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Single Line on General Multilayer Substrate (EM Quasi-Static): GM1LIN



GM1LIN models a section of single microstrip line arranged within an unshielded or shielded (top cover is optional) stratified inhomogeneous substrate. Substrate layers have arbitrary heights and are made of various materials; optionally the substrate may be suspended. Backing ground plane is always present. GM1LIN can account for the presence of optional metallic side walls in conjunction with a metallic cover (metallic enclosure). This model can evaluate the metal surface roughness effect using surface profile height "Rgh" specified via substrate GMSUB.



Name Description Unit Type Default
ID Element ID Text TL1
W Width of conductor Length W[1]
CL1 Conductor #1 layer number   1
L Conductor length Length L[1]
Acc Accuracy parameter   1
GMSUB Substrate Definition Text GMSUB1[2]
*SaveToFile Save/Do not Save Data to Text File   "No"
*FileName Name of text file with computed model parameters String Same as model name

[1] User-modifiable default. Modify by editing under $DEFAULT_VALUES in the default.lpf file in the root installation directory. See the AWR Microwave Office Layout Guide for details.

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

* indicates a secondary parameter

Parameter Details

GMSUB. Multilayer substrate parameters are listed in GMSUB model description. Substrate is comprised of layered substrate itself, optional metallic cover, backing ground plane and optional air layers separating substrate from backing ground plane (suspended substrate) and from cover (covered substrate). Optional metallic side walls are available in conjunction with metallic cover. Optional top and bottom air layers are specified by means of corresponding switches included as GMSUB parameters (see GMSUB description, parameter switches Cover and Gnd). GMSUB implies that thickness of conductors on each layer is specified via vector parameter T. All conductors on the same layer have similar thickness. This thickness may vary between layers. Each dielectric layer must have a corresponding entry in vector T even if this specific layer does not carry conductors. GM1LIN checks if the length of vector T is equal to the number of dielectric layers that might carry conductors. Surface roughness is specified by the "Rgh" parameter (RMS height of surface profile). If Rgh=0, then evaluation of the roughness effect is skipped.

CL1. Parameter CL1 specifies the number of layer that carries the conductor atop of it. It means that if conductor protrudes upward into layer #m (that is, it takes some bottom space from layer #m) but sits onto the layer #m+1, parameter CL1 must be set to value m+1. If the conductor has negative thickness and is recessed into the layer #m (that is, takes some top space from layer #m), parameter CL1 must be set to value m.

Acc. The parameter Acc is the accuracy parameter. The default value for Acc is 1. If Acc is less than 1 or greater than 10 it is set automatically to 2.

SaveToFile. Parameter is hidden by default and set to No. User can toggle this parameter to Yes and No. If Yes is selected model creates a text file (named by default model_name.txt) at the current project location. This text file contains 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). Model GM1LIN creates file gm1lin.txt that contains complex characteristic impedance Re(Zo), Im(Zo), complex effective dielectric constant Re(Eeff), Im (Eff) (please find traditional effective dielectric constant in column 12), and Loss (dB/m) in columns 2-6. Columns 7-10 contain R, L, G, and C. Column 11 contains propagation constant Beta in Rad/m. Note that column 12 contains traditional effective dielectric constant Er_Eff that does not account for loss. Total number of columns in file gm1lin.txt is 12.

Created text file might be linked or imported to project as a data file and frequency behavior of any above mentioned parameter may be viewed using the proper data measurement. Note that first column (frequency) is always in GHz so these measurements might be incompatible with other Cadence® AWR® Microwave Office® software measurements placed on the same graph; thus, user might prefer to place aforementioned data measurements on separate dedicated graph.

FileName. By default this parameter is hidden and is set to GM1LIN.TXT. User can change file name for each model instance to arbitrary name with length of file name not exceeding 64 symbols.

Parameter Restrictions and Recommendations

  1. Total number of layers cannot exceed 30.

  2. Accuracy parameter A is limited to 1<Acc<10. Larger value of Acc increases density of mesh used in computations. Accuracy of model parameters may gain slightly from increasing Acc at the expense of noticeable growth of computation time. As a rule of thumb, good trade-off between accuracy and computation time is to set Acc to 1.

  3. Number of dielectric layers must include only those layers that may carry conductors on their top surface. Layers are enumerated from top to bottom. Note that if GMSUB switch parameter Cover is set to "Metallic Cover" or "Metallic B ox" the topmost layer adjacent to cover is not included in count; likewise, if substrate switch parameter Gnd is set to "Suspended Substrate" the bottom air layer is not included in count. Actually, layer number 0 may be displayed in error messages, e.g. in case when substrate is covered and thickness of conductor atop the layer #1 exceeds 95% of thickness of layer located above layer #1, message refers to this "undercover" layer as layer #0.

  4. This model does not impose restrictions on the conductor thickness (thickness may be zero, positive, or negative). Negative thickness means that the conductor is recessed into the substrate. User supplies conductor thickness for each layer that may carry conductors (see description of vector parameter T in GMSUB documentation). See also below paragraph 4 regarding thickness of conductor in case of suspended substrate. Proceed with caution setting fictitious thicknesses for layers that do not actually carry conductors: excessive thickness may cause error message if it exceeds 95% of thickness of adjacent dielectric layer. To keep on the safe side you may set these thicknesses to zero.

  5. If substrate is suspended, (N+1)th entry of thicknesses vector T (see substrate parameters) refers to conductor that is expected to be located at the bottom surface of layer N; model automatically assigns negative thickness to this conductor. It means that such a conductor extends downwards from the bottom surface of the substrate.

  6. If GMSUB switch Cover is set to "Metallic Box" it means that conductor and substrate are confined within metallic enclosure. Top cover is placed at distance HC (sets in GMSUB) above dielectric layer #1, bottom ground plane is always present (position defined by GMSUB parameters Gnd and HB, see GMSUB documentation), and left and right side walls are offset by value of GMSUB parameter SW from respectively left and right edges of line conductor.

Implementation Details

Model implementation is based on EM Quasi-Static technique described in [1]. It accounts for losses in metal and in substrate dielectric. Dispersion is partly included. Evaluation of the surface roughness impact is based on the improved Hammerstad formula [2],[3].


The project LPF must contain a structure with a predefined name for the dielectric layer that carries a conductor. See “Structure Type Definitions” for more information on adding structures to LPF files. The structure name must be based on the template ML_LINE_X, where X is equal to the number of the dielectric layer specified with GMSUB (for example, ML_LINE_2 or ML_LINE_23). The conductor is comprised of material layers described in the structure ML_LINE_X.

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 the conductor the linetype index equal to the value of the CL1 parameter (equal to the number of the dielectric layer assigned to the conductor). This means the LPF file must contain linetypes definitions for each dielectric layer and these definitions must be listed in strict order corresponding to the order of dielectric layers from top to bottom of the dielectric stack.

Recommendations for Use

Primary RLGC parameters as well as characteristic line parameters might be of interest for circuit designer; however, AWR Microwave Office single line models do not cater this information to user explicitly. GM1LIN models accommodate unique opportunity to obtain exhaustive information about values of line parameters at any frequency from operational frequency range. Due to the fact that GM1LIN may be configured to represent any EM Quasi-Static model of a single line (except MM1LIN that allows conductive substrate) it also may be used as means of extracting additional information not available directly from such models as MEMLIN, SEMLIN, S1LIN etc. See documentation on substrate GMSUB for examples of implementation of commonly used single layer configurations (microstrip, stripline, suspended, inverted, etc.)

NOTE: The implementation of EM Quasi-Static models relies heavily on the involved numerical algorithms. This may lead to a noticeable increase in simulation time for schematics that employ many such models.

If thickness of any layer is too small in comparison with the thickness of another layer, simulation time may also noticeably grow.

Caution regarding units of data in saved text file: If a project that reads saved text file uses frequency, resistance, inductance or conductance units different from GHz, ohm, henry or siemens you may need to scale input values manually.


[1] M.B. Bazdar, A.R. Djordjevic, R.F. Harrington, and T.K. Sarkar, "Evaluation of quasi-static matrix parameters for multiconductor transmission lines using Galerkin's method," IEEE Trans. Microwave Theory Tech., vol. MTT-42, July 1994, pp. 1223-1228.

[2] E.O. Hammerstad (edited by F. Bekkadal), Microstrip handbook,Trondheim: Norwegian Institute of Technology, 1985

[3] S.P. Morgan, Jr., "Effects of surface roughness on eddy current losses at microwave frequencies," J. Appl. Phys., vol. 20, 1949, pp. 352-362

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