# Ansoft HFSS Engineering Note Lumped RLC Elements in HFSS...

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Ansoft HFSS Engineering Note

Lumped RLC Elements in HFSS Version 8

In Ansoft’s High Frequency Structure Simulator (HFSS), a specified impedance boundary condition hasalways referred to field values because HFSS is a full-wave field simulator. You may wish to model aphysical lumped resistance (R), inductance (L), or capacitance (C) element that is connected to the field ordistributed model.

HFSS Version 8 enables you to specify any combination of parallel-connected lumped RLC elements onsurfaces in terms of circuit definition by using lumped RLC boundaries. A typical application is the simu-lation of a Monolit Microwave Integrated Circuit (MMIC), in which the lumped elements are representedby thin sheets.

HFSS Version 8’s fast and interpolating frequency sweep options support the frequency dependence of animpedance, which consists of either a lumped inductance or a lumped capacitance, with the use oflumped RLC elements. HFSS’s 3D Boundary Manager supports any combination of parallel-connectedRLC elements on a surface. To model serial-connected lumped elements, define two serial-connected sur-faces for the serial elements.

This engineering note explains the difference between field and lumped impedances and presentsapplications for both cases.

Engineering Note AP03-0201

Field and Lumped ImpedancesFigure 1 shows a thin, rectangular sheet on which a lumped impedance boundary condition will bedefined.

Figure 1: Thin rectangular sheet

where:• l is the length of the sheet• W is the width of the sheet• Et is the tangential component of the electric field on the impedance boundary surface• Ht is the tangential component of the magnetic field on the impedance boundary surface• I is the current flowing on the sheet• c is a closed curve surrounding the sheet• U is the voltage drop• δ is the thickness of the sheet

The definitions for the lumped and field impedances are:

The circuit quantities U and I can be expressed by the field quantities as:

ZlumpedUI----= Zfield

Et

Ht-----=

U Et

l dl Etl= = Ht

c° dc Htw I==

Page 2 Lumped RLC Elements in HFSS Version 8

Substituting the field quantities into the impedance definition yields:

Zfield is measured in ohms/square. It is also denoted by Zϕ.

The shape of a lumped impedance surface is not always rectangular. An arbitrarily shaped surface istransformed into a rectangular-shaped surface by defining the length of the main current flow, as shownin the following figure:

Figure 2: Transformation of an arbitrarily shaped surface to anequivalent rectangular-shaped surface

The width of the equivalent rectangular surface is:

where S is the area of the sheet.

The relationship between the lumped and field impedances is:

Define the length of the current flow in the 3D Boundary Manager. The area of the surface is calculatedautomatically.

ZlumpedUI----

Etl

Htw---------- Zfield

lw----= = =

Zfield Zlumpedwl----=

l

wSl---≅

Zlumped Zfieldl2

S----= Zfield Zlumped

S

l2

----=

Lumped RLC Elements in HFSS Version 8 Page 3

The parallel-connected RLC lumped elements are assigned to the selected surface (see Figure 3) using theuser-defined current path:

The frequency dependence is taken into account as:

where:• j is the imaginary unit,• ω is the angular frequency, 2πf

Figure 3: Parallel-connected lumped RLC elements assigned to a boundary surface

Rfield RS

l2

----= Lfield LS

l2

----= Cfield Cl2

S----=

1Zfield------------

1Rfield------------ j ωCfield

1ωLfield-----------------–

+=

1–

Page 4 Lumped RLC Elements in HFSS Version 8

Parallel Plate Waveguide Terminated with aParallel Lumped RLC CircuitIn the following example, a parallel plate waveguide is terminated by a parallel-connected RLC circuit, asshown in Figure 4.

Figure 4: Parallel plate waveguide terminated by parallel lumped RLC elementsR = 33.75 Ohms, L = 0.1 nH, C = 2.533 pF

The magnitude of S11 was calculated using HFSS’s new lumped element boundary feature. The problemhas an analytical solution. The magnitude of parameter S11 can be calculated as:

where:

and Zw = 377 Ohms

The field values are given by:

Figure 5 shows good agreement between the results calculated by the analytical method and the HFSSresults. HFSS results were calculated using the interpolating sweep method, a frequency sweep in whichsolved frequency points are chosen so that the entire solution lies within a specified error tolerance.Approximately 2000 tetrahedra were used and the solution time was approximately 7 1/2 minutes on aPentium/266MHz PC.

S11Z2 Zw–

Z2 Zw+------------------=

1Z2-----

1Rfield------------ j ωCfield

1ωLfield-----------------–

+=

Rfield Rwl----= Lfield L

wl----= Cfield C

lw----=

Lumped RLC Elements in HFSS Version 8 Page 5

Figure 5: The magnitude of S11 compared to the analytical solution

Parallel Plate Waveguide Terminated with aSerial Lumped RLC CircuitA parallel plate waveguide is terminated by a serial-connected RLC circuit, as shown in Figure 6. Thisconnection type can not be specified directly in HFSS using the new lumped RLC boundary interface; thesurface can be subdivided into three serial-connected subsurfaces as an approximation, assigning asingle R, a single L and a single C value to them. Using this method for this example will not provide areasonable approximation because the spatial distribution of the RLC elements plays an important role.(The next application shows an example where this technique is applicable.)

Figure 6: Parallel plate waveguide terminated by serial RLC elements.The field values are: Rs = 75 Ohms, Ls = 100 nH, Cs = 2.533fF

where:• Rs, Ls, and Cs are the serial connections• fF represents 10-15

Page 6 Lumped RLC Elements in HFSS Version 8

This example can be solved using Ansoft Optimetrics in combination with HFSS. The impedance bound-ary condition is used to define the serial load as a function of the frequency:

Because the HFSS 3D Boundary Manager’s lumped element interface was not used, the field values, orohms/square values, of the loads must be used. Three new parameters must be introduced in the 3DBoundary Manager, namely, Zre, Zim and f, where:

After setting up the nominal HFSS project using the discrete frequency sweep option, Optimetrics mustdefine the parameter frequency as f. Figure 7 shows good agreement between the HFSS results and theanalytical solution.

Figure 7: Magnitude of S11 compared to the analytical solution

Zload Rs j ωLs1

ωCs----------–

+=

Zre Rs= Zim ωLs1

ωCs----------–

=

Lumped RLC Elements in HFSS Version 8 Page 7

Microstrip Line with a Serial-Connected Lumped ResistorThe lumped RLC boundary feature is useful for simulating the following example of a microstrip line.The microstrip line, which has a 100-ohm lumped resistor connected throughout a gap of the strip, isshown below:

Figure 8: Microstrip line with a lumped resistor throughout a gap

The HFSS model is shown below:

Figure 9: HFSS model of a microstrip line with a lumped resistor throughout a gap

The surface for the lumped resistor is defined to be as wide as the strip. If the width of the lumpedresistor surface was defined as very thin, an additional inductance would be introduced to the system.(The length of the surface does not play an important role.) Figure 10 shows the frequency response ofthe magnitude of S11. The HFSS results agree well with the analytical results obtained using Ansoft’sSerenade design environment.

Lumped resistorsurface

Port 1Port 2

Page 8 Lumped RLC Elements in HFSS Version 8

Figure 10: Magnitude of S11 of a microstrip line with a lumped resistor throughout a gap

Microstrip Line with a Serial-Connected Lumped LC Resonant CircuitThe following example is a microstrip line with a lumped, serial-connected resonant circuit connectedthroughout a gap of the strip. It is shown below:

Figure 11: Microstrip line with a a lumped LC circuit throughout a gapL = 10 nH, C = 3.96 pF

Lumped RLC Elements in HFSS Version 8 Page 9

The HFSS model is shown below:

Figure 12: HFSS model of a microstrip line with a lumped LC circuit throughout a gap

The lumped elements’ surfaces are defined to be equal to the strip’s width. Because the length of the sur-face does not play an important role, the serial-connected LC circuit can be modeled with two serial-con-nected surfaces, as shown in Figure 12. The inductance is assigned to one surface and the capacitance isassigned to the other surface. Figure 13 shows the frequency response of the magnitude of S11. The HFSSresults agree well with the analytical results obtained using Ansoft’s Serenade design environment.

Figure 13: The magnitude of S11 of a microstrip line with a lumped LC circuit throughout a gap

Lumped L

Lumped C

Page 10 Lumped RLC Elements in HFSS Version 8

Thick-film Chip Resistor Inserted in a Microstrip LineThe next example is a thick-film chip resistor inserted in a microstrip (see Figure 14). The equivalent cir-cuit of the chip resistor is measured in the absence of the microstrip line.

Figure 14: Thick-film resistor inserted in a microstrip linea = 6.578 mm, h = 0.508 mm, w = 1.518 mm, wr = 1.214 mm, εr=2.2, εrc=9.6

The chip resistor is replaced by its equivalent circuit distributed on the serial-connected surfaces, asshown in Figure 15. Note that the serial connection of surfaces possessing lumped element definition is anapproximation.

Figure 15: Thick-film chip resistor replaced by lumped circuit elementsand inserted back in a microstrip line

R = 10,820 Ω, L = 0.55 nH, C=24 fF

Lumped RLC Elements in HFSS Version 8 Page 11

Figure 16 shows the magnitude of S11 for different R values and compares them to measured values. TheHFSS results agree with the measured curves. The results were calculated by performing an interpolatingsweep. About 9446 tetrahedra were used and the solution time was approximately 13 minutes on a Pen-tium/266MHz PC.

Figure 16: Magnitude of S11 of the microstrip line

Figure 16 illustrates that the discrepancy between the field simulation results and the measurementsincrease with frequency. This is a result of the presence of parasitic capacitances and inductances intro-duced by the small air gap and impedance surfaces.

Page 12 Lumped RLC Elements in HFSS Version 8

The agreement is excellent in the lower frequency range, as shown in the following figure:

Figure 17: Magnitude of S11 of the microstrip line

ConclusionsHFSS Lumped RLC elements are useful for inserting lumped circuits into the field model, especially inthe case of MMIC structures. The usage of lumped elements reduces the problem size by replacing com-plex sub-structures with an equivalent circuit model. Both the fast frequency sweep and the interpolativefrequency sweep support lumped RLC elements.

Lumped RLC Elements in HFSS Version 8 Page 13

References[1] HFSS Version 8 Online Documentation. Ansoft Corporation, 2001.

[2] K. Guillouard, M. Wong, V.F. Hanna and J. Citerne, “A New Global Finite ElementAnalysis of Microwave Circuits Including Lumped Elements,” IEEE Trans. MTT, Vol. 44, No. 12, Decem-ber 1996, pp. 2587-2594.

[3] R. Gillard, S. Daugnet and J. Citerne, “Correction Procedures for the Numerical Parasitic ElementsAssociated with Lumped Elements in Global Electromagnetic Simulators,” IEEE Trans. MTT, Vol. 46, No.9, September 1998, pp. 1298-1306.

[4] J.A. Pedra, F. Alimenti, P. Mezzanotte, L. Roselli and R. Sorrentino, “A New Algorithm for the Incorpo-ration of Arbitrary Linear Lumped Networks into FDTD Simulators,” IEEE Trans. MTT, Vol. 47, No. 6,June 1999, pp. 943-949.

[5] L. Zhu and K.Wu, “Accurate Circuit Model of Interdigital Capacitor and Its Application to Design ofNew Quasi-Lumped Miniaturized Filters with Suppression of Harmonic Resonance,” IEEE Trans. MTT,Vol. 48, No. 3, March 2000, pp. 347-356.

[6] K. Hettak, N. Dib, A.F. Sheta and S. Toutain, “A Class of Novel Uniplanar Series Resonators and TheirImplementation in Original Applications,” IEEE Trans. MTT, Vol. 46, No. 9, September 1998, pp. 1270-1276.

Page 14 Lumped RLC Elements in HFSS Version 8

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