Using Scattering Parameter Element

A new S Element, in conjunction with the generic frequency-domain model (.MODEL SP ), provides a convenient way to describe a multi-terminal network. Currently, S (scattering) and Y parameters are supported. S Element can be used in AC and DC analyses.

In particular, the S parameter in S Element represents the generalized scattering parameter S for a multi-terminal network, which is defined as:

where boldface lower-case and upper-case symbols denote vectors and matrices, respectively. vinc and vref are the incident and reflected voltage wave vectors (see Terminal Node Notation). The S parameter can be converted to Y parameter using the following formula:

where Yr is the characteristic admittance matrix of the reference system, which is related to the characteristic impedance matrix Zr by:

Similarly, Y parameter can be converted to S parameter as follows:

Figure 6-1: Terminal Node Notation

Syntax

The syntax of the S Element is:

Sxxx nd1 nd2 ... ndN ndR FQMODEL=name [TYPE=val Zo=val Zof=name]

`nd1 nd2 ... ndN`	N signal nodes (see Terminal Node Notation).
`ndR`	Reference node.
`FQMODEL`	`.MODEL` statement of type sp, which defines the frequency behavior of S or Y parameter.
`TYPE`	Parameter type: `S` : scattering parameter (default) `Y` : Y parameter
Zo	Characteristic impedance value of the reference line (frequency-independent). For multi-terminal cases (N>1), the characteristic impedance matrix of the reference lines is assumed to be diagonal and its diagonal values are set to Zo. More general types of a reference line system can be specified using Zof. Default=50 .
Zof	Name of the frequency-varying model that defines the frequency behavior of the reference system. If both Zo and Zof have been defined, then Zof has precedence.

Frequency Table Model

The Frequency Table Model is a generic model that can be used to describe frequency-varying behavior. Currently, it is used by S Element and .NOISENPT.

Syntax

The syntax of the .MODEL model card is:

.MODEL name sp [N=val FSTART=val FSTOP=val NI=val SPACING=val
+ MATRIX=val VALTYPE=val INFINITY=matrixval INTERPOLATION=val
+ EXTRAPOLATION=val] [DATA=(npts ...)] [DATAFILE=filename]

`name`	Model name.
`N`	Matrix dimension (number of signal terminals). Values other than 1 must be specified before setting `INFINITY` and `DATA` . Default=1.
`FSTART`	Starting frequency point for data. Default=0.
`FSTOP`	Final frequency point for data (used only for the `LINEAR` and `LOG` spacing formats).
`NI`	Number of frequency points per interval. Used only for the `DEC` and `OCT` spacing formats. Default=10.
`npts`	Number of data points.
`SPACING`	Data sample spacing format: `LIN (LINEAR)` : uniform spacing with the frequency step of (`FSTOP-FSTART` )/(`npts` -1). Default. `OCT` : octave variation with `FSTART` as the starting frequency and `NI` points per octave. npts determines the final frequency. `DEC` : decade variation with `FSTART` as the starting frequency and `NI` points per decade. `npts` determines the final frequency. `LOG` : logarithmic spacing with `FSTART` and FSTOP as the starting and final frequencies. `POI(NONUNIFORM)` : nonuniform spacing. Data points are paired with frequency points.
`MATRIX`	Matrix (data point) format: `SYMMETRIC` : symmetric matrix. Only the lower-half triangle portion of a matrix is specified. Default. `HERMITIAN` : similar to `SYMMETRIC` but off-diagonal terms are complex-conjugate of each other. `NONSYMMETRIC` : nonsymmetric matrix. A full matrix is specified.
`VALTYPE`	Data type of matrix elements: `REAL` : real entry `CARTESIAN` : complex number in real/imaginary format. Default. `POLAR` : complex number in polar format. Angles are specified in radian.
`INFINITY`	Data point at infinity. Typically real-valued. Data format must be consistent with `MATRIX` and `VALTYPE` specifications. This point is not counted in `npts` .
`DC`	Data port at DC. Typically real-valued. Data format must be consistent with `MATRIX` and `VALTYPE` specifications. This point is not counted in npts. It is required to specify DC point or data point at frequency=0.
`INTERPOLATION`	Interpolation scheme: `STEP` : piecewise step. Default. `LINEAR` : piecewise linear `SPLINE` : b-spline curve fit
`EXTRAPOLATION`	Extrapolation scheme during simulation: `NONE` : no extrapolation is allowed. Star-Hspice will terminate if data point is required outside of the specified range. `STEP` : the last boundary point is used. Default. `LINEAR` : linear extrapolation using the last two boundary points. If the data point at the infinity is specified, then no extrapolation is performed and the infinity value is used.
`DATA`	Specifies data points. Syntax for `LIN` spacing: `.MODEL name sp SPACING=LIN [N=dim] + FSTART=f0 DF=f1 DATA=npts d1 d2 ...` Syntax for `OCT` or `DEC` spacing: `.MODEL name sp SPACING=DEC` or `OCT + [N=dim] FSTART=f0 + NI=n_per_intval DATA=npts d1 + d2 ...` Syntax for `POI` spacing: `.MODEL name sp SPACING=NONUNIFORM + [N=dim] DATA=npts f1 d1 f2 d2 + ...`
`DATAFILE`	This option allows users to specify data points in an external file. The content of this file must be only raw numbers without any suffixes, comments or continuation letters. The order of data must follow the DATA statement. This feature is useful as this data file does not have limitation on line length so users can enter a large number of data points.

NOTE: The interpolation and extrapolation are performed after S parameter data are converted to Y parameter internally.

Example

The two outputs from the resistor and S parameter modeling should be matched exactly in this example. See Input File Listing for the input file listing and Transmission line with a resistive termination for an illustration of a transmission line with a resistive termination.

Figure 6-2: Transmission line with a resistive termination

Table 6-1: Input File Listing

Header, options, and sources	`*S parameter ex1: x-line with a resistive + termination` `.OPTIONS POST` `V1 i1 0 ac=1v`
Analysis	`.AC lin 500 0Hz 30MegHz` `.DC v1 0v 5v 1v`
Transmission line (W element)	`W1 i1 i2 i3 0 o1 o2 o3 0 RLGCMODEL=wrlgc N=3 L=0.97` `.MODEL wrlgc sp MODELTYPE=RLGC N=3` `+ Lo = 2.78310e-07` `+ 8.75304e-08 3.29391e-07` `+ 3.65709e-08 1.15459e-07 3.38629e-07` `+ Co = 1.41113e-10` `+ -2.13558e-11 9.26469e-11` `+ -8.92852e-13 -1.77245e-11 8.72553e-11`
Termination	`x1 o1 o2 o3 0 terminator`
Frequency model definition	`.MODEL fmod sp N=3 FSTOP=30MegHz` `+ DATA= 1` `+ -0.270166 0.0` `+ 0.322825 0.0 -0.41488 0.0` `+ 0.17811 0.0 0.322825 0.0 -0.270166 0.0`
Resistor elements	`.SUBCKT terminator n1 n2 n3 ref` `R1 n1 ref 75` `R2 n2 ref 75` `R3 n3 ref 75` `R12 n1 n2 25` `R23 n2 n3 25` `.ends terminator`
Equivalent S parameter element	`.ALTER S parameter case` `.SUBCKT terminator n1 n2 n3 ref` `S1 n1 n2 n3 ref FQMODEL=fmod` `.ENDS terminator` `.END`

This is an example of a transmission line with a capacitive network termination.

Table 6-2: Input File Listing
Frequency model definition	`.MODEL fmod sp N=3 FSTOP=30MegHz` `+ DATA= 2` `+ 1.0 0.0` `+ 0.0 0.0 1.0 0.0` `+ 0.0 0.0 0.0 0.0 1.0 0.0` `+ 0.97409 -0.223096` `+ 0.00895303 0.0360171 0.964485 -0.25887` `+ -0.000651487 0.000242442 0.00895303 0.0360171` `+ 0.97409 -0.223096`
Using capacitive elements	`.SUBCKT terminator n1 n2 n3 ref` `C1 n1 ref 10pF` `C2 n2 ref 10pF` `C3 n3 ref 10pF` `C12 n1 n2 2pF` `C23 n2 n3 2pF` `.ENDS terminator`

The two outputs from the resistor and S parameter modeling will differ slightly due to the linear frequency dependency related to the capacitor. This difference can be removed by using the linear interpolation scheme in .MODEL.

This is an example of a transmission line with S parameter.

Figure 6-3: 3-Conductor Transmission line

Table 6-3: Input File Listing

Header, options and sources	`*S parameter ex3: modeling x-line using + S parameter` `.OPTIONS POST` `vin in0 0 ac=1`
Analysis	`.AC lin 100 0 1000meg` `.DC vin 0 1v 0.2v`
Transmission line	`X1 in1 in2 out1 out2 0 x-line`
Termination	`R1 in0 in1 28` `R2 in2 0 28` `R3 out1 0 28` `R4 out2 0 28`
W Element RLGC model definition	`.MODEL m2 W ModelType=RLGC, N=2` `+ Lo= 0.178e-6` `+ 0.0946e-7 0.178e-6` `+ Co= 0.23e-9` `+ -0.277e-11 0.23e-9` `+ Ro= 0.97` `+ 0 0.97` `+ Go= 0` `+ 0 0` `+ Rs= 0.138e-3` `+ 0 0.138e-3` `+ Gd= 0.29e-10` `+ 0 0.29e-10`
Frequency model definition	`.MODEL SM2 sp N=4 FSTART=0 FSTOP=1e+09 + SPACING=LINEAR` `+ DATA= 60` `+ 0.00386491 0` `+ 0 0 0.00386491 0` `+ 0.996135 0 0 0 0.00386491 0` `+ 0 0 0.996135 0 0 0 0.00386491 0` `+ -0.0492864 -0.15301` `+ 0.00188102 0.0063569 -0.0492864 -0.15301` `+ 0.926223 -0.307306 0.000630484 -0.00154619 + 0.0492864 -0.15301` `+ 0.000630484 -0.00154619 0.926223 -0.307306 + 0.00188102 0.0063569 -0.0492864 -0.15301` `+ -0.175236 -0.241602` `+ 0.00597 0.0103297 -0.175236 -0.241602` `+ 0.761485 -0.546979 0.00093508 -0.00508414 + -0.175236 -0.241602` `+ 0.00093508 -0.00508414 0.761485 -0.546979 + 0.00597 0.0103297 -0.175236 -0.241602` `+ ...`
Equivalent S parameter element	`.SUBCKT terminator n1 n2 n3 ref` `S1 n1 n2 n3 ref FQMODEL=SM2` `.ENDS terminator`

Star-Hspice Manual - Release 2001.2 - June 2001