Using the W Element

The W Element, multiconductor lossy frequency-dependent transmission line, provides advanced modeling capabilities for transmission lines.

The W Element provides:

• Exact analytical solution for AC and DC analyses
• No limit on the number of coupled conductors
• No restrictions on the structure of RLGC matrices; all matrices can be full.
• No spurious ringing as that produced by the old U Element (see Spurious Ringing in U Element)
• Accurate modeling of frequency-dependent loss in the transient analysis

Figure 18-5: Spurious Ringing in U Element

The W Element supports the analyses:

• AC
• DC
• Transient
• Parameter sweeps in DC, AC, and transient analyses
• Optimization
• Monte-Carlo

Using Time-Step Control

The W Element provides accurate results with just 1-2 time steps per excitation transient (0.1 ns in the above example). It supports Star-Hspice'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. Star-Hspice's default time-step 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. Star-Hspice 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 0.5-1 of the excitation transient.

.OPTION RISETIME

The . OPTION RISETIME used by U Elements to compute the number of lumped segments, also affects the transient simulation of W Elements with frequency-dependent parameters. It has no effect on AC analysis and W Elements with constant parameters (R s = G d = 0).

The option overrides W Element's internal frequency-range 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.

W Element and Field Solver Updates

Accuracy Improvements for W Element

Accuracy has been improved for:

• Short transmission lines with frequency-dependent parameters
• Voltage level changes due to reflection (for the frequency-dependent parameters only)

Field Solver Bug Fix

A slight accuracy problem with the Star-Hspice internal field solver for the case with both top and bottom ground planes has been discovered and fixed.

Dielectric Loss Modeling

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.

.OPTION RISETIME Setting

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:

• Positive value: the inverse of this user-specified value is used as the maximum frequency.
• No setting (recommended): the risetime is automatically determined from source statements. This method works for most cases; in special cases where the netlist contains the dependent source (which scales or shifts the frequency information) the risetime should be explicitly set.
• Zero: the internal W Element-bound computing algorithm is used for each individual transmission line without using the frequency information contained in source statements.

Imaginary Term Handling for the Skin-Effect

As of the 1999.4 release of Star-Hspice, to depict the correct frequency response at high frequency, the imaginary term of the skin-effect 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

W Element Transmission Line Properties Inputs

The W Element supports four different formats to input transmission line properties:

• Model 1: RLGC-Model specification.
• Model 2: U-Model specification, including:
• RLGC input for up to five coupled conductors
• Geometric input (planar, coax, twinlead)
• Measured-parameter input
• Skin effect
• Model 3: Star-Hspice internal field-solver model
• Model 4: External file containing RLGC information. This format is supported only for the purpose of backward compatibility and Model 1 should be used instead. Note that this model does not allow parameterized RLGC values.

Syntax

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=YES|NO> <FGD=val>

Figure 18-6: Terminal Node Numbering

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.

Input Model 1: W Element RLGC Model

The section, Using Transmission Line Equations and Parameters describes the W Element inputs R, L, G, C, R s (skin-effect), and G d (dielectric-loss) per-unit-length matrices. There are no limitations on the number of coupled conductors, shape of the matrices, line loss, length or amount of frequency dependence. The RLGC text file contains frequency-dependent RLGC matrices per unit length.

The W Element also handles frequency-independent (RLGC) and lossless (LC) lines. It does not support RC lines.

Since RLGC matrices are symmetric, only the lower-triangular 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 ]

Optional Parameters (default values are zero)

Example

The following is example.sp input netlist file showing the RLGC file input usage of the W Element:

* W-Element example, four-conductor 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 four-conductor lossy
.MODEL example_rlc W MODELTYPE=RLGC N=3
+ Lo=
+ 2.311e-6
+ 4.14e-7 2.988e-6
+ 8.42e-8 5.27e-7 2.813e-6
+ Co=
+ 2.392e-11
+ -5.41e-12 2.123e-11
+ -1.08e-12 -5.72e-12 2.447e-11
+ 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=
+ 5.242e-13
+ -1.221e-13 5.164e-13
+ -1.999e-14 -7.747e-14 4.321e-13
.end

Star-Hspice Simulation Results shows a plot of Star-Hspice simulation results (a) DC Sweep, b) AC response, and c) transient waveforms). It shows that the transmission-line behavior of interconnects has significant and complicated effect on the signal integrity, and accurate transmission line modeling is necessary for verification of high-speed designs.

Figure 18-7: Star-Hspice Simulation Results

(a) DC Sweep

(b) AC Response

(c) Transient Waveforms

Input Model 2: U Model

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 measured-parameter interfaces.

To use the W Element with the U model, specify Umodel=U-model_name on the W Element card.

The W Element supports all U-model modes, including:

• Geometric, Elev =1
• planar geometry, Plev =1
• coax, Plev =2
• twinlead, Plev =3
• RLGC, Elev =2
• Measured parameters, Elev =3
• Skin-effect, Nlay =2.

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.

Using RLGC Matrices

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 U-model's RLGC matrices are related to the W Element's RLGC matrices, and how they are used by the W Element.

Handling the Dielectric-loss Matrix

Since the U model does not input the dielectric loss matrix Gd, the W Element defaults Gd to zero when it uses the U-model input. In future Star-Hspice releases, the W Element will have its own .MODEL with Gd capability. For this release, use RLGC file to specify nonzero Gd.

Handling the Skin-effect Matrix

The skin-effect resistance R s is used differently by U and W Elements. In a W Element, the R s matrix specifies the square-root dependence of the frequency-dependent resistance,

In a U Element, R is the value of skin resistance at the frequency:

where the core resistance R c is equivalent to the W Element's DC resistance R o . The frequency at which U Element computes R s is:

Table 18-1: RLGC Matrices in W Element and U Model

If you do not specify the RISETIME option, the U Element uses Tstep from the . tran card.

Example

The following Star-Hspice netlist is for a 4-conductor line shown in
4-Conductor Line.

* W Element example, four-conductor 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

Figure 18-8: 4-Conductor Line

Input Model 3: Field-Solver Model

Instead of RLGC matrices, you can directly use geometric data with the W Element using a new built-in field solver in Star-Hspice. To use the W Element with a field solver, specify FSmodel=model_name on the W Element card. The Star-Hspice field solver is described in Extracting Transmission Line Parameters.

Input Model 4: W Element RLGC File

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 lower-triangular parts of the matrices are specified in the RLGC file. However, unlike the RLGC model, the RLGC file is order-dependent. The parameters in the RLGC file are in the following order:

Comments and Separators

An asterisk `*' comments out everything until the end of its line. You can separate numbers using any of the characters: space, tab, newline, `,', `;', `(`, `)', `[`, `]', `{` or `}'.

Example

The netlist example used for the RLGC model in the previous section is rewritten using RLGC file below:

* W- Element example, four-conductor 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 four-conductor lossy
* frequency-dependent line
* N (number of signal conductors)
3
* Lo
2.311e-6
4.14e-7 2.988e-6
8.42e-8 5.27e-7 2.813e-6
* Co
2.392e-11
-5.41e-12 2.123e-11
-1.08e-12 -5.72e-12 2.447e-11
* 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
5.242e-13
-1.221e-13 5.164e-13
-1.999e-14 -7.747e-14 4.321e-13

The RLGC file does not support Star-Hspice scale suffices such as n (10 -9 ) or p (10 -12 ).