Extracting Transmission Line Parameters

Star-Hspice includes a built-in 2-D electromagnetic field solver, which is highly optimized for interconnects in stratified media. Its implementation makes use of the W Element and supports optimization and statistical analysis within transient simulation. The solver is based on an improved version of the boundary-element method1 and filament method that is also implemented in Raphael2.

Filament Method

This section describes the filament method for the skin effect resistance and inductance solver.

The 2D filament method is introduced in release 2001.2 to extract frequency dependent resistance and inductance by taking magnetic coupling into account. This solver is invoked when COMPUTERS=yes is set in . fsoption .

The principle of the filament method is that the original conductor system is divided into thin filaments. The distributed magnetic coupling of the inside and outside of the conductor is derived from the coupling of these filaments.

Once conductors are divided into thin filaments, the impedance matrix of the filament system is given as . Then, the current matrix i f can be solved by:

Here, vf is an excitation vector for the filament system. As a result, the partial current matrix of conductor system i p can be calculated as a summation of the filament current as follows:

The partial impedance matrix Z p is solved by:

Loop impedance matrix components which are needed for W element analysis are calculated from partial impedance matrix components based on the following relationship:

Here, n is the number of signal (non-reference) conductors in the system.

Modeling Geometries

In geometry modeling:

• There is an arbitrary number of dielectric layers.
• The conductor cross-section can be arbitrarily shaped including an infinitely thin strip.
• There is no limit on the number of conductors.
• The current dielectric region must be planar.
• All conductors must be nonoverlapping.
• Magnetic materials are not supported.

Using Geometric Modeling Output

Geometric modeling outputs the Maxwellian (short-circuit) transmission line matrices: C, L, Ro , Rs , Go , and Gd (see Using Transmission Line Equations and Parameters).

Solver Limitations

The Star-Hspice field solver has the following limitation: the arithmetic average values of conductivities and loss tangents are used for inhomogeneous media when it computes the conductance matrices, Go and Gd .

Using the Field-Solver Statement Syntax

The Star-Hspice input syntax related to the field solver contains five new statements: . MATERIAL , . LAYERSTACK , . SHAPE and . FSOPTIONS , and a . MODEL W statement. Include these new statements in a netlist to define the material properties, stacking of materials, material shapes, field solver options and the transmission-line model as follows.

Defining Material Properties

Use the . MATERIAL statement to define the properties of a material.

Syntax

.MATERIAL mname METAL|DIELECTRIC <ER=val> <UR=val> 
+ <CONDUCTIVITY=val> <LOSSTANGENT=val>

Handling Metals

The Star-Hspice field solver assigns the following default values for metal: CONDUCTIVITY = -1 (perfect conductor), ER = 1, UR = 1. PEC is a predefined metal name with the default values and cannot be redefined.

Handling Dielectrics

The Star-Hspice field solver assigns the following default values for dielectrics: CONDUCTIVITY = 0 (lossless dielectric) , LOSSTANGENT = 0 (lossless dielectric), ER = 1, UR = 1 . AIR is a predefined dielectric name with default values and cannot be redefined.

Creating Layer Stacks

A layer stack defines a stack of dielectric or/and metal layers. Each transmission line system is associated with exactly one layer stack. But a single-layer stack can be associated with many transmission line systems.

Syntax

.LAYERSTACK sname <BACKGROUND=mname>
+ <LAYER=(mname,thickness) ...>

In the layer stack:

• Layers are listed from bottom to top.
• Metal layers (ground planes) are located only at the bottom, top, or both top and bottom.
• Layers are stacked in y-direction, and the bottom of a layer stack is at y=0.
• All conductors must be located above y=0.
• Background material must be dielectric.

Limiting Cases

Free space without ground: . LAYERSTACK mystack

Free space with a (bottom) ground plane:
.LAYERSTACK halfSpace PEC 0.1mm

Defining Shapes

Use the SHAPE statement to define a shape (used to describe the conductor cross-section).

Syntax

.SHAPE sname Shape_Descriptor

Defining Rectangles

Use a shape descriptor that defines a rectangle.

Syntax

RECTANGLE WIDTH=val HEIGHT=val <NW=val> <NH=val>

Figure 18-9: Coordinates of a Rectangle

Defining Circles

Use a shape descriptor that defines a circle. A circle is discretized as an inscribed regular polygon with N edges. Do not use the CIRCLE descriptor to model actual polygons; instead use the POLYGON descriptor.

Syntax

CIRCLE RADIUS=val <N=val>

Figure 18-10: Coordinates of a Circle

Defining Strips

Shape descriptor that defines an infinitesimally thin strip.

Syntax

STRIP WIDTH=val <N=val>

Figure 18-11: Coordinates of a Strip Polygon

Use a shape descriptor that defines a polygon. The specified coordinates are in the local coordinate with respect to the origin of a conductor.

Syntax

POLYGON VERTEX=(x1 y1 x2 y2 ...) <N=(n1,n2,...)>

Figure 18-12: Coordinates of a Polygon

Example

Rectangular polygon using the default discretization:

POLYGON VERTEX=(1 10 1 11 5 11 5 10)

Rectangular polygon using five segments for each edge:

POLYGON VERTEX=(1 10 1 11 5 11 5 10) N=5

Rectangular polygon using the different number of segments for each edge:

POLYGON VERTEX=(1 10 1 11 5 11 5 10) N=(5 3 5 3)

Field-Solver Options

Use the FSOPTIONS statement to set various options for the solver.

Syntax

.FSOPTIONS name <ACCURACY=LOW|MEDIUM|HIGH>
+ <GRIDFACTOR=val> <PRINTDATA=YES|NO> <COMPUTEG0=YES|NO>
+ <COMPUTEGD=YES|NO> <COMPUTERO=YES|NO> <COMPUTERS=YES|NO>

The L and C matrices are always computed.

For each accuracy mode, the solver uses either the predefined number of segments or the user-specified value for discretization. It then multiplies this number by the GRIDFACTOR to obtain the final number of segments.

Using the Field Solver Model

Use the field-solver model to specify a W Element transmission-line geometry model.

In the field-solver model:

• The list of conductors must appear last.
• Conductors cannot overlap each other.
• Floating conductors are assumed to be electrically disconnected, and nonzero fixed charge is not supported.
• Metal layers in the layer stack are treated as the reference node.
• Conductors defined as REFERENCE are all electrically connected and correspond to the reference node in W Element.
• Signal conductors must be ordered according to the terminal list in the W Element statement; for instance, the ith signal conductor, counting without reference and floating conductors, is associated with the ith input and output terminals specified in the corresponding W Element. Floating and reference conductors can appear in any order.

Syntax

.MODEL mname W MODELTYPE=FieldSolver LAYERSTACK=name
+ <FSOPTIONS=name> <RLGCFILE=name>
+ <OUTPUTFORMAT=RLGC|RLGCFILE>
+ CONDUCTOR=( SHAPE=name <MATERIAL=name> <ORIGIN=(x,y)>
+ <TYPE=SIGNAL|REFERENCE|FLOATING> ) ...