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Rectangular Spiral RFIC Inductor (FEM Quasi-Static): FMRIND2



This circuit component models an RFIC microstrip rectangular inductor with a strip underpass. The inductor is located atop the insulating dielectric and covered with a passivation layer. This model is based on an evaluation of self and mutual inductances, capacitances, admittances, and resistances between all segments. Calculation of these circuit parameters is based on an accurate 2D FEM quasi-static model of coupled microstrip lines arranged on/into the dielectric (silicon oxide) layer above the conducting substrate. This model accounts for the passivation layer, optional ground straps surrounding the inductor, and for the presence of a conducting (high-doped) layer between insulated layers and the substrate. Simulation speed-up tools include disk cache and AFS (Advanced Frequency Sweep).


Cross-sectional View


Name Description Unit Type Default
ID Element ID Text MI1
NS Number of linear segments (>=4)   15
L1 Length of first segment Length 80 um
L2 Length of second segment Length 155 um
L3 Length of third segment Length 165 um
LN Length of last segment Length 35 um
AB Angle of underpass departure Angle 0 deg
W Conductor width Length 10 um
S Conductor spacing Length 5 um
WB Width of underpass conductor Length 10 um
HB Height of underpass conductor above substrate Length 2 um
LB Length of underpass conductor extension beyond inductor Length 0 um
TB Thickness of underpass conductor Length 1 um
RhoB Underpass metal bulk resistivity normalized to gold   1
MRFSUB Substrate definition Text MRFSUB1[1]
*IsGndStrap Ground straps presence (No/Yes)   No
*GndGap Distance between ground strap and inductance edge Length 10
*GndWid Width of ground strap Length 10
*GndLevel Height of ground strap above substrate Length 10
*IsHDLl High-doped layer presence atop of substrate (No/Yes)   No
*Cond_HDL Bulk conductance of high-doped layer Siemens/m 700
*H_HDL Height of high-doped layer Length 2 um
*PassWrap Flat/Conforming passivation (Flat passivation/Conforming passivation)   Flat passivation
*HP Thickness of conforming passivation layer between turns Length 2 um
UseAFS Use/Do not use AFS for model speed up (UseAFS/NoAFS)   UseAFS

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

* indicates a secondary parameter

Parameter Details

NS. The number of linear conductor segments forming an inductor. NS should be greater than 4 and less than NSMAX. The value of NSMAX can be evaluated from the condition LNMAX >0, where

LNMAX = L2-(NS-2)(W+S)/2 for even NS

LNMAX = L3-(NS-3)(W+S)/2 for odd NS

The layout feasibility check is run before performing calculations.

LN. The length of the last segment LN should not exceed LNMAX (see LNMAX). If the LN value is too large the model automatically sets LN to LNMAX and issues a warning. LN also should not be less than (W+WB)/2. If the LN value is too small the model automatically sets LN to (W+WB)/2 and issues a warning.

AB. The angle AB (degrees) defines the direction of underpass departure from the end of the last segment. Only 0, 90, 180 and 270 are allowed for AB. The Zero angle has an underpass that is parallel to L1 and goes in the opposite direction. The angle is measured counterclockwise. Any intermediate value of AB is set to the closest acceptable value.

The underpass is not allowed to overlap the last segment. If this occurs, the model changes AB so that the underpass departs in the opposite direction. NOTE:: The layout cell overrides the setting for AB and sets the underpass exit to the opposite direction if overlapping occurs.

HB. The height of the underpass is the distance between the upper substrate boundary (the top of the high-doped layer if present) and the bottom of the underpass conductor.

LB. The length of the part of underpass conductor that sticks out from the external edge of conducting turns.

MRFSUB. See MRFSUB. Note that notations H1, H2, H3, Er1, Er2, Er3, Tand1, Tand2, Tand3, and Sig3 in "Cross-sectional View" are MRFSUB respective parameters.

Out90deg (Layout cell parameter only): Note that the layout cell of this model has an Out90deg parameter (to edit these parameter values select the corresponding layout cell, right-click and choose Shape Properties to display the Cell Options dialog box, then click the Parameters tab). Setting this parameter to a nonzero value means that the orientation of a face at port 2 provides a connection to an external circuit via a right (90deg) bend. Correspondingly, setting this parameter to zero means that the orientation of a face at port 2 provides an "in line" (no bend) connection to an external circuit. The default value is zero. Setting it to a nonzero value (for example, to 1) does not affect the electrical properties of the model; no bend component is added automatically. You can attach any bend model to port 2 if needed.

HP. This parameter is ignored if the PassWrap parameter is "Flat passivation", otherwise HP provides the thickness of the passivation layer that covers the gap between turns. This model implies that the passivation layer has the same thickness at the sides and bottom of the gap (See the "Cross-sectional View" section).

UseAFS. This model can optionally use Advanced Frequency Sweep ("UseAFS" is the default). If UseAFS is set to "NoAFS" then this model simulates at each frequency point from the specified frequency sweep. If UseAFS is set to "UseAFS", then this model does not simulate at each frequency point; instead, it simulates at several automatically selected frequency points and uses results to obtain a very accurate frequency-dependent approximation valid through the entire frequency sweep. For information about AFS interaction with a disk cache, see the "Implementation Details" section.

Parameter Restrictions and Recommendations

  1. NS should be greater than 4 and less than NSMAX. The value of NSMAX can be evaluated from the condition LNMAX >0 (see the "Parameter Details" section).

  2. There are no limits on T except possible aggravations due to an overly thin T (see the "Implementation Details" section). Note that the conductor must stay within the passivation layer so the conductor thickness T must be less than 0.95*H1.

  3. When PassWrap is set to Yes, the passivation layer skirts the conductor contour and the passivation thickness varies: on the conductor top it equals H1-T; at the valley between conductors (both sides and bottom) the passivation thickness is 1/3*(H1-T).

  4. To exclude passivation, set MRFSUB parameters Er1 to 1 and Tand1 to 0. Set H1 large enough (H1>>T) to avoid an overly thin air layer between the top of the conductor and the top of the mock "passivation" layer (see the "Implementation Details" section).

  5. To model a suspended MEMS (micro-electromechanical systems) inductor, set Er2 to 1.

  6. FMRIND2 does not allow the use of the Cond_HDL frequency-dependent model material parameter and substrate material parameters Er1, Er2, Er3, Tand1, Tand2, Tand3, and Sig3.

Implementation Details

2D Finite Element Method (FEM) in conjunction with quasi-static problem formulation provides a very stable solution for RFICs most common dimensions and frequency range. The FEM engine is partially based on the FEMM solver ([1]); it comprises a mesher ([2]) and two independent solvers: an electrical solver and a magnetic solver. The mesher generates a mesh that covers the entire cross-section including the cross-section of conductors. Usually, this method consumes a reasonable amount of computing resources; however, in certain situations memory consumption and run time may escalate because some specified dimensions force the mesher to generate overly dense mesh. Commonly, this happens due to an error in parameter specifications that results in creation of extremely narrow layers.

The following figure demonstrates the typical distribution of current across conductors cross-section (conforming passivation). Note that the model provides mesh fine enough (and large enough) to reveal small details of skin effect and current crowding.

Disk Cache and AFS.

Depending on the UseAFS setting, FMRIND2 caches either model Y-matrices at each sweep frequency (UseAFS is "NoAFS") or frequency-dependent approximation (UseAFS is "UseAFS").

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

When UseAFS is "UseAFS", this model includes the first and last (extreme) sweep frequencies along with the model parameters in the cache search criteria. This means that once approximation results are written to the cache, all subsequent sweeps with arbitrary frequency step and identical extreme frequencies are served with AFS approximation obtained from the cache without needing to run AFS again. However, any sweep with even one extreme frequency distinct from those in the cache initiates a new run of the AFS engine.


This element uses line types to determine its layout. By default, the layout uses the first line type defined in your Layout Process File (LPF). You can change the element to use any of the line types configured in your process:

  1. Select the item in the layout.

  2. Right-click and choose Shape Properties to display the Cell Options dialog box.

  3. Click the Layout tab and select a Line Type.

  4. Click OK to use the new line type in the layout.

See “Cell Options Dialog Box: Layout Tab ” for Cell Options dialog box Layout tab details.

See “The Layout Process File (LPF)” for more information on editing Layout Process Files (LPFs) and to learn about adding or editing line types.

Recommendations for Use

Computation time substantially grows with mesh size. Mesh inside conductors may heavily contribute to the total mesh size because the size of a mesh cell inside a conductor is governed by the value of the 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: 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.


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

[2] 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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