Element RLGC model is:
.MODEL name W MODELTYPE=RLGC N=val Lo=matrix_entries + Co=matrix_entries [ Ro=matrix_entries Go=matrix_entries + Rs=matrix_entries Gd=matrix_entries Rognd=val Rsgnd=val + Lgnd=val ]
Number of signal conductors (same as that in the element card) 

DC inductance matrix per unit length for grounds (reference line) 

The following is
example.sp
* WElement example, fourconductor line
W1 N=3 1 3 5 0 2 4 6 0 RLGCMODEL=example_rlc l=0.97
V1 1 0 AC=1v DC=0v pulse(4.82v 0v 5ns 0.1ns 0.1ns 25ns).AC lin 1000 0Hz 1GHz
.DC v1 0v 5v 0.1v
.tran 0.1ns 200ns
* RLGC matrices for a fourconductor lossy
.MODEL example_rlc W MODELTYPE=RLGC N=3
+ Lo=
+ 2.311e6
+ 4.14e7 2.988e6
+ 8.42e8 5.27e7 2.813e6
+ Co=
+ 2.392e11
+ 5.41e12 2.123e11
+ 1.08e12 5.72e12 2.447e11
+ Ro=
+ 42.5
+ 0 41.0
+ 0 0 33.5
+ Go=
+ 0.000609
+ 0.0001419 0.000599
+ 0.00002323 0.00009 0.000502
+ Rs=
+ 0.00135
+ 0 0.001303
+ 0 0 0.001064
+ Gd=
+ 5.242e13
+ 1.221e13 5.164e13
+ 1.999e14 7.747e14 4.321e13
.end
StarHspice Simulation Results shows a plot of StarHspice simulation results (a) DC Sweep, b) AC response, and c) transient waveforms). It shows that the transmissionline behavior of interconnects has significant and complicated effect on the signal integrity, and accurate transmission line modeling is necessary for verification of highspeed designs.
The W Element accepts the U model as an input thus providing backward compatibility with the U Element, and taking advantage of the U model's geometric and measuredparameter interfaces.
To use the W Element with the U model, specify
Umodel=Umodel_name
on the W Element card.
The W Element supports all Umodel modes, including:
The only exception is
Llev
=1, which adds the second ground plane to the U model, and is not supported by the W Element. To model the extra ground plane, add an extra conductor to the W Element in
Elev
=2, or use an external lumped capacitor in
Elev
=1 and 3. See Ideal and Lumped Transmission Lines, for information on the U model.
RLGC matrices in the W Element's RLGC file are in the Maxwellian format. In the U model, they are in self/mutual format (see Determining Matrix Properties for conversion information). When using the U model, the W Element performs the conversion internally. RLGC Matrices in W Element and U Model shows how the Umodel's RLGC matrices are related to the W Element's RLGC matrices, and how they are used by the W Element.
Since the U model does not input the dielectric loss matrix Gd, the W Element defaults Gd to zero when it uses the Umodel input. In future StarHspice releases, the W Element will have its own .MODEL with Gd capability. For this release, use RLGC file to specify nonzero Gd.
The skineffect resistance R
In a U Element, R is the value of skin resistance at the frequency:
where the core resistance R
If you do not specify the
RISETIME
option, the U Element uses Tstep from the .
tran
card.
The following StarHspice netlist is for a 4conductor line shown in
4Conductor Line.
* W Element example, fourconductor line, U model
W1 1 3 5 0 2 4 6 0 Umodel=example N=3 l=0.97
.MODEL example U LEVEL=3 NL=3 Elev=2 Llev=0 Plev=1 Nlay=2
+
+ L11=2.311uH
+ L12=0.414uH L22=2.988uH
+ L13=84.2nH L23=0.527uH L33=2.813uH
+
+ Cr1=17.43pF
+ C12=5.41pF Cr2=10.1pF
+ C13=1.08pF C23=5.72pF Cr3=17.67pF
+
+ R1c=42.5 R2c=41.0 R3c=33.5
+
+ Gr1=0.44387mS
+ G12=0.1419mS Gr2=0.3671mS
+ G13=23.23uS G23=90uS Gr3=0.38877mS
+
+ R1s=0.00135 R2s=0.001303 R3s=0.001064
V1 1 0 AC=1v DC=0v pulse(4.82v 0v 5ns 0.1ns 0.1ns 25ns)
.AC lin 1000 0Hz 1GHz
.DC v1 0v 5v 0.1v
.TRAN 0.1ns 200ns
.END
Instead of RLGC matrices, you can directly use geometric data with the W Element using a new builtin field solver in StarHspice. To use the W Element with a field solver, specify
FSmodel=model_name
on the W Element card. The StarHspice field solver is described in Extracting Transmission Line Parameters.
RLGC matrices can also be specified in an external file (RLGC file). This external file format is more restricted than the RLGC model; for example, it cannot be parameterized and does not support the ground inductance and resistance. This format does not provides any advantage over the RLGC model and should not be used. (It is supported for the backward compatibility purpose only.)
Similar to the RLGC model, only the lowertriangular parts of the matrices are specified in the RLGC file. However, unlike the RLGC model, the RLGC file is orderdependent. The parameters in the RLGC file are in the following order:
Number of signal conductors (same as that in the element card) 

An asterisk `*' comments out everything until the end of its line. You can separate numbers using any of the characters: space, tab, newline, `,', `;', `(`, `)', `[`, `]', `{` or `}'.
The netlist example used for the RLGC model in the previous section is rewritten using RLGC file below:
* W Element example, fourconductor line
W1 N=3 1 3 5 0 2 4 6 0 RLGCfile=example.rlc l=0.97
V1 1 0 AC=1v DC=0v pulse(4.82v 0v 5ns 0.1ns 0.1ns 25ns).AC lin 1000 0Hz 1GHz
.DC v1 0v 5v 0.1v
.tran 0.1ns 200ns
.end
This calls the following
example.rlc
RLGC file:
* RLGC parameters for a fourconductor lossy
* frequencydependent line
* N (number of signal conductors)
3
* Lo
2.311e6
4.14e7 2.988e6
8.42e8 5.27e7 2.813e6
* Co
2.392e11
5.41e12 2.123e11
1.08e12 5.72e12 2.447e11
* Ro
42.5
0 41.0
0 0 33.5
* Go
0.000609
0.0001419 0.000599
0.00002323 0.00009 0.000502
* Rs
0.00135
0 0.001303
0 0 0.001064
* Gd
5.242e13
1.221e13 5.164e13
1.999e14 7.747e14 4.321e13
The RLGC file does not support StarHspice scale suffices such as n (10