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General Multilayer Conducting Substrate Coupled Lines (FEM Quasi-Static): GFMCLIN

Symbol

Summary

GFMCLIN models a section of several (1 to 50) edge- and/or offset-broadside- coupled microstrip lines arranged within unshielded or shielded (optional upper cover) stratified inhomogeneous substrate. Substrate layers have arbitrary heights and are made of various materials; optionally the substrate may be suspended. A backing ground plane is always present. GFMCLIN can account for the presence of optional metallic side walls in conjunction with a metallic cover, and for the trapezoidal shape of conductors cross-section. You can apply a solder mask over the top layer of conductors. GFMCLIN can also model a surface finish made of metal with magnetic properties, and account for the presence of magnetic substrate layers. This model has the option of modeling frequency-dependence of substrate permeability. Simulation speed-up tools include disk cache and AFS (Advanced Frequency Sweep).

GFMCLIN implements the Finite Element Method (FEM) quasi-static modeling technique. GFMCLIN is a dynamic or scalable model; it accepts a number of lines as input so the model and its schematic symbol expands/shrinks as the number of lines increases/decreases.

GFMCLIN differs from GMCLIN as follows:

  • Allows you to specify conductance for dielectric layers.

  • Allows you to specify bulk resistivity for each metal layer (GMCLIN assigns identical Rho to all metal layers).

  • Allows you to place side walls of metallic enclosure at unequal distances from a conductor structure.

  • Accounts for actual distribution of current density inside a conductor.

  • Solves for line parameters at each frequency from frequency sweep (GMCLIN interpolates frequency behavior between higher and lower frequency points).

  • Allows placement of additional lateral (coplanar) grounds to model an RFIC environment.

  • Allows modeling of magnetic substrates with frequency-dependent permeability of substrate layers as well as magnetic surface finish.

Topology

Definitions of SW and SWRight depend on the presence/absence of ground straps.

Definition of positive etch undercut (spacing S is defined as the difference between offsets).

Definition of negative etch undercut (spacing S is defined as the difference between offsets).

Configuration of optional conformal solder mask. Case undercut≥0.

Configuration of optional conformal solder mask over the surface finish metal. Case undercut≥0.

Configuration of optional conformal solder mask. Case undercut<0.

Parameters

Name Description Unit Type Default
ID Element ID Text TL1
N Number of conductors   2
L Conductor length Length L[1]
GMSUB Substrate Definition Text GMSUB1[2]
*IsGndStrap Switch "IsGndStrap"=No Ground Straps/Ground Straps   "No Ground straps"
*GndGap Distance between ground strap and adjacent conductor Length 10 micron
*GndWid Width of ground strap Length 10 micron
*GndHeight Height of ground strap above backing ground Length 1 micron
*SaveToFile Switch "Save to txt file"=Yes/No   "No"
*FileName Name of text file with computed model parameters String Same as model name
UseAFS Switch "UseAFS"=UseAFS/NoAFS   "UseAFS"
*UseUnd Switch “UseUnd”=No undercut/Use undercut   "No undercut"
*IsSldMask Switch “IsSldMask“=No conformal solder mask/Conformal solder mask   “No conformal solder mask”
*Hsmt Thickness of conformal solder mask layer Length 10 micron
*Ersm Relative dielectric constant of conformal solder mask layer   1
*TDsm Loss tangent of solder mask layer   0
*IsSurFin Switch “IsSldMask“=No surface finish/Yes surface finish mask   “No surface finish”
*Hsf Thickness of surface finish metal Length 10 micron
*Rhosf Resistivity of surface finish metal normalized to gold   1
*MusfP Real part of relative permeability of surface finish metal   1
*MusfPP Imaginary part of relative permeability of surface finish metal   0
*IsMagSub Switch “IsMagSub“=Not magnetic substrate/Magnetic substrate   “Not magnetic substrate”
*FreqProf Frequency sweep of substrate relative Mu   1 GHz
*SubMurF Frequency profile of substrate relative Mu (real part)   1
*SubMuiF Frequency profile of substrate relative Mu (imaginary part)   1
*SubCntrl Permissions to apply Mu frequency profile to substrate layers   0
*IsSubF Switch "IsSubF" = Substrate Mu constant vs frequency/Substrate Mu varies vs frequency   "Substrate Mu constant vs frequency"
Wi, i=1..nn- number of lines Width of conductor No i Length W[1]
Offsi, i=1..nn- number of lines Offset of conductor No i Length W[1]
CLi, i=1..nn- number of lines Number of layer containing conductor No i   1

[1] User-modifiable default. Modify by editing under $DEFAULT_VALUES in the default.lpf file in the root installation directory. See “Intelligent Cells (iCells)” for details.

[2] Modify only if the schematic contains multiple substrates. See “Using Elements With Model Blocks” for details.

* indicates a secondary parameter

Parameter Details

See GMnCLIN and GMCLIN for a detailed description of the majority of the GFMCLIN parameters. Parameters specific to GFMCLIN (or used differently) are described as follows:

GMSUB: RhoV. GFMCLIN uses the Rho parameter differently than the GMnCLIN and GMCLIN models do. Instead, GFMCLIN gets information about conductor resistivity from the vector parameter RhoV. This parameter contains bulk resistivity (relative to gold) for the conductor metal specified for each dielectric layer. GFMCLIN waits for the RhoV vector to contain an entry for each dielectric layer, even for layers that do not carry conductors. Thus, the length of the RhoV vector must be equal to N if the substrate is grounded. If the substrate is suspended, RhoV must have N+1 entries.

GMSUB: Sigma. This vector parameter specifies the conductances of materials used for dielectric layers. Sigma must supply conductance for each dielectric layer (except the suspended substrate air layer under the substrate, so the total number of entries for Sigma must always be N).

GMSUB: SigmaC. Specifies the conductance of the dielectric that makes the layer under the metallic cover (if present).

GMSUB: SW and SWRight. GFMCLIN uses these parameters only if the GMSUB Cover parameter is "Metallic Box"; all other values of Cover make SW and SWRight irrelevant. See the last two figures under the "Topology" section for more information on how GFMCLIN interprets SW and SWRight.

If IsGndStrap is "No Ground Straps," GFMCLIN considers SW as the distance from the left edge of the leftmost conductor to the left sidewall of the metallic box/enclosure. SWRight is the distance from the right edge of the rightmost conductor to the right sidewall.

If IsGndStrap is "Ground Straps," GFMCLIN interprets SW as the distance from the left edge of the left ground strap to the left sidewall of the metallic box/enclosure. SWRight is the distance from the right edge of the right ground strap to the right sidewall.

Note that the SW and SWRight parameters may have different values (GMnCLIN considers the distances to the left and right side walls identical and equal to SW).

GMSUB: Undercut parameter. GFMCLIN optionally uses this vector parameter to apply its values as etch undercuts to conductors on each layer. Etch undercut specifies non-rectangular (trapezoidal) distortion of conductor cross-section due to manufacturing errors. Undercut may take positive, zero, and negative values (see the figures in "Topology"). All conductors that belong to the same layer have an identical undercut equal to the corresponding entry of vector Undercut. Note that conductor width is always defined as the top side of a cross-sectional trapezoid. Spacing between adjacent conductors is measured between the closest top vertices of respective trapezoids. See the restriction on the Undercut value in "Parameter Restrictions and Recommendations". Note that the vector parameter Undercut must contain exactly N entries if the GMSUB Gnd parameter is "Grounded Substrate", and exactly N+1 entries if Gnd is "Suspended Substrate". This model does not check length and does not use the contents of the GMSUB Undercut parameter if the UseUnd parameter is "No undercut".

GMSUB: MuP, MuPP. These vector parameters specify the real (MuP) and imaginary (MuPP) parts of permeabilities of materials used for dielectric layers. If control parameter IsMagSub = "Non-magnetic substrate" (default) then parameters MuP and MuPP are not used. If control parameter IsMagSub = "Magnetic substrate" then MuP and MuPP must supply permeabilities for each dielectric layer (except the suspended substrate air layer under the substrate, so the number of entries for MuP and MuPP must always be N).

OffsX. The relative horizontal offset of the conductor #X left edge from the left edge of the left-most conductor. All offsets must be positive. Offset of the left-most conductor (or conductors) may be set to zero. GFMCLIN looks for the smallest offset and subtracts it from other offsets. The left edge of the left-most conductors marks a reference plane to determine the distance to lateral ground straps and optional metallic sidewalls.

CL1. Specifies the number of the layer that carries the conductor on top of it. If the conductor protrudes upward into layer #m (it occupies the lower part of layer #m but sits on layer #m+1), you must set CL1 to m+1. If the conductor has a negative thickness and is recessed into layer #m (it occupies the upper part of layer #m), you must set CL1 to m.

IsGndStrap. This switch either places ("Ground Straps") or does not place ("No Ground Straps") identical perfectly conducting straps (lateral grounds) at both sides of the conductor structure. The default is "No Ground Straps".

GndGap. The distance between the left edge of the left-most (or right edge of the right-most) conductor and lateral ground strap (if present). If IsGndStrap is set to "No Ground Strap" the value of this parameter is irrelevant.

GndWid. The width of the lateral ground straps (if present). If IsGndStrap is set to "No Ground Strap" the value of this parameter is irrelevant.

GndHeight. The height of the lateral ground straps (if present) above the backing ground. If IsGndStrap is set to "No Ground Strap" the value of this parameter is irrelevant.

SaveToFile. This parameter is hidden by default and set to No. You can toggle the parameter to Yes. If you select Yes, GFMCLIN creates a text file named default model_name.txt at the current project location. This text file contains a table of values of RLGC line parameters at each project frequency. Each row contains RLGC values computed at the frequency specified in the first column (frequency in GHz, R in ohms/m, L in H/m, G in S/m, C in F/m).

The structure of this text file is essentially the same if N>2 (see the description of the text file structure for N=1 in GM1LIN).

The model outputs RLGC matrices to a table of rows and columns. The total number of columns in the table is 4*N*N, where N is the number of lines. All columns are numbered.

Each row of this table starts with the frequency value in GHz. Entries of each RLGC matrix at this frequency are placed column-wise one after another in a single row, so that all columns of every RLGC matrix can be found in this row. Thus, entries of R-matrix go first in the row in this order: R11, R21, R31.. RN1. Now goes the second column: R12, R22, R32,..RN2 and so on. Column-wise entries of L-matrix are located after R-matrix . Entries of G-matrix follow entries of L-matrix and entries of C-matrix complete the row.

GFMCLIN at N=2 implies the existence of two modes, namely, C and P (see [2]), and places additional columns in the output text file. Note that if a system of coupled lines is fully symmetrical (as it might be for edge-coupled microstrip lines; whereas broadside coupled microstrip lines are always asymmetrical), C mode corresponds to even mode and P mode corresponds to odd mode.

GFMCLIN at N=2 outputs complex characteristic impedances Re(Zc1), Im(Zc1), Re(Zp1), Im(Zp1), Re(Zc2), Im(Zc2), Re(Zp2), Im(Zp2); complex effective dielectric constants Re(EeffC), Im(EeffC), Re(EeffP), Im(EeffP) (find traditional effective dielectric constants in columns 38, 39), and losses for C and P modes LossC (dB/m), LossP(dB/m) to columns 2-15. Entries of R, L, G, and C matrices are distributed among columns 16-31 in corresponding order (see above). Columns 32-37 contain Re(Rc), Im(Rc), Re(Rp), Im(Rp), BetaC, and BetaP; where Rc is ratio of C mode voltage in the second line to C mode voltage in the first line; Rp is the same ratio in P mode (see details in [2], section 4.3.1) and BetaC and BetaP are propagation constants of C and P modes in Rad/m. Note that columns 38 and 39 contain traditional effective dielectric constants ErC_Eff and ErP_Eff (they do not account for losses). The total number of columns in the output text file is 39.

You can link or import the created text file to a project as a data file and view the frequency behavior of any of the above parameters using the proper data measurement. Note that the first column (frequency) is always in GHz, so these measurements might be incompatible with other Cadence® AWR® Microwave Office® measurements placed on the same graph; you may prefer to place these data measurements on a separate dedicated graph.

FileName. By default this parameter is hidden and is set to gfmclin.txt. You can change the file name for each model instance to an arbitrary name with a length not exceeding 64 symbols.

UseAFS. This model can optionally use Advanced Frequency Sweep (UseAFS is the default setting of this switch). If UseAFS is "NoAFS" the model simulates at each frequency point from the specified frequency sweep. If UseAFS is "UseAFS" the model does not simulate at each frequency point. Instead, it simulates at several automatically selected frequency points and uses results to obtain very accurate frequency-dependent approximation for each entry of RLGC matrix valid through the entire frequency sweep. See "Implementation Details" for the specifics regarding Advance Frequency Sweep (AFS) interaction with disk cache. See also restriction on usage of UseAFS parameter with magnetics in "Parameter Restrictions and Recommendations".

UseUnd. This parameter specifies if the model uses the GMSUB vector parameter Undercut (previously described). The model does not check length and does not use the contents of the GMSUB Undercut parameter if the UseUnd parameter is "No undercut".

IsSldMask, Hsm, Ersm, TDsm. Conductors on top of a dielectric stack can be covered by a conformal dielectric layer that does not belong to the regular dielectric stack. This layer is called “solder mask,” a common term used in the PCB industry. Any material used as a conformal passivation layer fits as well. The IsSldMask parameter informs the model if the Hsm, Ersm, TDsm parameters are relevant or not. Note that a solder mask can be applied only to conductors that sit on top of a dielectric stack, and only if their thickness is positive (they are not recessed but stick out of the dielectric). If the model cannot find conductors eligible for the solder mask application it does not apply the solder mask. See the restriction on the Hsm value in the "Parameter Restrictions and Recommendations" section.

IsSurFin, Hsf, Rhosf, MusfP, MusfPP. Conductors on top of a dielectric stack may have a protective coating called surface finish. Popular PCB surface finish ENIG (Electroless Nickel Immersion Gold) contains nickel that exhibits noticeable magnetic properties. GFMCLIN allows you to add a single protective metal layer to top conductors (for ENIG, the presence of a very thin top protective gold layer is neglected) if IsSurfFin = "Surface finish metal," and specify its parameters: thickness (Hsf), relative resistivity (Rhosf), and relative complex magnetic permeability MusfP+J*MusfPP (here P and PP stand for one and two primes - standard denotations for real and imaginary part of permeability). Note that surface finish can be applied only to conductors that sit on top of a dielectric stack, and only if their thickness is positive (they are not recessed but stick out upward from dielectric). If the model cannot find top conductors eligible for surface finish application it does not apply the surface finish at all. See also restriction on usage of UseAFS parameter with magnetics in "Parameter Restrictions and Recommendations".

IsMagSub. Informs the model if GMSUB parameters MuP and MuPP are relevant. If IsMagSub = "Magnetic substrate," then the model checks vectors MuP and Mupp (real and imaginary parts of relative permeabilities) for errors and applies their values to material properties of substrate dielectric layers. If IsMagSub = "Non-magnetic substrate" then the model applies default free space permeability values to all substrate dielectric layers. See also restriction on usage of UseAFS parameter with magnetics in "Parameter Restrictions and Recommendations".

FreqProf, SubMurF, SubMuiF, SubCntrl. These parameters provide frequency-dependent permeability for selected substrate layers. Vector parameters FreqProf, SubMurF, and SubMuiF combined define Mu (permeability) frequency profile: FreqProf is a frequency sweep (valid only for substrate permeabilities), SubMurF and SubMuiF are values of real and imaginary parts of substrate permeabilities specified at FreqProf frequencies. Note that only a sole Mu frequency profile is allowed, meaning that all layers to which this profile applies are assumed made of the same material. Entries of vector SubCntrl should be either 1 or 0: SubCntrl[k] =1 grants permission to apply the Mu frequency profile to permeability of layer #k; SubCntrl[k] =0 prohibits applying the Mu frequency profile to permeability of layer #k.

Note that the sizes of vectors SubMurF and SubMuiF must be equal to the size of vector FreqProf; and the size of vector SubCntrl must be equal to the number of substrate layers.

IsSubF. Informs the model if the permeability frequency profile is relevant. If IsSubF="Substrate Mu constant vs frequency" then permeabilities of all substrate layers are assumed constant vs frequency. If IsSubF="Substrate Mu varies vs frequency" then the model attempts to apply the permeability frequency profile specified by parameters FreqProf, SubMurF, and SubMuiF to selected substrate layers; layer selection is provided by the SubCntrl parameter entries.

Parameter Restrictions and Recommendations

  1. Total number of layers cannot exceed 30.

  2. Number of conductors N cannot exceed 50.

  3. See detailed information on parameter restrictions and recommendations in GMnCLIN under "Conductor Numbering and Disposition". The GMFCLIN, GMnCLIN, and GMCLIN models are very particular about correct conductor numbering.

  4. Do not use very small (for example, below 0.1) values of RhoV (bulk resistivity of conductors in layers, vector parameter of GMSUB) and Rhosf (bulk resistivity of surface finish metal) because GFMCLIN cannot model perfect conductors and may have issues with metals of very low bulk resistivity. To provide high accuracy of modeling current distribution inside the conductors, maximum mesh cell size is proportional to the metal skin depth at the highest frequency of the frequency sweep. Skin depth is proportional to the square root of bulk resistivity so mesh may contain millions of cells for low resistivity metals. Extremely big mesh may result in a long simulation time and lead to other computational issues.

  5. Do not use infinitely thin conductors and conductors with a thickness less than 0.1 micron.

  6. Do not use excessively big (for example, above 20) values of real/imaginary parts of surface finish metal permeability MusfP and MusfPP, because GFMCLIN may have difficulties with very big mesh. To provide high accuracy of modeling current distribution inside the conductors, maximum mesh cell size is proportional to the metal skin depth at the highest frequency of the frequency sweep. If magnetic surface finish is present, skin depth is inversely proportional to the square root of surface finish metal permeability so large values of permeability may contribute to the creation of multimillion cell mesh. Extremely big mesh may result in a long simulation time and lead to other computational issues.

  7. If UseAFS is "UseAFS" and GFMCLIN cannot obtain approximation data from a disk cache, AFS approximation is activated. AFS needs to perform a simulation at seven frequency points minimum, so a frequency sweep must have at least seven frequency points. If the number of frequency points is less than seven the model stops and issues a corresponding error message. If UseAFS is "UseAFS" and GFMCLIN successfully gets data from a disk cache, it uses cached approximation data at each specified frequency point even if the number of frequency points is less than seven. If UseAFS is "NoAFS" the model performs calculations at each frequency point.

  8. Note that the option UseAFS="UseAFS" is incompatible with the use of magnetic properties (IsSurFin="Surface finish metal" and/or IsMagSub="Magnetic substrate"); this model always simulates magnetics at each point of the frequency sweep.

  9. The absolute value of the undercut for each layer is capped at W/2 (where W is conductor width) if the undercut is negative. A positive undercut is limited by the maximum etch factor EF (defined as EF=Undercut(i)/T where T is conductor thickness, Undercut(i) is the i-th entry of vector parameter Undercut, and i is the layer number) at EF≤2.95. This value is defined by the abilities of the FEM mesher to cope with fine mesh that develops at small acute angle adjoining the trapezoid base.

    Mesh in the vicinity of the trapezoid base (shown density plot of magnetic field) where etch factor = 2.7.

  10. Positive undercut also limits permissible values of minimal spacings between adjacent conductors on the same layer because conductor offsets (and accordingly, spacings) are measured to (between) top cross-sectional vertices (see the figures in "Topology"). GFMCLIN issues an error message if the distance between adjacent base vertices of neighboring conductors gets less that 0.1 micron. The same occurs for the minimum allowable values of the GndGap parameters and the GMSUB SW and SWRight parameters.

  11. The application of a "solder mask" onto an existing top-layer layout may limit the minimal spacing allowed between adjacent conductors. This limitation comes from drawing limitations that imply an "inverse trapezoid" shape of the solder mask layer between conductors and disallows the "V-notch" shape when the top horizontal part of the solder mask layer between conductors vanishes (see the following figure). If said limitation is met, GFMCLIN issues an error message such as: "Spacing #1 in layer #1 must be greater than 0.1 micron (also check undercut and optional solder mask)." Note that if no solder mask parameters effect specified spacing, the error message does not mention the solder mask. Typically, this occurs with a thick solder mask layer and relatively small spacing specified and may be interpreted as a recommendation to substitute a flat layer for a conformal layer (to set IsSldMask to “No solder mask” and merely add a flat solder mask layer to dielectric stack).

    Limiting case (a V-notch in the solder mask layer with a horizontal stretch missing) for spacing between adjacent conductors if a solder mask is present.

  12. If the thickness of the conformal mask layer Hsm exceeds five thicknesses of the top layer conductors (if any), the model issues a warning: "Conformal solder mask requested. Solder mask thickness Hsm is greater than 5T (five conductor thicknesses) so conformal fit is not feasible. Additional flat top layer may provide same results as conformal layer." This is an explicit recommendation to substitute a flat layer for a conformal layer, that is, to set IsSldMask to "No solder mask" and merely add a flat solder mask layer to the dielectric stack.

  13. GMFCLIN allows "interdigital" positioning of conductors that belong to adjacent layers so that they all take up space within a common dielectric layer (see the following figure). GMCLIN does not allow this arrangement because it checks the total height of conductors and compares it to the height of the dielectric layer Hk into which they protrude, not paying attention to their lateral offset.

    GFMCLIN allows this layout while GMnCLIN and GMCLIN consider it a user error.

  14. Permeability frequency profile parameters FreqProf, SubMurF, and SubMuiF may be defined as data file(s) as well as scripting equations. Use equation functions col() or row () to read the profile from the data file. To use scripting equations you need to place scripting function calculating (and returning) vectors SubMurF and SubMuiF into the project scripting module named "Equations". You can reference these functions in schematic equations (see “Using Scripted Equation Functions” ).

Implementation Details

GFMCLIN implementation is based on the FEM technique described in [1] and applied to quasi-static approximation of Maxwell equations. It accounts for losses in metal and in substrate dielectric. Dispersion is included partly as frequency-dependence contribution that comes from losses (substrate polarization and eddy current loss, conductor resistive loss). Non-TEM dispersion is not included.

The 2D Finite Element Method (FEM) in conjunction with the quasi-static problem formulation provides a very stable solution for RFIC's most common dimensions and frequency range. The FEM engine is partially based on the FEMM solver ([3]); it comprises a mesher ([4]) and two independent solvers: an electrical solver and a magnetic solver. The mesher generates a mesh that covers the entire cross-section including a cross-section of conductors. Usually, this method consumes a reasonable amount of computing resources; however, in certain situations memory consumption and run time may increase because specified dimensions force the mesher to generate overly dense mesh. Commonly, this happens due to an error in the parameter specification that results in creation of extremely narrow layers.

Another cause may also result in fine mesh. Generally, the densest mesh is concentrated in the vicinity (and within) conductors. This is intentional because a model accurately defines fields inside conductors and sets the smallest mesh cell size inside the conductor to a value proportional to either the skin depth of the conductor metal at the highest evaluation frequency or to the minimal cross-sectional dimension, whichever is less. If you specify, for example, a gold conductor with cross-sectional dimensions of 10x1 microns, at the highest frequency 20 GHz, you can presume the mesh will be of reasonable size. Setting the conductor width to 2000 microns or the highest frequency to 200 GHz may substantially hinder the modeling process, however.

The following figure demonstrates the typical distribution of an electric current across a conductor cross-section and contours of magnetic potential (conductors are at 1A of impressed current each). Note that this model provides mesh fine enough (and large enough) to reveal the small details of skin effect and current crowding.

The following figure demonstrates the distribution of an electric field and equipotential lines (conductors are at potentials 1 and 0). Note how the closely located ground strap affects field distribution.

Eventually, the model extracts RLGC per-unit-length matrices from computed electric and magnetic fields and uses them to obtain external circuit parameters.

Disk Cache and AFS

Depending on the setting of the UseAFS switch, the model caches either RLGC matrices at each sweep frequency (UseAFS is "NoAFS") or frequency-dependent approximations for each RLGC matrix entry (UseAFS is "UseAFS").

If UseAFS is "NoAFS" then all frequencies in a sweep are part of the cache search criteria and all subsequent runs of identical models at the same frequency sweep use disk cache for speed-up. However, if even one frequency differs from those in a cache (or one frequency added to a sweep) the model runs a full simulation.

When UseAFS is "UseAFS" the model includes first and last (extreme) sweep frequencies along with model parameters into cache search criteria. Once approximation results are written to cache, all subsequent sweeps with arbitrary frequency step and the same extreme frequencies are handled with AFS approximation obtained from the cache without needing to run AFS again. Any sweep with even one extreme frequency distinct from those in the cache results in running the AFS engine.

Layout

The project LPF must contain some structures with predefined names for each dielectric layer populated with conductors (note that every conductor has the number of the assigned dielectric layer specified in the respective parameter CLn, where n is the conductor number). Structure names must be based on the template ML_LINE_X, where X is equal to the number of the dielectric layer. All conductors that belong to layer X are comprised of material layers described in ML_LINE_X.

For example, if GMCLIN defines seven conductors, substrate GMSUB defines eight dielectric layers, and conductors are distributed over dielectric layers in accordance with the following table:

Conductor # CL value
1 1
2 2
3 3
4 3
5 3
6 6
7 6

From the table you can see that conductor #1 sits on dielectric layer #1, conductor #2 sits on dielectric layer #2, conductors #3, #4, and #5 are on layer #3, and conductors #6 and #7 sit on layer #6. This arrangement indicates that only layers #1, 2, 3, and 6 are populated with conductors and you need to specify structures ML_LINE_1, ML_LINE_2, ML_LINE_3, and ML_LINE_6.

If a structure with the corresponding name is not found, the name of the missing structure is drawn on the error layer.

Note that the number of dielectric layers (and X in ML_LINE_X) defined in GMSUB cannot exceed 30.

Note also that the layout cell assigns to each conductor #n the linetype index equal to the value of the corresponding parameter CLn, that is equal to the number of the dielectric layer assigned to conductor #n.

Recommendations for Use

See the GMnCLIN "Recommendation for Use" section for details and usage examples.

Computation time substantially grows with mesh size. Mesh inside conductors may heavily contribute to total mesh size because the size of a mesh cell inside a conductor is governed by the value of skin depth at the highest simulation frequency. Mesh does not vary with frequency, so the same fine mesh works at lower frequencies. Frequency-independent mesh results in improved stability and consistency, but with some sacrifice in solution time.

Note that AFS may dramatically reduce simulation time for sweeps that contain hundreds or even thousands of frequency points (AFS is incompatible with the use of magnetic properties).

NOTE: The implementation of FEM Quasi-Static models relies on temporary intermediate text files. This model creates these files temporarily in the project directory and subsequently deletes them. There may be several dozen files and they may use up to 100 MB of disk space, so ensure that your hard drive has sufficient free space.

Caution regarding units of data in saved text files: If a project that reads saved RLGC text files uses frequency, resistance, inductance, or conductance units different from GHz, Ohm, Henry, or Siemens, you may need to scale input values manually.

How to use frequency-dependent substrate permeabilities (Mu frequency profile)

To use frequency-dependent substrate permeabilities, you must first set general magnetic substrate permission: IsMagSub="Magnetic substrate". Next you need to set permission to apply the Mu frequency profile IsSubF="Substrate Mu varies vs frequency". Fill entries of substrate vector parameters MuP and MuPP (Mu constant vs frequency) including entries for layers intended for use with frequency-dependent permeabilities (use any values for respective entries, for example MuP=1 and MuPP=0). For permitted (see the following details on the SubCntrl role) layers, profile values overwrite values specified by MuP and MuPP anyway. Fill vector parameters that define the Mu frequency profile: FreqProf, SubMurF, SubMuiF, SubCntrl. You should fill out all SubCntrl entries (the number of SubCntrl entries must be equal to the number of all substrate layers). A non-zero value of SubCntrl entry #k is a permission to overwrite permeability of substrate layer #k by the Mu frequency profile. A zero value of SubCntrl entry means that the permeability of the respective layer keeps the value specified by substrate parameters MuP and MuPP. Note that only a sole Mu frequency profile is allowed-- all layers to which this profile applies are assumed made of the same material.

Relation between frequency sweep and Mu frequency profile

If the entire frequency sweep is within FreqProf range then the model silently interpolates real and imaginary values of Mu using SubMurF and SubMuiF as lookup tables. If first and/or last sweep frequencies are out of the FreqProf range, then GFMCLIN issues a respective warning and extrapolates beyond the FreqProf range as a constant value equal either to the first and/or last FreqProf entries.

References

[1] Jianming Jin,"The Finite Element Method on Electromagnetics," 2nd edition, Wiley, NY, 2002.

[2] R. Mongia, I. Bahl, and P. Bhartia, RF and Microwave Coupled-Line Circuits, Artech House, Norwood, MA, 1999.

[3] FEMM (by David Meeker) home page: https://www.femm.info/wiki/HomePage

[4] Jonathan Richard Shewchuk. Triangle. A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. Follow this link for information and download: http://cs.cmu.edu/~quake/triangle.html

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