Ten Things every Designer shoulD Know when using AXieM

This guide describes ten tips to help designers effectively use AXieM™. The intent

of this guide is to highlight the most commonly encountered issues when working

in AXieM. references are given at the end of the guide, where the interested

reader can find more information. The tips are broken into four groups: ports,

electromagnetic (eM) environment, meshing, and simulation.

PorTs:

Tip 1: when deembedding a port, try not to put any metal too close to the

port, except the line to which it attaches.

Tip 2: if you have a ground plane below (or above) your ports, use explicit

grounding, and not implicit grounding.

eM environMenT:

Tip 3: when drawing the eM problem, look often at the 3D eM view.

Tip 4: understand the difference between drawing layers and eM layers.

Tip 5: use the sTACKuP block to create new eM projects.

Meshing:

Tip 6: Creating a mesh is a two step process in AXieM.

Tip 7: look at your mesh before you simulate.

Tip 8: Don’t use thick metal unless it is required for an accurate answer.

siMulATion:

Tip 9: when results from AXieM will be used for nonlinear circuit

simulations, make sure a frequency point close to DC is included in

the AXieM simulation.

Tip 10: AXieM has two types of solvers: direct and iterative.

AXIEM™

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Dr. John M. Dunn Awr Corporationjdunn@awrcorp.com

Bio:

Dr. John Dunn, a recognized expert in eM modeling and simulation for high-frequency and high-speed circuit applications, is a senior applications engineer at Awr and develops and presents Awr training mate-rial to customers world-wide.

Before joining Awr, he was head of the interconnect modeling group at Tektronix and a professor of electrical engineering at the university of Colorado, Boulder, where he led a research group in eM simulation and modeling.

Dr. Dunn received his Ph.D. and M.s. degrees in applied physics from harvard university and is a senior member of ieee.

DeTAileD DesCriPTion of The TiPs

PorTs:

TiP 1: When deembedding a port, try not to put any metal too close to the

port, except the line to which it attaches. A good rule of thumb, is to keep any

other metal at least a distance of two substrate heights away if possible.

edge ports in AXieM can usually be deembedded. (sometimes a port cannot

be deembedded; the most common case is explicitly grounded edge ports

whose ground straps attach to a finite ground plane.) figure 1 illustrates the

concept. The port in the left picture is too close to the neighboring line for

the deembedding algorithm to be accurate. in contrast, the port in the right

picture is sufficiently far away from neighboring metal. notice that the length

of deembedding arrow, which sets the reference plane, does not affect the

accuracy of the answer, so long as the port is 2X away from other metal.

A very common place to see this problem is in the feed lines of filter

structures. figure 2 shows a typical problem situation. The filter on the

left has feed lines that are too short. The ports, 1 and 2, are only 1X

the substrate height from the filter, and the deembedding assumptions

are violated. The filter on the right has the feed lines lengthened to 3X the

substrate height, which results in accurate deembedding.

in tightly constrained layouts, it is not always possible to obey the guideline

of the port being a distance 2X the substrate height from any other nearby

metal. if this is the case, the guideline can be relaxed with the caveat that

the deembedding is suspect. for example, the designer could try moving the

nearby metal to see if it makes a noticeable difference in the results. The exact

allowable minimum separation depends on the accuracy needed and the specific

geometry. if you are concerned, try a few simple simulations where the line is

deembedded with nothing else nearby, and then deembedded with other metal

close to it. in this way, you can gain experience with how sensitive deembedding

is to the proximity of metal in your process environment.

other issues:

specialized ports: AXieM has specialized ports that include coupling to

neighboring ports in the deembedding algorithm:

• Coupled, parallel lines: Typically, this is used for the excitation of differential pairs of lines.

• internal (sometimes called serial) port: Microwave office® 2010 supports a deembedded internal port,

used in the middle of a line.

• grouped ports: Calibrated port groups are usually used for gaps in lines, where a circuit model will

eventually be placed across the gap. for example, a designer uses AXieM, with a chip capacitor’s

s-parameter file derived from measured data.

Figure 1. A common filter problem. The feed lines for the left structure are too short.

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Figure 2. A common filter problem. The feed lines for the left structure are too short.

setting the ports up for deembedding: By default, ports are

deembedded, and the grounding reference is implicit. you can

control deembedding for a port by checking the de-embed box on

an individual port’s dialog box, as shown on the left of figure 3. you

get to this box by double clicking on the port in the AXieM layout,

as shown on the left side of figure 3. you can toggle deembedding

on and off by checking the deembed ports box in the eM projects

options. There is a useful menu that shows the status of all the

ports in your AXieM project: edit > Port Properties.

occasionally it is not possible to deembed a port even if you have

requested it. The problem usually occurs with internally grouped

ports with other metal nearby. it is a good idea to check the log file

to see if the ports are really being deembedded. The log file can be

seen by clicking on the information button under the eM project in

the project browser. (it is the button labeled with an “i”.)

TiP 2: If you have a ground plane below (or above) your ports, use explicit grounding, and not implicit

grounding. If the ground plane below is infinite, set the ports up for deembedding. By default, AXIEM uses

implicitly grounded ports, and deembedding is turned on. The designer should change the ports to use explicit

grounds with deembedding if it makes sense to do so.

A common problem for users of AXieM is correctly

setting the edge port grounding scheme. should they

use explicit or implicit grounding? every port has a local

ground reference associated with it. The local ground

is where the current coming out of the port originates.

figure 4 shows the two grounding schemes. The left

picture shows the eM layout with an explicit ground (port

1) and an implicit ground (port 2). notice the explicit

ground has a ground symbol beside it. The ground strap

is connected to the metal above or below the port when

an explicit ground is used. The strap is made of metal;

current literally flows on it in the simulation. The right

figure shows the two ports in the 3D eM view. The

ground strap is shown for the explicitly grounded port 1. Port 2 has no ground strap, as it uses the implicit

grounding scheme. The current for the implicit port comes from infinity, where universal ground is defined.

(This concept is most familiar to antenna engineers, where the ground for voltage is defined to be infinitely far

away from the antenna.)

The explicit scheme is recommended for normal use. it does require that there be a metal plane above or

below the port, so that the ground strap can be connected. The advantage of the ground strap is that it very

clearly defines the path of the return current, and thereby the port’s local ground. The implicit ground can lead

to confusing situations where it is hard to interpret the s-parameters.

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Figure 4. Explicit and Implicit Grounding Schemes for Edge Ports

Figure 3. The deembedding is turned on at the individual port level. Deembedding can be completely turned off at the project level.

in extreme cases, the implicit grounding scheme can even lead to non-physical results, for example

s-parameters becoming greater than 1 (or more generally, non-passive.) if possible, both explicit and implicit

grounds should be deembedded to remove the port’s parasitics. explicitly grounded ports can only be

deembedded when the ground plane is infinite in extent. implicitly grounded ports can always be deembedded

in principle; however, the designer should be wary of deembedding an implicit port with no infinite ground plane,

as the current has no way of returning from infinity.

other issues:

Does it ever make sense to use the implicit ground? yes, in three situations:

• sometimes there is no ground plane to attach the ground strap. for example, in coplanar lines there is no

metal above or below the ports.

• The implicit port inherently has lower parasitics than the explicitly grounded port. Therefore, if

deembedding is not possible, it might make sense to use the implicit port. it is important to remember,

however, that the return current for the implicit port is from infinity. if no infinite ground plane exists,

it is not possible for the current to return from infinity, and the designer should be very careful. Typical

situations where the implicit ground may have problems are at high frequencies, especially where the

substrate thickness is large enough that multi-moding is a concern.

• stripline usually works best if the ground planes extend to infinity and implicit ports are used. explicit ports

have the problem that the grounding strap cannot connect to both grounds at the same time, and the

symmetry of the launch is broken. Connection to both grounds with an explicit port is planned to be added

in a future release.

Packages can be a problem when there are internal, finite sized ground planes. in this situation it is usually

best to explicitly ground the port to the ground plane, even though the port cannot be deembedded. The

careful designer should run some simple examples to determine the port’s parasitics. if necessary, it is

possible to carry out a manual deembedding procedure. Please see the references at the end of this article for

details on how this is carried out.

eM environMenT

TiP 3: When drawing the EM problem, look often at the 3D EM view. Many common setup mistakes become

immediately obvious when viewing the 3D structure. The normal EM layout shows drawing layers, not EM

layers. The 3D EM view uses EM layers, and shows what AXIEM uses for the simulation.

The 3D eM view is much more than just a pretty picture. The 3D eM view will help the designer avoid many

common mistakes:

• shapes drawn on the wrong layer are obvious.

• Mistakes due to drawing layers being incorrectly mapped to the eM layers will be immediately apparent, as

the shape won’t draw in the 3D view. (see tip 4 on drawing and eM layers.)

• The mesh can be viewed to see if it is reasonable for the structure. (see tip 6 on meshing.)

• grounding straps are visible for explicitly grounded ports, so that the ground return layer being used is obvious.

• shape degradation due to shape pre-processing is visible. The DC connectivity of the nets is highlighted by

color so that unintentional shorts or opens are obvious. (see tip 6 on meshing.)

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it is easy to make mistakes when importing shapes into the eM environment.

The eM 2D layout window shows drawing layers, not eM layers, and the

designer can think that he or she has the shape included in the simulation

when it isn’t. The solution is to look at the 3D eM layout, which shows eM

layers. incorrectly mapped shapes will not show up in the 3D eM view. This is

illustrated in figure 5.

All shapes in Microwave office are drawn on drawing layers. The general

rule is that if you can see a shape, it must be drawn on a drawing layer. for

example, schematic layout and artwork cell layout both use drawing layers to

draw shapes. AXieM needs more information than just a shape on a drawing

layer; it also needs to know on which layer in the eM stackup to place the

shape, what type of metal to use for the shape. This is accomplished by

setting up the eM layer mapping, where a given drawing layer is mapped to

a given eM layer. The problem is that if the eM mapping file is not properly

configured, the shapes cannot be used by the eM simulator.

other issues:

Microwave office has two different 3D viewers:

schematic layout 3D view, and eM 3D view. The eM 3D

view has a box drawn around the structures as a visual

reminder that you are looking at an eM layout. (The box

can be turned off in the menu at the top of the software:

options > Default eM options > layout Tab > show

enclosure outline.)

The mesh can be shown in 3D view by making an

annotation. By right clicking on the eM project in the

project browser, and selecting Add Annotation > Planar

eM > eM Mesh. This is shown in figure 6. Additional

annotations allow the designer to look at the current

density on the metal, the calibration structures used by

AXieM if the ports are deembedded, and the electric

field density in various planes.

TiP 4: Understand the difference between drawing layers and EM layers. Drawing layers are needed for

drawing shapes. EM layers tell AXIEM where to place the shape in the EM stackup, and what metal to use

when making the shape. There is an EM layer mapping that tells AXIEM how to map shapes on drawing layers

to EM layers. This mapping must be correctly configured if shapes are imported into AXIEM through DXF or

GDS file import or through EM extraction.

Designers should understand the concept of drawing and eM layers, and how drawing layers are mapped to

eM layers in AXieM. Two common errors can occur if the mapping file is not correctly configured:

• shapes are imported into AXieM from schematic layout using eM extraction. The shapes are not

recognized by AXieM. The problem is that the eM layer mapping is not set up properly in the sTACKuP

block. The designer should check the eM 3D viewer to see if the shapes are on the correct eM layers.

(see tip 3 and figure 6.)

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Figure 6. The mesh can be viewed in 3D by adding an annotation.

Figure 5. The blue line on the left is not correctly mapped to EM layers. It does not appear in the 3D EM layout view. Notice that the port is also red, indicating something is wrong.

• The designer imports layout into AXieM from a layout tool external to Microwave office; for example, a

DXf formatted layout is imported from AutoCad. AXieM will not work properly if the eM layer mapping is

wrong. The shapes will not appear in the eM 3D viewer, as pointed out in tip 3.

other issues:

every AXieM project has an eM mapping file. The file is located under the eM layer Mapping tab of the

enclosure setting. The mapping file tells AXieM how drawing layers are mapped to eM layers. when an eM

project is created, the eM mapping file comes from either a sTACKuP block or the lPf file. it is recommended

that the designer use a sTACKuP block when creating an eM project. This is discussed in tip 5.

it is possible to use line types instead of the eM mapping file when setting up AXieM. line types are used in

microwave office for setting the drawing layer(s) for transmission lines and distributed discontinuity models:

bends, tees, and crosses. line types are most commonly used in MMiC designs, where the transmission line

is drawn on several drawing layers at the same time. it is recommended that line types not be used when

setting up AXieM, unless the user is extremely familiar wit the software. using the eM layer mapping file is

straight forward; a drawing layer maps to an eM layer.

TiP 5: Use the STACKUP block to create new EM projects. Place the block in the Global Definitions area.

Create a template and use it for new projects. Every time you make a new project the STACKUP block will then

be available in Global Definitions.

when you create a new eM project, you would like it to be pre-configured with the correct layers, materials,

and eM layer mapping. A convenient way to do this is to use a sTACKuP block. The sTACKuP block is used

to create the enclosure settings for the AXieM project. (every AXieM project has an enclosure tab, which can

be seen under the eM project in the project browser.) The sTACKuP element is also used by eM extraction, in

which portions of the schematic layout are sent to AXieM.

The stackup element is placed on the global Definitions page. (This is located about a quarter of the way

down the project browser.) when an eM project is created, you can request that the project use a sTACKuP

element on the global Definitions page. (There can be more than one

sTACKuP element in the global Definitions.) This is

shown in figure 7, where the sTACKuP element named

“Default eM” is being used. in the case of eM extraction,

the sTACKuP element can be placed either in the global

Definitions page, or on the specific schematic that is set

up for extraction.

with one exception, the sTACKuP element has the same

format as the enclosure block that is created in the eM

project: Material Definitions, Dielectric layers, Materials,

and eM layer Mapping. The exception is the enclosure

tab in the enclosure block. for AXieM, this page contains

the grid settings. The default grid settings can be

changed in the eM project after the project is created.

if the sTACKuP block is used with an eXTrACTion block

placed in a schematic, the grid settings can be set in the

eXTrACTion block.

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Figure 7. The STACKUP block in the global definitions page. AXIEM projects can use it to set up the EM project.

other issues:

Templates can be used as a way to set up new project. A template is basically a blank project that is used

every time you start a new project. (it is not used when opening an existing project.) The designer can set

many of the more common project settings in a template, for example: units, frequencies, drawing layers,

libraries being used, user options, and anything that is placed in the global Definitions page, for example

sTACKuP blocks and equations. The procedure for making a template is:

1. Create a new project. set up your frequencies, units, etc. as you desire. import a sTACKuP element into

the global Definitions page, and set up the fields as desired.

2. go to the menu at the top of the software: options > Default eM options, and set any other default

AXieM options you would like; for example, whether or not to deembed all ports, or to enable advanced

frequency sweeping (Afs).

3. save the template. This is accomplished by using the menu at the top: file > save Project As … and

making sure it is saved as a template file, which has the extension “.emt”, as opposed to a normal project

which has an extension “.emp”.

4. use the template. go to the menu at the top: options > environment options and go to the file locations

tab. set the Default Project Template to be the template you created. The template will now be used when

you create a new project. Again, it is not used for existing projects.

The default grid size can be set up in two different ways. if using eM extraction, the eXTrACT block on the

schematic has fields for the default grid that will be used when the eM project is created. if not using eM

extraction, the default grid is set in the lPf file. every Microwave office has at least one default lPf file. The

grid settings are set by exporting the lPf file as an AsCii file using Project > Process library > export lPf.

The mesh settings are at the bottom of the lPf file in the eM_enClosure section. The X and y dimensions

are given in meters, and the total number of cells. (A box is used as eMsight™ uses the same settings.) for

example, an X dimension of 1 meter with 1000 cells, will result in an X grid setting of 1 millimeter.

Meshing

TiP 6: Creating a mesh is a two step process in AXIEM. First the shapes are decimated. Decimation simplifies

the shapes by reducing the number sides of the shapes. (Decimation can be turned off.) Second, the shapes

are meshed after decimation. The mesh in AXIEM will completely cover the decimated shapes, and fit their

boundaries exactly.

The meshing process in AXieM occurs in two steps. first, the shapes in layout are decimated if desired. All

shapes in AXieM are polygons. (As a matter of fact, all shapes in Microwave office are polygons, in any of

the layout environments.) Decimation simplifies the shapes by getting rid of small sides of the polygon. The

resulting polygon has fewer vertices, with longer sides. hopefully, this will result in a simpler mesh. The grid

settings control how small a side decimation will remove. The X and y grid settings are in the eM enclosure,

under the enclosure tab. The setting is only a guideline for AXieM. for example a 1 X 1 mil grid setting will try

to decimate polygon sides of less than about a 1 mil, with medium level decimation set.

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why would the designer want to use decimation? There are three commonly encountered cases when it is

useful. first, a layout that is imported from an external layout tool often has a large number of many sided

polygons. These small sides do not matter electrically, but AXieM is forced to create a very large mesh, as the

mesh must exactly match the boundaries of the polygons. Decimation can therefore substantially reduce the

size of the problem in these situations. second, decimation is useful when working with circles, most typically

vias. Circles are actually n sided polygons in Microwave office. (By default they are 36 sides.) This can result in

a large mesh, which electrically is not needed. Decimation can reduce the number of sides of the “circle” and

result in a smaller mesh. Third, MMiC technology requires that lines be drawn on multiple process layers, with

small size differences between the lines. Decimation can be used to remove the small size differences between

the lines, resulting in a smaller mesh.

Decimation can be controlled in the mesh settings

menu for AXieM. This can be set for a specific project

under the Mesh tab of the project’s option menu, as

shown in figure 8. The decimation can be set from

none to very high, with Medium being the default. The

project defaults for meshing are set in the options >

Default eM options > Mesh at the top of the software.

once decimation has completed, the layout is meshed.

The mesh size is set in the Advanced options area of

meshing, as shown in figure 8. The number entered is

relative to the grid. The default value is 1. in this case,

the grid size is also the desired size of the smallest

cells in the mesh. note that AXieM has to create a

mesh that exactly fills the shape, so it may well have

to create small cells. The grid is only a suggested

guideline. The options under meshing also allow the

designer to set the mesh density from low to high, as

shown in figure 8. (The “no variable mesh setting” is

not used by AXieM.)

other issues:

The Advanced Meshing menu contains a large number of meshing and decimation options. There are two

different sets of algorithms used for decimation. The newer and preferred algorithm is shape pre-processing.

The older algorithm (and the default) is called alternative mesh decimation in the menu. shape pre-processing

recognizes the geometrical character of shapes; for example, a circle has certain properties. As the shapes

are simplified, it attempts to make sure that nets are not shorted out to themselves or other shapes. The

older algorithm operates on the shapes without any geometrical intuition. it is therefore easier for problems

to occur. Many of the shape preprocessing options are especially useful to MMiC designers; for example

capacitor areas are maintained as the shapes are decimated.

it is possible to change decimation and mesh options for single shapes. select the shape in the eM layout and

right click and bring up its properties menu. There is a mesh menu for the shape. This is useful, for example,

with ground planes where a very low mesh density is desired.

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Figure 8. Decimation is set in the Mesh page of the Options menu for the EM project.

TiP 7: Look at your mesh before you simulate. Make sure that the

overall mesh looks reasonable for the structure you are simulating.

The mesh is most easily seen in the EM 3D view.

A simulation can only generate results as the underlying mesh. The

mesh is an approximation to the current on the metal in the circuit.

A good way to build intuition with meshing is to imagine the current

flow. The mesh should follow this intuitive thinking. you can see the

mesh in the 3D view, which is another reason to look at the 3D view,

as suggested earlier. The mesh is seen in the 3D view by creating

an annotation. right click on the eM project in the browser, Add

Annotation, and select eM Mesh as shown in figure 9. The mesh

is now visible in the 3D viewer. There is a script that ships with the

software to automate adding the mesh annotation:

scripts > eM > Toggle eM Mesh.

other issues:

The current on a transmission line is largest on the outside edges. Therefore, it is common to create an edge

mesh on the side of the line as shown in figure 9. over the years, it has been found empirically that the edge

mesh is an efficient way of adding cells where you get the most “bang for your buck”. edge meshing can be turned

off in the meshing options. how many cells should be across the line? A good rule of thumb is three to seven.

one is normally not enough if you are hoping for accurate phase information. An exception to using one cell per

unit width is in signal integrity applications where you are only interested in an idea of the coupling between lines

and the overall phase delay. More than seven cells is seldom needed, even for tightly coupled line filters.

Discontinuities: Current hugs the inside corner of microstrip bends. you have to have enough cells to get this

delay in situations where an accurate bend model is required. The most critical measurement in discontinuity

models is the phase of the s-parameters. Don’t rely on looking at only their magnitudes to access the accuracy

of the simulation. Again, 3 to 7 cells wide is normally a good idea.

vias: Meshing vias involves a couple of different issues. first, the pad of the via must be meshed. usually, a

fairly coarse mesh is adequate. The overall effect of the pad is to add capacitance, which is dominated by its

area. Therefore, decimation is usually a good idea, although check to make sure that the shape has not been

simplified so much that the pad area is severely altered. second, in circuits with a lot of vias, for example

multi-layer boards the problem is that most of the mesh is used for the vias, when they don’t have that much

effect on the final outcome. for example, picket fencing with vias is common on boards and can lead to a huge

mesh. in these cases, the designer might consider reducing the number of vias, or merging them together.

The shape pre-processor has a setting for merging of vias. The third issue is when a via go through multiple

power planes. The coupling capacitance to the plane can be important. To properly model this, the meshed

via should have a number of cells in the vertical direction. fortunately, AXieM makes at least one cell for

each separate substrate layer. The board with multiple planes has to have multiple substrate layers, and this

problem usually takes care of itself.

ground Planes: finite size ground planes need to be meshed, and the size of the mesh can get large. The

current normally flows on the plane underneath the signal line. Therefore, the maximum density of the mesh

should be under the line. This is carried out automatically in AXieM, where the mesh on the line is mimicked on

the ground beneath it. farther away from the line, it is wasteful to have a fine mesh. The meshing on the plane

can be set to low in the local options of the shape under the meshing tab. This is shown in figure 8.

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Figure 9. The mesh can be viewed by adding an annotation, EM_MESH.

how do you know if you mesh will give an accurate answer without being overly detailed? it is often a good idea

to start with a simple test problem that captures the essence of the meshing problem you are investigating.

for example, you have a number of lines on a board over a finite ground plane. start with just one line and see

how many cells you need on the line width before you are satisfied with the answer. reduce the number of cells

on the ground plane to see if it matters. Then try two lines and see if the coupling is reasonable. By spending

a bit of time increasing your intuition, you will be able to ascertain about how fine a mesh you need for your

situation. A common problem is to start with a very complicated problem where you have no idea if the mesh

is accurate.

TiP 8: Don’t use thick metal unless it is required for an accurate answer. Thick metal is needed when the gap

between lines is on the same order of magnitude as the thickness of the line. Examples where you have to use

it are spiral inductors on MMICs, and tightly coupled lines in LTCC processes.

AXieM has the ability to simulate with thick metal. The vertical sidewalls of the line are meshed and the

currents included. By default, the thick metal option is turned off. it is set in the meshing options tab: Model as

zero thickness, as shown in figure 8. you can override the global setting on a shape-by-shape basis. figure 10

shows a line with the thick line option turned on and off. note that the 3D view will show the line with thickness

if it is turned on. This is yet another reason to look at the 3D eM view.

The thickness of the line is set in the enclosure settings under the Materials tab. This somewhat confusingly

named tab does not mean bulk materials. Bulk materials properties are set in the Material Properties tab,

where the electrical properties of the dielectrics and conductors are set, for example, fr4, alumina, and

copper. The materials tab is used to tell a shape two things: what metal the conductor is made of, and how

thick it is. what does AXieM do with the thickness if the setting is for zero thickness? The answer is it doesn’t

use it, so long as the metal is more than a skin depth thick at the frequencies of operation! This is actually the

same situation as in the laboratory. Microwave frequency currents flow predominantly on the bottom side of

a microstrip line. The thickness of the metal only matters for low frequency power lines. AXieM calculates the

skin depth for the line. if the skin depth is less than the thickness of the line, AXieM replaces the conductor

with an infinitely thin sheet of material defined by an impedance boundary condition. The impedance boundary

condition gives a good answer so long as the real conductor being modeled is thicker than a skin depth. if the

skin depth is greater than the metal thickness, AXieM again uses an infinitely thin sheet of material defined by

an impedance boundary condition. in this case, the impedance boundary condition is derived from the classic

DC current situation of the current flowing uniformly throughout the conductor, with an equivalent surface

resistance in ohms/sq.

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Figure 10. The 3D view shows when thick metal is turned on.

simulating with thick metal has two potential drawbacks. first, the number of unknowns is increased, and the

resulting simulation takes longer. The increase in unknowns can be significant. remember that the number of

unknowns is more than doubled as both the top and bottom surfaces of the thick conductors must be meshed.

second, numerical instabilities can occur if the metal is electrically not very thick. for example, metal thickness

in thin film processes is typically a few microns thick. The cells on the top and bottom sides of the line are

almost on top of one another and the matrix becomes badly conditioned. (in the limit that the thickness goes

to zero, there are more unknowns than equations, as there are two current cells for each unknown current on

the line. There is therefore no unique solution to the problem.)

Therefore, it is usually best not to use non-zero thickness metal unless it matters to the simulation. here are

the most common situations where it makes sense to use thick metal:

• Closely Coupled lines: The general rule is if the spacing between the lines is 3X the thickness of the lines,

use thick metal. for example, in typical board processes, the line is about 1 mil thick with the spacing

between lines about 10 mils. Thus the separation to line thickness is 10X and there is no need for a thick

metal approximation. in integrated circuit (iC) technology, separations between lines can be less than the

thickness of the line, requiring thick metal in AXieM. for example, MMiC technology can have lines on top

of the MMiC being 7 or more microns thick (when all the conducting layers the line is made of are added

together). The spacing between lines can be as small as 0.5 microns. Clearly, thick metal is required.

• spiral inductors in MMiCs: This is one of the most critical cases for coupled lines.

• lines used as sidewalls for packages or channelized waveguide problems: AXieM does not have the notion

of sidewalls, for example the side of a metal package or channelized waveguide. however, it is possible to

approximate the walls by either making a very thick line, or using a brick of via material. The via also has

currents on its vertical sides. in effect, it works the same as the thick line.

siMulATion

TiP 9: When results from AXIEM will be used in nonlinear circuit simulations, make sure a frequency point

close to DC is included in the AXIEM simulation.

AXieM simulations produce s-parameters. These s-parameters are sometimes used by themselves, but

are more commonly inserted into circuit schematics. The circuit simulator then uses the s-parameters as

a sub-circuit in the schematic. A problem can occur if the circuit simulation is nonlinear, most commonly

when harmonic balance is used. (The problem also exists for time domain simulators, for example hspice.)

harmonic balance requires a DC solution. The s-parameters must therefore be extrapolated down to DC. The

extrapolation can be inaccurate if the lowest frequency in the s-parameter file is not sufficiently close to DC.

The error can manifest itself as an incorrect bias point for the circuit, or in extreme cases results in non-

convergence of the simulator. The DC bias simulation never finishes.

The solution to the problem is to make sure that the s-parameter simulations for AXieM include a frequency

point close enough to DC that the extrapolation by the circuit simulator will be accurate. By simply looking

at the s-parameters on a smith chart, the designer can usually get a good idea if the extrapolation will be

accurate. it is possible to have AXieM simulate at DC if desired. (note that this should not be attempted with

eMsight, Awr®’s other planar simulator. eMsight becomes unstable at very low frequencies.) sometimes,

s-parameter files are used that have been generated by other eM simulators or experimental measurements.

The DC problem is the same. in this case, examine the data to see if the s-parameters are easily extrapolated

to DC. if not, the s-parameter file can be modified by simply adding a line for low frequency. for example, if the

s-parameter data are for a transmission line, the s-parameters at DC would be an s11 = 0, and s21 = 1.

(This assumes a perfectly conducting line.)

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TiP 10: AXIEM has two types of solvers: direct and iterative. The iterative solvers have the advantage of

being able to solve much larger problems than the direct solvers. The direct solvers can be faster for smaller

problems. By default, AXIEM switches from direct to iterative solve at 2000 unknowns.

AXieM works by solving a matrix equation for the unknown currents on the cells of the mesh. each element

of the matrix represents between two of the cells. The diagonal elements are the self interaction of a cell

with itself. The majority of the time spent solving a problem in AXieM occurs in two areas. first, the matrix

elements must be determined. second, the resulting matrix must be solved. AXieM has two ways of carrying

out these two steps. The default method for small problems (by default less than 2000 unknowns) uses a

direct solve technique. for problems larger than 2000 unknowns, the default behavior is to use an iterative

solver, which is much faster than the direct method for filling and solving the matrix. it is possible to change

the default settings, so that the iterative or direct solver is always used. however, the default settings have

been chosen to give optimal performance for most problems.

other issues:

The matrix takes order n2 to solve, where n is the number of unknowns. The number of unknowns is roughly

the same as the number of cells. if you double the number of cells, it takes four times longer to fill the matrix.

The time to solve the matrix with the direct solver goes as order n3. Doubling the size of the problem takes

eight times longer. Because there are a large number of numerical operations for calculating each matrix

element, the matrix fill actually dominates the total simulation time until a few thousand unknowns. By 10,000

unknowns, the solve time is dominating.

iterative solvers asymptotically take order nln(n) amount of time for both filling and solving the matrix. The

method uses never fills the whole matrix; rather, it works with a compressed version somewhat similar to

image compression methods. The smaller matrix is then solved using iterative matrix methods. for large

problems, the iterative solver is tremendously faster than the direct. for example, 30,000 can be solved on

a 32 bit machine with 2 gBytes of rAM in about 10 minutes per frequency on a single core machine. solving

this problem with a direct solver would require about four hours per frequency point, and would require six

gBytes of rAM, necessitating a 64 bit machine.

The iterative solvers require the matrix be well conditioned. Conditioning is a property of a matrix which

indicates how amenable it is to solution on a computer with finite precision arithmetic. Typically, the matrix

must be pre-conditioned to get the iterative method to work well. There is no one best pre-conditioner for

all situations. sometimes, the default pre-conditioner does not work. AXieM will then try other alternative

pre-conditioners before giving up and issuing an error message. it is possible to tune the pre-conditioner

and iterative solver settings in the AXieM page of the options menu of the eM project. normally, this is not

necessary unless convergence problems occur. Poor conditioning can sometimes be fixed by a better mesh.

long, thin triangles tend to lead to poorly conditioned matrices. sometimes putting some conductor loss into

the problem will help the conditioning. for example, make the ground plane a real conductor like gold or copper

instead of a perfect conductor.

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referenCes AnD fuTher inforMATion

The interested reader can find more information about AXieM in several locations:

• Manuals: AXieM information is in the simulation manual, under the eM simulation chapter. The manual

can be found in the software by going to the help menu at the top of the software: help > Contents and

index. AXieM information is under section 8.5 of AwrDe simulation and Analysis guide.

• examples: The software comes with built in examples showing various features of AXieM. starting with the

help menu at the top of the software, go to open example. The example browser appears. you can type

the word AXieM in the bottom box to see all examples with AXieM in them.

• KnowledgeBase (KB): The KB contains many articles and examples on AXieM. you can get to the KB by

going to the website: www.awrcorp.com. There is a link to it on the right side of the homepage. you can

also get to KB from the software by going to help > Awr web site > KnowledgeBase. note that there

are examples in the KB that do not ship with the software.

• online Training: There are free, online training modules available on the website. you can get to online

training by going to the website. Then, from the support menu at the top of the homepage for Training.

This page has the link to online training. There are three eM training modules of relevance for AXieM:

setting up eM in Microwave office, AXieM Concepts, and Advanced eM Concepts for Planar simulators.

• scripts: scripts are included in the software that can be helpful when setting up eM projects. The scripts

can be run by going to the top of the software: scripts > eM and picking the appropriate script.

specific references for the topics covered in this article are listed below:

Ports: Deembedding and grounding options

• Manual: section 8.5.3 of the manual explains the various port options, and how the deembedding

algorithm works.

• KnowledgeBase:

• APPnoTe: Making sense of the Different Types of Ports in AXieM

• APPnoTe: AXieM for the eMsight user

• examples:

• AXieM_Coupled_line_Deembedding.emp: explains coupled lines.

• AXieM_Mutual_Ports.emp: Mutual ports are aware of each other, when deembedded.

• online Training

• AXieM Concepts: explains ports and calibration in lectures 1 and 2.

• Advanced eM Concepts: lecture1 explains deembedding. lectures 2 covers internal ports. lecture 3

explains differential ports.

The eM environment: layers, eM extraction, Advanced frequency sweep (Afs), and other issues

• Manual:

• Afs is explained in section 8.5.7 of the simulation and Analysis guide. section 8.1 explains how to set

up eM extraction.

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• scripts:

• show_eM_stackup: shows in a diagram the drawing layer and eM layers. This is useful for making sure

the mapping layer is set correctly.

• Create stackup: Creates the eXTrACT block and sTACKuP block form the a substrate on a schematic,

for example: MsuB. This is useful for quickly configuring extraction for simple structures.

• online Training

• setting up eM in Microwave office: explains how eM is setup, including drawing and eM layers,

and eM extraction.

• new Technologies for eM: Part 7 explains how Afs works.

• examples: several examples show AXieM and eM extraction. search using the keywords: AXieM and extract.

Mesh and Decimation options

• Manual: section 8.5.5 of the simulation and Analysis guide explains meshing and decimation in detail,

including figures and examples. in section 8.45.13, advanced issues, there is a discussion on meshing and

shape pre-processing which discusses high aspect ratio meshes, which can affect simulation performance.

• online Training:

• AXieM Concepts: lecture 3 explains meshing and solver options.

iterative and Direct solver settings

• Manual: section 8.5.6 explains the solver settings and gives recommendations for the best settings.

section 8.5.10 explains how to overcome convergence issues for the iterative solver.

• online Training:

• AXieM Concepts: lecture 3 explains the direct and iterative solvers.

• new Technologies for eM: Parts 2, 3, 4, and 5 explain iterative solver technology and the issues that

affect convergence.

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Copyright © 2011 Awr Corp. All rights reserved. Awr, the Awr logo and Microwave office are registered trademarks and eMsight and AXieM are trademarks of Awr Corporation. All others are trademarks of their respective holders.