Mesh

A mesh is a grid-like pattern of triangles and rectangles, and each triangle or rectangle is a cell. This pattern of cells is based on the geometry of a circuit and, optionally, user-defined parameters, so each circuit will have a unique mesh calculated for it. The mesh is then applied to the circuit in order to compute the current within each cell and identify any coupling effects in the circuit during simulation. From these calculations, S-parameters are then calculated for the circuit. The mesh that was calculated for the double patch example is shown below.

Creating a mesh consists of two parts:

This chapter describes how to define mesh parameters and calculate the mesh. It also includes a description of how the mesh generator works and gives guidelines for setting mesh parameters for different applications.

Defining a Mesh


Choose Momentum > Mesh > Setup to set up mesh parameters, which enable you to control the number of cells that are used to create the mesh. The more cells, the more accurate the simulation will be, but too many cells will slow down a simulation and provide little improvement in accuracy. You can choose not to set up mesh parameters, and default values will be used to create the mesh.

If you choose to define mesh parameters, you can set them for:

For more information about how a mesh is generated, refer to About the Mesh Generator. For suggestions to consider when setting mesh parameters, refer to Guidelines for Meshing.

Procedures for setting up mesh parameters follow.

Defining Mesh Parameters for the Entire Circuit

Global mesh parameters affect the entire circuit. To set up global parameters:

  1. Choose Momentum > Mesh > Setup.
  2. The Global parameters are displayed.
  3. Enter the mesh frequency in the Mesh Frequency field and select the units. The wavelength of this frequency will be used to determine the density of the mesh. In general, set the value of the mesh frequency to the highest frequency that will be simulated. For more information, refer to Adjusting Mesh Density.
  4. Enter the Number of Cells per Wavelength. This value will also be used to determine the density of the mesh. The relationship between wavelength and cells per wavelength can be described by the following example:

    If the circuit is 3 wavelengths long and the number of cells per wavelength is 20, the length of the circuit will be divided into 60 cells. For more information, refer to Adjusting Mesh Density.

  5. Any curved areas in the circuit will be meshed using facets. In the Arc Facet Angle field, enter the number of degrees that will be included in a single facet. The maximum is 45 degrees per facet. The lower the value, the better the resolution and the denser the mesh will be. The minimum value is equal to the Arc/Circle Resolution which is set when the object is drawn. For more information, refer to Processing Object Overlap.
  6. Enable Edge Mesh to add a relatively dense mesh along the edges of objects. Since most current flows along the edges of objects, the edge mesh can improve the accuracy and speed of a simulation.
    If you want the edge mesh to be sized automatically, leave the Edge Width field blank. Otherwise, specify the edge width and select the units. For more information about the edge mesh, refer to About the Edge Mesh.
    Note
    An edge mesh that is specified with a width larger than the cell size set by the wavelength/number_of_cells_wavelength, will be ignored. This is because such edge meshes would be very inefficient. However, if these edge mesh values must be used, you can decrease the number_of_cells_wavelength, which is specified in the Number of Cells per Wavelength field.
  7. Enable Transmission Line Mesh to specify the number of cells along the width of a geometry. It is most useful for circuits with straight-line geometry.
    Enter the number of cells that the width will be divided into in the Number of Cells Wide field. This will be the total number of cells along the width of the circuit. For more information about the transmission mesh, refer to About the Transmission Line Mesh.
  8. Enable Thin layer overlap extraction in order to extract objects for the following situations:
    • Two objects on different layers overlap
    • The objects are separated with a thin substrate layer
      If this is enabled, the geometry will be altered to produce a more accurate model for the overlap region. For more information, refer to Processing Object Overlap.
      Note
      This should always be enabled when modeling thin layer capacitors.
  9. Enable Mesh reduction in order to obtain an optimal mesh with fewer small cells and an improved memory usage and simulation time. For more information on Mesh Reduction, refer to Effect of mesh reduction on simulation accuracy.
  10. Enable Horizontal side currents (thick conductors) to activate horizontal side currents on thick conductors. When enabled, this feature provides improved modeling of thick conductors by making use of horizontal currents on side walls. This feature:
    • Automatically uses edge mesh on side walls when the global mesh option is enabled (see 6.).
    • Provides higher accuracy for thick conductors with a width/thickness aspect ratio up to and below 1.0.
    • Makes substrate database recalculation unnecessary, by taking advantage of new reconstruction technology for the Green functions.
    • Can be visualized in post processing by selecting Momentum > Post-Processing > Visualization.
      Note
      For optimal simulation performance, we recommend that you disable the edge mesh for expanded layers. To do this, un-check the "Edge Mesh" box on the Global tab. If edge mesh is required for individual layers, use the Layer tab to set the edge mesh for a specific layer.

      Only in simulations using extremely high frequencies, or in cases where extreme coupling is present between neighboring conductors, is it necessary to use a combination of edge mesh and horizontal side currents.

      When the Horizontal side current option is disabled, meshing reverts to the previous model for thick conductors (i.e., only the vertical currents on side walls are used).

  11. If you want to revert to default parameters, click Reset.
  12. Click OK to accept the global mesh parameters.

Global Mesh Control dialog box.

Defining Mesh Parameters for a Layout Layer

You can define mesh parameters that affect the objects on a single layout layer. If you have global parameters set, they will not be used where mesh parameters are defined for a layout layer.

To set up layout layer parameters:

  1. Choose Momentum > Mesh > Setup.
  2. Click the Layer tab.
  3. From the Layout Layer list, select the metallization layer that you want to specify mesh parameters for.
  4. Enter the Mesh Density - cells/wavelength. This value, along with the wavelength of the frequency specified in the Frequency field, will be used to determine the density of the mesh. (Recall that the frequency is a global parameter).

    The relationship between wavelength and cells per wavelength is best described by example. If the portion of the circuit on this layer is 2 wavelengths long and the number of cells per wavelength is 20, the length of the circuit on this layer will be divided into 40 cells. For more information, refer to Adjusting Mesh Density.

  5. Enable Edge Mesh to add a relatively dense mesh along the edges of the objects on this layer. Since most current flows along the edges of objects, the edge mesh can improve the accuracy and speed of a simulation.

    If want the edge mesh to be sized automatically, leave the Edge Width field blank. Otherwise, specify the edge width and select the units. For more information about the edge mesh, refer to About the Edge Mesh.

  6. Enable Transmission Line Mesh to specify the number of cells along the width of the geometry on this layer. It is most useful for circuits with straight-line geometry.

    Enter the number of cells that the width will be divided into in the Number of Cells Wide field. This will be the total number of cells along the width of the circuit on this layer. For more information about the transmission mesh, refer to About the Transmission Line Mesh.

  7. If you want to change the settings for the selected layer, click Reset to return to default values or Clear to erase your settings.
  8. Select another layer and repeat these steps for setting the mesh parameters.
  9. Click OK to accept the mesh parameters for the layers.

Defining Mesh Parameters for an Object

You can define mesh parameters that affect a single object. If you have global or layout layer parameters set, they will not be used where mesh parameters are defined for an object.
To set up object parameters:

  1. Choose Momentum > Mesh > Setup.
  2. Click the Primitive tab.
  3. In the Layout window, select the object that you want to specify mesh parameters for.
  4. Enter the Mesh Density - cells/wavelength. This value, along with the wavelength of the frequency specified in the Frequency field, will be used to determine the density of the mesh. (Recall that the frequency is a global parameter).

    The relationship between wavelength and cells per wavelength is best described by example. If the object is 1/2 wavelengths long and the number of cells per wavelength is 20, the length of the object will be divided into 10 cells. For more information, refer to Adjusting Mesh Density.

  5. Enable Edge Mesh to add a relatively dense mesh along the edges of the object. Since most current flows along the edges of objects, the edge mesh can improve the accuracy and speed of a simulation.

    If want the edge mesh to be sized automatically, leave the Edge Width field blank. Otherwise, specify the edge width and select the units. For more information about the edge mesh, refer to About the Edge Mesh.

  6. Enable Transmission Line Mesh to specify the number of cells along the width of the object. It is most useful for circuits with straight-line geometry.

    Enter the number of cells that the width will be divided into in the Number of Cells Wide field. This will be the total number of cells along the width of the object. For more information about the transmission mesh, refer to About the Transmission Line Mesh.

  7. If you want to change the settings for the selected object, click Reset to return to default values or Clear to erase your settings.
  8. Select another object and repeat these steps for setting the mesh parameters.
  9. Click OK to accept the mesh parameters for the objects.

Seeding an Object

For the majority of circuits, it is not necessary to seed an object, and it is not recommended because all internal mesh processes will be skipped. If an object is seeded incorrectly, an inefficient mesh will result, affecting simulation speed and accuracy. You should have a good understanding of electromagnetics and computational geometry to be able to use this meshing feature efficiently.

Primitive seeding enables you to specify the exact number of cells to be applied to a geometry:

The example below illustrates the position of the o,u-axis and the position of point V with respect to OU on a simple shape. Regardless of the object seeding is applied to, OV must be perpendicular to OU in order to create a correct mesh. This mesh was defined to be three cells wide along the o,u-axis, and five cells high.

To seed a primitive:

  1. Determine the method for entering mesh coordinates. You can:
    • Type coordinates directly into the Coordinate Entry dialog box
    • Select coordinates by clicking on objects in the Layout window
      If you choose select coordinates on the object, make sure that the vertex snap mode is on, and check your other snap modes to make sure that you can completely align the mesh with the structure. If snap modes are on when you select a coordinate, the system will snap to the nearest point that satisfies an enabled snap mode. This means that you may have difficulty aligning the mesh with the object if snap modes other than vertex snap are enabled. Snap modes can be found in the Layout window under the Options menu.
  2. If a mesh is displayed on the layout, choose Momentum > Mesh > Clear.
  3. Choose Momentum > Mesh > Setup.
  4. Click the Primitive Seed tab.
  5. In the Layout window, select the object that you want to seed. If necessary, zoom in.
  6. Specify the o,u-axis. The axis determines the orientation of the mesh. Select the axis using one of the following two methods:
    • Position the mouse and click to define the origin of the o,u-axis. Move the mouse to the end of the axis and click again.
    • From the Layout menu bar choose Insert > Coordinate Entry and use the Coordinate Entry X and Coordinate Entry Y fields to specify the origin of the o,u-axis. Click Apply. Enter the coordinates that define the end of the axis and click Apply.
  7. The Primitive Mesh Control dialog box is displayed. Enter the number of cells that you want along the o,u-axis.
  8. Specify point V. The point must be positioned so that OV is perpendicular to OU. Select the point using one of the following two methods:
    • Position the mouse and click to define the point and click.
    • From the Layout menu bar choose Insert > Coordinate Entry and use the Coordinate Entry X and Coordinate Entry Y fields to specify the coordinates of point V. Click Apply.
  9. The Primitive Mesh Contro l dialog box is displayed. Enter the number of cells that you want along the ov-line.
  10. The following information will appear for the seeded object:
    • The number and name of the layout layer that the object is on
    • Data describing the seeded object, including the type of object (for example, path or polygon) and its coordinates
    • The angle of the o,u-axis with respect to the x-axis
    • The length of each cell along the o,u-axis (the distance of OU divided by the number of cells)
    • The length of each cell along OV (the distance of OV divided by the number of cells)
      An example is shown below:
  11. If you want to change the settings for the selected object, click Clear to erase your settings.
  12. Click OK to complete the command.
    In the illustration below, the o,u-axis is positioned along the base of the polygon, and it is the length of the polygon. The number of cells along the axis is set to three. The number of cells from OU to V is set to five. The resulting mesh is displayed. Any other mesh parameters that had been specified were used in other parts of the circuit.

Mesh Connectivity

If you choose to seed an object, and you have global, layout layer, or object mesh parameters set, these other parameters will not be used on the seeded object. In addition, the mesh cells must connect in an appropriate way throughout the circuit in order to achieve accurate results. This is referred to as mesh connectivity. Be aware that in order to achieve mesh connectivity, the boundaries of seeded regions may be transformed. The only way to correct this is to modify the seeding of the neighboring objects. If you choose to seed one object, you should consider seeding the entire circuit.

Which cells are altered to assure connectivity is governed by creating a mesh that generates the fewest number of unknowns.

Resetting and Clearing Mesh Parameters

If you want to change mesh parameter setting, you can:

  1. Choose Momentum > Mesh > Setup.
  2. Select the tab, Global , Layer , Primitive , or Primitive Seed , that contains the parameters you want to erase or reset.
  3. Choose one of the following options:
    • For layout parameters, select the layout layer name.
    • For object mesh parameters or seeding, select the object from the Layout window.
      Hint
      You may want to clear the mesh from the layout before attempting to select an object.
  4. Click Clear to erase the settings, or click Reset to set them to default values.
    Note
    If you have trouble selecting an object, exit the dialog box, select the object, then reopen the dialog box.

Precomputing a Mesh

Note
In order to calculate a mesh, you must first precompute the substrate and apply ports to the circuit. For information on how to precompute the substrate, refer to Substrates. For information on how to apply ports, refer to Adding a Port to a Circuit, and to Ports.


Choose Momentum > Mesh > Precompute to calculate the mesh. Using the specified frequency and any user-defined mesh parameters, a pattern of rectangles and triangles is computed and applied to the circuit. During a simulation, the surface current in each cell is calculated, and this information is then used to solve S-parameters for the structure.

To precompute the mesh:

  1. Choose Momentum > Mesh > Precompute.
  2. In the Precompute Mesh dialog box, enter the frequency you want to use for precomputing the mesh. The wavelength of this frequency will, in part, determine the number of cells in the mesh. For more information about mesh calculations, refer to About the Mesh Generator.
  3. Click OK to start calculating the mesh.

When the computations are complete, the mesh will be displayed on the layout.

Viewing Mesh Status

After mesh computations have started, any messages regarding the computations will appear in the Momentum Status window. Messages usually refer to any errors or warnings, or indicate when the mesh is complete.

If you close the status window and want to reopen it, from the Layout menu bar choose Window > Restore Status.

Stopping Mesh Computations

To stop the mesh process:

  1. From the Momentum Status window, choose Simulation/Synthesis > Stop Simulation.
    The mesh computations will stop and no information will be saved.

Viewing the Mesh Summary

If the mesh computation is successful, you can view mesh statistics. Some of the information returned includes:

Viewing a Mesh Report

A mesh report can offer more information on some warnings that are displayed in the Momentum Status window related to ports and resolution. It also reports any unconnected vias, these are vias that do not connect at both sides.

To view a Mesh Report:

  1. Choose Momentum > Mesh > Show Report.

Clearing a Mesh

You can delete the view of the mesh from the circuit. Clearing a mesh only deletes the view from the Layout window; it does not erase the mesh calculations.

To remove the mesh from the display:

  1. Choose Momentum > Mesh > Clear.
  2. If you want to redisplay the mesh, choose Edit > Undo. Otherwise, you must recompute the mesh in order to view it.

About the Mesh Generator

The mesh generator provides the algorithm that divides the circuit geometry into cells (rectangles and triangles). When the Mesh Reduction option is selected, the mesh is automatically reduced to remove slivery cells of low quality and to remove electromagnetically redundant cells resulting in a mesh with polygonal cells. By discretizing the surface, it is possible to calculate a linear approximation of the arbitrary, varying surface current. The linear approximation involves applying a rooftop function to the cells. The better the linear approximation fits the actual current, the more accurate the results. Thus, a dense mesh generally provides better results at microwave frequencies.

The mesh generator attempts to apply an optimal pattern of cells so that an accurate simulation can be achieved with a minimal number of cells. In Momentum mode, the minimal number of cells can be rather high, resulting in a dense mesh. For a given mesh density, the mesh reduction technology achieves an optimal mesh with significantly fewer cells, hence improving the simulation performance with reduced memory usage and simulation time. Since the current in each cell is calculated in a simulation, a very dense mesh can increase simulation time.

The mesh parameters that you specify provide the mesh maker with the information required to divide your geometry into the various cell shapes and sizes. If you do not want to set mesh parameters, default ones will be used instead. In Momentum mode, the default mesh setting is 30 cells/wavelength using edge mesh. In RF mode, the default mesh setting is 20 cells/wavelength not using edge mesh. Because RF mode is an approximation with respect to the MW mode, the lower setting in RF is a better default providing the best accuracy/efficiency trade-off.

Adjusting Mesh Density

Two mesh parameters, Mesh Frequency and cells/wavelength are used in combination in determining mesh density.

Using the wavelength of the frequency, a linear function is approximated, also referred to as a rooftop basis function. The higher the frequency, the more wavelengths fit across the structure. The cells/wavelength is the minimum number of cells that fit under each wavelength. The more cells, the better the sinusoid is represented, and the more accurate the simulation is. For example, if you use 30 cells per wavelength, the maximum deviation between the sinusoid and the linear approximation is about 1%. These parameters affect longitudinal current.

Higher frequencies will result in a greater number of cells (increased density) for a mesh. Similarly, increasing the minimum number of cells per wavelength will also increase the density. In general, for optimal density, it is better to increase the number of cells per wavelength rather than increasing the mesh frequency. The optimal value for the mesh frequency is the highest frequency that will be simulated. This may avoid having to recalculate the substrate frequency band if it is not sufficient.

If you enter a value for the mesh frequency, but you have already seeded the layout, the system will ignore the frequency you enter and the mesh frequency will only be used to compute the mesh for the remaining areas of the circuit.

You should be aware that the value entered for the number of cells per wavelength is only a lower limit and not the exact value used by the mesh generator. The following discussion explains how the actual number of cells used by the mesh generator may be greater. For example, suppose you enter 20 for Cells per Wavelength. In general, the cell size used when the geometry is infinitely large corresponds with the number of cells per wavelength. But when other details, edges, and user-defined mesh settings are included, cells might appear that are smaller than resulting in more cells per wavelength than the value of 20 that you entered. Here are two specific cases where the actual number of cells per wavelength is greater:

Effect of Mesh Reduction on Simulation Accuracy


Mesh reduction is a technology that aims at removing mesh complexity originating from the meshing of geometrically complex shapes. In a normal situation, the user specifies the mesh density (the number of cells per wavelength) that needs to be used in the simulation in order to obtain a specific accuracy. However, due to geometrical constraints, the mesher can be forced to use more cells than strictly needed by the wavelength criterion. In this case, the mesh introduces "redundant" degrees of freedom in the solution process. ("redundant" with respect to the electromagnetic behavior). Mesh reduction is a technology that automatically removes these redundant degrees of freedom, prior to the solution of the problem. Hence, it should have a negligible impact on the accuracy of the results.

About the Edge Mesh

The edge mesh feature automatically creates a relatively dense mesh pattern of small cells along the edges of metal or slots, and a less dense mesh pattern of a few large cells in all other areas of the geometry. Because most of the current flow occurs along the edges of slots or metals, the edge mesh provides an efficient solution with greater accuracy.

Use the edge mesh to improve simulation accuracy when solving circuits where the modeling of current flow in any edge area is a critical part of the solution. This includes circuits where the characteristic impedance, or the propagation constant are critical for determining the electrical model, circuits in which close proximity coupling occurs, or circuits where edge currents dominate the circuit behavior. Applications for using the edge mesh include:

Edge mesh is available for all levels of meshing: global, layout layer, and object meshing.

Setting the Width of the Edge Mesh

When using an edge mesh, you can either specify the edge mesh width or leave it blank. If you leave it blank, an appropriate width will be determined and used to create the mesh. One way to get a visual approximation is to position the mouse on the primitive edge and click, then move the mouse inward and note the differential value., which is displayed at the bottom of the Layout window.

About the Transmission Line Mesh

Use the transmission line mesh when you want to specify the number of cells between parallel lines in a layout. This feature can save computation time and memory because it will create a mesh that is appropriate for straight line geometry.

For example, the simulation results for a single transmission line with one or two cells across the width will be equal. If you have coupled lines, the results will differ.

Combining the Edge and Transmission Line Meshes

Both transmission line mesh and edge mesh can be used together. The total number of cells wide will be the total number of transmission line cells plus edge cells. The minimum value permitted when using this combination is 3.

The edge and transmission line mesh affect the transverse current in the circuit. The more cells specified using edge mesh and transmission line mesh, the more accurate transverse current approximations will be.

The plot below illustrates the hairpin example simulated with and without and edge mesh. Although the simulation that includes the edge mesh takes more time, the results are closer to the actual measured results of the filter.

Using the Arc Resolution

The Arc Resolution parameter enables you to control the number of triangular cells that appear in the mesh. Triangular cells are used to generate a mesh on the curved area of an object. The larger the value in the Arc Resolution field, the fewer the number of triangular segments will be used on the curved object.

The maximum value for the Arc Resolution is 45 degrees. The minimum value depends on the original facetting used when the curved object was drawn. For example, the Double Patch Antenna is drawn with an Arc/Circle Resolution of 30 degrees, and the Arc Resolution is set to 45 degrees. The actual value used to refacet the object will be in between these values. The angle is chosen so that the facet length is smaller or equal to the cell size, so refacetting will not affect the cells per wavelength that is specified for computing mesh density.

Note
In order for the mesh generator to produce an accurate mesh, the mesher must be able to recognize the polygon translation it receives as an arc. Therefore, a poorly defined layout resolution may prevent arc recognition and by that arc refacetting. For more information on layout resolution, refer to Mesh Precision and Gap Resolution.

The VIASTUB example is shown below, the Arc Resolution is set to 45 degrees, the coarsest setting, and 0.01degrees, which effectively turns off refacetting. The mesh for a stub based on each angle setting is displayed. The simulation for the denser mesh was longer, required more memory, and produced little improvement in the results.

Arc Resolution = 45 Arc Resolution = 0.01
Process size 6.18 MB 12.791 MB
User time 12 min 20 min
Elapsed time 15 min 24 min
Rectangular cells 96 80
Triangular cells 108 200
Via cells 16 36
Unknown currents 337 453

Mesh Patterns and Simulation Time

The mesh generator is relatively fast, even for complex meshes. But be aware that the complexity of the mesh can have a significant on effect simulation time. In particular, the number of cells in the mesh (especially triangular cells) and the number of unknown currents, can affect simulation time.

Simulation times will be faster when the mesh consists mostly of rectangular cells. A simple mesh is one consisting of a few rectangles of similar size. A worst-case complex mesh would consist of many dissimilar triangles. You should try to minimize the number of triangular cells in the mesh.

The second variable, number of unknown currents, depends on the density, or total number of cells in the mesh. You should try to minimize the total number of cells in the mesh. This reduces the number of unknown currents, and thus reduces the size of the matrix to be solved during simulation. The amount of time required to solve the matrix is N*N*N, where N is the number of unknown currents.

For example, a thru-line at a global seeding of 30 might produce a 50 x 50 matrix to solve. Since the time required to solve the matrix is proportional to the matrix size, the same thru-line at a seeding of 60 might produce a 200 x 200 matrix because number of cells would be twice as dense in both X and Y dimensions. This means that it will take longer to solve.
Adjustments to your mesh parameters can be made to control complexity of the mesh and, in turn, the amount of time required to simulate.

For complex circuits, where simulation times may be long even with a simple mesh, reducing the complexity of a mesh can save significant amounts of simulation time.

Mesh Patterns and Memory Requirements

The number of unknown currents, which is calculated when the mesh is precomputed, is based on the complexity of the mesh. The more unknowns, the larger the matrix that must be solved during simulation. The amount of memory required to solve is proportional to N*N, where N is the number of unknown currents.

Processing Object Overlap

The parameter Thin layer overlap extraction should be used in designs that include thin layers that are both close together and overlapping. It is possible that mesh cells can be generated that cross the overlap region, and this is not desirable.

As an example, consider two layers, one above the other, and close together. They carry a large charge density where they overlap, which increases proportionally to 1/distance. If there is no metal above the layers, the charge density is nearly zero where there is no overlap, and the change is very rapid-nearly a step-at the point of overlap.

If no overlap extraction is performed, the mesher can create cells that will cross the border of the overlap. In the actual circuit, this cell would have a partially high charge density area where the overlap is present, and a partially low charge density area where there is no overlap. However, Momentum simulates cells with a constant charge density, and approximating the strongly-varying charge in the cell with a constant is not an adequate representation. Thus, by enabling thin layer extraction, no cells will be created that cross an overlap region.

Because enabling this feature for all possible overlap in a circuit would create too dense a mesh, some empirical rules are implemented that switch the overlap extraction off if the layers are not close (h > 0.02 estimated cell size) or if the overlap area is small. To calculate the estimated cell size, the mesh frequency, the global number of cells per wavelength, and an estimation of the effective refractive index of the substrate are used.

If you are calculating your mesh at low frequencies, the estimated cell size is high, and you may not want thin layer overlap extraction. In this case, disable the Thin layer overlap function.

Mesh Generator Messages

When a mesh is generated, you may see a message similar to this:

On some layers, the mesher used the maximum allowable cell size for the given substrate. You will not be able to generate a coarser mesh on these layers.

This means that the coarsest mesh has been achieved for the objects on certain layers. This is because the maximum cell size has been limited due to the accuracy of the Green's functions that were calculated for the substrate.

For example, consider a layout with 20-cell mesh when the mesh frequency is 10 GHz. Generally, you would get a 10-cell mesh if you set the mesh frequency to 5 GHz. But if, with the lower mesh frequency, the cell size would be larger that the maximum allowed (the limit being based on the accuracy of the Greens' function of the substrate), the mesh would contain more than 10 cells.

Another message that may occur at meshing reports:

"POLYLINE requires two unique points"

This occurs if the layout resolution, (set at the Layout Units tab in Options > Preferences... ) is inadequate for slanting the meshing line. Increasing the resolution to a finer value will make the error disappear.

Guidelines for Meshing

The default mesh will provide an adequate and accurate answer for many circuit applications. For most other circuit applications, the using the global mesh parameters will be all that is needed to provide greater accuracy. In a few special cases, you may need to use the layer or primitive mesh controls.

For applications such as highly accurate discontinuity modeling or for geometries that have tightly coupled lines, the default mesh may not be dense enough in particular areas to provide enough accuracy. In such cases, edge mesh should be used or the mesh density must be increased. For example, noise floor and dynamic range are typically small numbers. In some cases, geometry solutions may show a low value of S21, like -60 dB, using a dense mesh. Such values are different for a default mesh, which may result in -40 dB for the same circuit.

In any one design, you can use any combination of the four types of mesh control. In general, greater mesh density can provide more accuracy. But greater density takes more computation time (more cells to solve) and, additionally, triangles always take longer to compute than rectangles.

Meshing Thin Layers

Thin layers must be meshed so that the mesh cells are entirely within or entirely outside of the overlapping area. If the mesh cells and object boundaries are not aligned correctly, the simulation data may be less accurate.

For more information, refer to Processing Object Overlap.

Meshing Thin Lines

When the geometry has narrow lines, like thin transmission paths in a spiral, it may be difficult to have a mesh that is more than one cell across the width if the default global mesh is used. If needed, use Edge Mesh or Transmission Line Mesh to capture the current distribution across the line.

Meshing Slots

Slots should be meshed exactly the same as strips-there is no difference. For example, the edge mesh can be used for slots because the current distribution is basically the same, that is, it is concentrated on the edges of a slot.

Adjusting the Mesh Density of Curved Objects

Vias or other curved objects, when drawn in a layout, have a default value for the number of facets used to draw the object, based on the command Options > Preferences> Entry/Edit >Arc/Circle Resolution (degrees). If the value is small, a relatively large number of facets are used to draw the circle, and this can result in more triangular cells created the curved areas during the mesh process. To change the number of facets for all arcs and circles, use the command shown above. To change them for a single object, select the object, then choose Edit > Modify > Arc/Circle Resolution. Then increase the number of degrees for the radius, as desired, to reduce the number of triangles. Be aware that this does alter the geometry of the circuit.

For information on how the mesh parameter Arc Resolution affects a mesh, refer to Processing Object Overlap.

Discontinuity Modeling

A microstrip transmission line with a bend, using the default mesh, may have a cell size equal to the width of the line (one cell per line-width). If it is long and the bend is not severe, then the default mesh may be adequate because the discontinuity is proportionally small compared to the line length. However, if the reference planes are moved inward or if the bend is more severe, the discontinuity and resulting parasitics are in greater proportion to the rest of the line. In that case, the default mesh may result in simulation data with an error.

To correct this inaccuracy, the mesh should be increased and edge mesh used. When the area near the discontinuity is meshed so that the cell size is equal to a third of the line-width (three cells per line-width) the resulting error is reduced. The denser mesh allows for current crowding (parasitic series inductance) at the interior corner of the bend and charge build-up (parasitic shunt capacitance) at the outer edge of the bend.

Solving Tightly Coupled Lines

An example of a tightly coupled line would be a microstrip coupled line filter on a 25 mil Alumina substrate (Er = 9.8) where the line width is 25 mils and the separation between the lines is 2.5 mils. The filter response is sensitive to coupling between the lines and the default mesh is 1 cells per line-width. In this case, the reflection coefficient data does not match measurement data. To solve this design properly, edge mesh must be used.

Editing Object Seeding

The recommended way to seed primitives is to use the o,u,v-coordinate system:

  1. Select the object.
  2. Choose Momentum > Mesh > Setup.
  3. Click Primitive Seed.
  4. Click Clear.
  5. Select new seed parameters.

It is possible to modify these values by editing the properties of the object. This method is not supported or recommended. Select the object, then choose Edit > Properties. Seed values are displayed and can be changed.

Mesh Precision and Gap Resolution

This section will apply mainly to designs that are imported into Advanced Design System.

Mesh resolution is directly related to the Layout Precision dbu (data base units) value. All gaps or other unresolved layout vertices will be resolved by the mesh generator if their distance is less than 2 dbu.

Use the Layout command Options > Preferences > Layout Units to change the units for your fabrication or layout process as needed.

 

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