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Circular Spiral RFIC Inductor (FEM Quasi-Static): FMCIND2



This circuit component models an RFIC microstrip circular spiral inductor with a strip underpass. The inductor is located atop an 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 spiral turns. The calculation of these circuit parameters is based on an accurate FEM quasi-static model of coupled microstrip circular rings 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 the optional conducting (high-doped) layer between insulated layers and the substrate. Simulation speed-up tools include disk cache and AFS (Advanced Frequency Sweep).


Cross-sectional Views

Figure 1. Suspended Underpass (CMOS RFIC)

Figure 2. On-substrate Underpass (GaAs RFIC)


Name Description Unit Type Default
ID Element ID Text MI1
NT Number of turns   3
W Conductor width Length 10 um
S Conductor spacing Length 2 um
RI Internal radius of a spiral Length 20 um
UExit Underpass exits toward near/far side of spiral (Switch "Near exit/Far exit")   Far exit
UPass Underpass floats in insulating oxide/sits immediately on substrate surface (Switch "Suspended/On-substrate underpass)   Suspended
WB Width of underpass conductor Length 10 um
HB Height of underpass conductor above substrate/Height of inductor above underpass (Switch "Suspended/On-substrate underpass) Length 2 um
LB Length of underpass conductor extension beyond inductor Length 0 um
TB Thickness of underpass conductor Length 1 um
ErB Relative dielectric constant of dielectric above underpass (used only if UPass="On-substrate")   1 um
TandB Loss tangent of dielectric above underpass (used only if UPass="On-substrate")   1 um
RhoB Underpass metal bulk resistivity normalized to gold   1
MRFSUB Substrate definition Text MRFSUB1[1]
*IsGndStrap Ground straps present (Switch 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
*IsHDL High-doped layer present atop of substrate (Switch 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 (Switch 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 (Switch UseAFS/NoAFS)   UseAFS

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

* indicates a secondary parameter

Parameter Details

NT. Number of turns; must represent an integer number of half-turns that is equal to 1, 1.5, 2, 2.5 and so on. This model accepts any value for NT in the range 1..50 but if NT does comply with the above limitation the model changes NT to the closest suitable value and issues a warning.

UExit. This switch allows the direction of the underpass either to the nearest turn (Near the exit, see the "Topology" section) or to span the internal opening before "diving" under the conducting turns (Far exit). Certain combinations of UExit and NT values are prohibited (see the "Parameter Restrictions and Recommendations" section).

UPass. This switch allows you to select the inductor design. Setting "Suspended underpass" (see "Cross-sectional Views", Figure 1) implies that all inductor turns are located atop insulating dielectric (oxide) and that the underpass is "floating" in oxide above the substrate surface. Setting "On-substrate underpass" (see "Cross-sectional Views", Figure 2) implies that the substrate is non-conductive, all inductor turns sit immediately on the substrate, and the portion of turn metal is elevated above the substrate and makes an arc above the underpass trace.

HB. Usage depends on the UPass setting:

UPass=Suspended substrate - Height of the underpass is the distance between the substrate top (top of high-doped layer if present) and the bottom of the underpass conductor.

UPass=On-substrate underpass - HB is essentially the elevation of the portion of inductor turns above the underpass.

ErB, TandB. Usage depends on UPass setting:

UPass=Suspended substrate - the model ignores ErB and TandB.

UPass=On-substrate underpass - ErB and TandB represent the characteristics of material filling spacing between arched inductor turns and the underpass strip (often air).

LB. The length of the extension of underpass conductor beyond the external edge of the inductor body.

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

H1, H2, Er1, Er2, Tand1, Tand2, Tand3, Sig3. Settings depend on the setting of switch UPass:

UPass=Suspended substrate - parameters must be set as shown in "Cross-sectional Views" Figure 1.

UPass=Suspended substrate - parameters must be set as shown in "Cross-sectional Views" Figure 2. If the substrate height is Hsub then you should set H2=0.25*Hsub and H3=0.75*Hsub (you must make sure that H2+H3=Hsub). Ensure also that Er2=Er3=ErSub,Tand2=Tand3=TandSub where ErSub and TandSub are substrate characteristics.

IsGndStrap. "Yes" installs additional (to backing ground plane) lateral ground implemented as ground straps around the inductor (see the "Topology" section). "No" makes the model use only a backing ground plane. The latter value of this switch makes the model ignore parameters GndGap, GndWid, and GndLevel. This parameter must be left at the default value "No" if parameter UPass=On-substrate underpass.

IsHDL. "Yes" converts the upper portion of the substrate into a high-doped layer. This layer has height H_HDL, dielectric constant Er3, loss tangent Tand3, and conductance Cond_HDL. "No" makes this model ignore parameters H_HDL and Cond_HDL. IsHDL must be left at the default value "No" if parameter UPass=On-substrate underpass.

PassWrap. The default value "Flat passivation" provides a flat passivation layer covering inductor turns. "Conforming passivation" makes a thin passivation layer to conform the cross-sectional contour as shown in "Cross-sectional Views" Figure 1.

HP. This parameter is ignored if PassWrap=Flat passivation, otherwise HP provides the thickness of 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 "Cross-sectional Views" Figure 1).

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

Layout cell NSeg. Note that the corresponding layout cell of this model has parameter NSeg (to edit NSeg, select the corresponding layout cell, right-click and choose Shape Properties to display the Cell Options dialog box, then click the Parameters tab). NSeg defines the order of regular circumscribed polygon used to draw the spiral shape. The default value is 64. Larger values of Nseg (up to 6000 allowed) make the contour smoother at the cost of slower drawing. Also, low values of Nseg may cause variation of dimensions W and S of the drawn spiral. In this case increasing Nseg will allow to obtain accurate representation of intended design. Note that lower limit of Nseg is 64 and upper limit of Nseg is 6000.

Layout cell BrGap (since v7.51). You should select the FMCIND2 layout cell on the Layout tab of the Element Options dialog box. The layout cell of this model has parameter BrGap (to edit BrGap select the corresponding layout shell, right-click and choose Shape Properties to display the Cell Options dialog box, then click the Parameters tab). This parameter is valid only for certain line types, like Plated Metal Line, when the inductor body is comprised of two metals (top and bottom) connected by a via along all windings, and the bridge is built on the bottom metal. In this case, the bridge conductor may be short-circuited by windings at the bottom metal level. To avoid this, this layout cell provides a gap in the bottom metal to allow the bridge to exit from the inductor center untouched. BrGap is a user-defined extension to the width of this gap (the default is 5 microns). You should use the layout 3D view to check the actual gap width. In rare cases when parameter W is small and BrGap is relatively large, approximately half of the internal winding may be stripped of the bottom metal; in this case decreasing BrGap may help to restore the bottom metal back to internal winding.

Parameter Restrictions and Recommendations

  1. 1<=NT<=50

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

  3. Selection PassWrap=Yes makes the passivation layer conform to the conductor contour (see "Cross-sectional Views" Figure 1). Note that PassWrap=Yes makes passivation thickness vary: on the conductor top it equals H1-T, at the valley between the conductors (both sides and bottom) the passivation thickness is Hp. Models limit the width of this valley (gap between passivation dielectric walls) at 0.1 micron.

  4. To exclude passivation, set MRFSUB parameters Er1=1 and Tand1=0. Assign a reasonable value to H1 that well exceeds 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=1.

  6. Setting UPass=On-substrate implies that the inductor is located on a non-conducting lossy substrate, IsGndStrap is set to "No ground straps", IsHDL is set to "No HDL", the sum of H2 and H3 is equal to the substrate height, and the material characteristics of layer H2 are identical to those of layer H3. Passivation switch PassWrap can be set to any desirable option.

  7. FMCIND2 does not allow you to use frequency-dependent model material parameter Cond_HDL and substrate material parameters Er1, Er2, Er3, Tand1, Tand2, Tand3, and Sig3.

  8. Certain combinations of NT and UExit are not allowed. This model does not allow the bridge to cross port 1, and changes the bridge exit to avoid this crossing (a warning is issued and the layout displays the actual bridge position). If NT=n (n is an integer) then Near Exit is prohibited; if you set UExit=Near Exit, the model resolves this conflict by pointing the bridge "south" between Near Exit and Far Exit (Far Exit may add excessive bridge length). If NT=n+1/2, then Far Exit is prohibited; if you set UExit=Far Exit then this model overrides and sets UExit=Near Exit.

Implementation Details

The spiral is treated as a set of concentric rings connected in series with each other and with a capacitively coupled strip underpass. The problem is solved as an axisymmetric 2D layout of interacting lossy thick metal traces sitting atop an insulation layer. The underpass is treated as a lossy thick transmission line running inside an insulation layer (alternatively, the underpass may be placed atop a substrate). The entire stackup has a conducting substrate underneath an insulating layer.

Lateral grounds are optional and are implemented as PEC infinitely thin rings (the ring shape is mandatory due to the axial symmetry of layout); you can place them arbitrarily within the insulation layer).

The Passivation layer can be either flat or conformal.

The 2D Finite Element Method (FEM) in conjunction with the quasi-static problem formulation provides a very stable solution for RFICs most common dimensions and frequency range. An FEM engine is partially based on a FEMM solver ([1]); it comprises the mesher ([1]) and two independent solvers: an electrical solver and a magnetic solver. The mesher generates 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 an overly dense mesh. This commonly occurs 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 a conductor cross-section (conforming passivation). Note that this 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 setting of UseAFS, the model caches either model Y-matrices at each sweep frequency (UseAFS=NoAFS) or frequency-dependent approximation (UseAFS=UseAFS).

If UseAFS=NoAFS then all frequencies in a sweep are part of cache search criteria. This means that 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 is added to the sweep) this model runs full-blown simulation.

When UseAFS=UseAFS this model includes first and last (extreme) sweep frequencies along with 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 the need to run AFS again. However, any sweep with even one extreme frequency distinct from those in the cache demands 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. The 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: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 take up to 100 MB of disk space, so make sure that your project 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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