Extracting and Simulating Equivalent Circuit Models

Extracting and Simulating Equivalent Circuit Models
No Boundaries workshop Title page – Extracting and Simulating Equivalent Circuit Models. Due to the fast growth of the wireless communications market the use of passive components has increased. The electromagnetic simulation of these components has become an important issue because of the high operating frequencies, small size and low power consumption. The component manufacturers have to provide not only S-parameter data, but also lumped equivalent circuit models. This presentation describes electromagnetic and electrical modeling methods for passive components using Ansoft HFSS, Ensemble and Harmonica simulators present within the Serenade Design Environment. The S-parameters of passive components will be extracted using Ansoft HFSS and Ensemble. The equivalent circuit will be generated from the extracted S-parameters using Harmonica’s optimization engine on a proposed circuit topology. Peter Shin and Harpreet Randhawa, Application Engineers

Ansoft Serenade Design Environment
The Serenade Design Environment consists of Ansoft HFSS, Ensemble, Spicelink and Serenade Desktop.

Ansoft Electormagnetics
Divide and Conquer the Components! Rewrite Maxwell’s equations for the digital computer Break geometry into pieces Write “Discrete” Maxwell’s equations on/in each piece Solve and visualize the physics Extract fields, s-parameters, currents, and equivalent circuits

Ansoft Serenade Desktop
Circuit & System Simulation Harmonica : Linear & Nonlinear Circuit Simulator Amplifiers : LNA, PA, Driver, AGC, Buffer Mixers : Frequency converters (active or passive) RF Source : Oscillators, Synthesizers Modulators Front End Components: Limiters, Switches, Duplexers, Filters Symphony : System Simulator Transmitters, Receivers, Modulators, Demodulators for wire & wireless CDMA, TDMA, FDMA The Serenade Desktop is an environment that serves as the interface to both the Symphony and Harmonica simulation engines as well as their respective utilities.

Presentation Outline MCM Overview MCM Helical Inductor S-parameter Extraction Equivalent Circuit Model Generation RFIC / MMIC Overview Spiral Inductor Overview RFIC Spiral Inductor S-parameter Extraction Building UDM The MCM helical inductor will be presented first, followed by RFIC (Radio Frequency Integrated Circuit) spiral inductor structures. Measurement methods and their correlation to simulated data will also be discussed.

MCM Overview Multi-Chip-Module (MCM) technology appeared at IBM, NEC and Mitsubishi around 1980’s Several types such as MCM-C (ceramic based), MCM-D (silicon based), MCM-L Capacitors and inductors can be integrated into the multilayer structure reducing both cost and size MCM technology facilitates direct chip attach A brief overview of MCM (Multi-Chip-Module) technology is discussed. Multichip Modules combine many components in a single package. This design approach significantly improves performance parameters such as speed, heat dissipation, power management and size. The result is a high performance, cost-effective module that performs the function of several modules. DuPont makes thick film materials for ceramic Multichip Modules (MCM-C) that outperform printed wiring board (MCM-L) and thick film (MCM-D) approaches Reference:

MCM Overview – Technology Low Temperature Co-fired Ceramic (LTCC) technology meets the requirements for MCM-C design Benefits/Features of LTCC Hi Q/ Low Loss / Low T Allows direct attach of Si and GaAs IC’s Ag & Au based conductors Enhances performance, decreases cost, reduces size and improves reliability Ceramic interconnect technology has long been the interconnect technology of choice in military and aerospace applications where size and performance are critical. Ceramic solutions are also widely used in high-volume automotive and telecommunications applications where cost/performance tradeoffs are closely examined. Recent studies have shown that DuPont Low Temperature Co-fired Ceramic (LTCC) Green Tape™ has lower attenuation than conventional laminate materials such as FR-4 over the frequency range GHz. Use of silver conductors, and the capability for integrating inductors, capacitors and resistors into the substrate, provide further options for size and cost reductions. Reference:

Design of Helical Inductor using Serenade Design Environment
Ansoft Serenade Design Environment Helical Inductor Design Design of Helical Inductor using Serenade Design Environment A design of a 2 turn Helical Inductor is carried out using Ensemble and Harmonica simulators present within the Serenade Design Environment. A 2.5D edge port model of the helical inductor is created and simulated using Ensemble and the s-parameters are generated and normalized to 50 Ohm. The s-parameters are then imported into Harmonica and the equivalent circuit model is optimized to the s-parameters to extract the equivalent circuit model parameters.

Helical Inductor Design – Substrate type Substrate material used is a 20-layer LTCC 951 Green TapeTM by DuPont 951AX type is selected with the following properties: Layer thickness (fired) = 8.5 mils Dielectric constant = 7.8 Loss Tangent = Metal type = Silver (Ag) The substrate material being used is a 20-layer LTCC 951 Green Tape by DuPont. This material is available in three different thickness (fired) namely 951AT (3.8mil), 951A2 (5.5mil) and 951AX (8.5mil). The 951AX is selected for this design and it has the following properties: Layer Thickness (fired) = 8.5mils Dielectric constant = 7.8 Loss Tangent = (0.15%) Metal type = Silver (Ag) High Q and low temperature coefficient of resonant frequency are features of many ceramic materials which contribute to enhanced performance. The low thermal expansion of ceramics (TCE) contributes to minimum variations in performance with changes in temperature. The excellent TCE match to Si, GaAs and SiGe facilitates bare chip attach.

Ansoft Ensemble Helical Inductor Design – Setup procedure
Ensemble project is setup using these steps: Stack up Layers A 2.5D Edge Port model is created in Ensemble. Stack up layers: Trace 4 Dielectric (8.5mil, 1 layer) Trace 3 Trace 2 Trace 1 Dielectric (25.5mil, 3 layers) Ground plane ( 0 reference) Cross-sectional view

Ansoft Ensemble Helical Inductor Design – Create a model in 2D Modeler
Overall Dimensions = (66 x 76 x 51) mils Metal Width = 13 mils Number of Turns = 2 Via diameter = 8 mils Dielectric thickness: 8.5 mils Distance above the ground plane = 25.5 mils Why Helical inductors? Helical inductors exhibit superior performance in terms of area, Q factor and inductance than the conventional planar spiral inductors for the same number of turns. Port 1 The diagram of a 2 turn helical inductor is shown above and as it can be seen that helical type has only half a turn on each layer. This configuration occupies less area than that of a conventional planar inductor since the turn is expanded vertically instead of horizontally. For the same numbers of turns and dimensions, the helical inductor shows superior performance in terms of area, quality factor (Q) and inductance than the conventional planar inductor. The overall dimensions of the 2-turn helical inductor are 66 x 76 x 51 mils. Conductor width is 13 mils and the via diameter is 8mils. Reference: Sutono A., Pham A., Lasker J., Smith W. R., “ Development of Three Dimensional Ceramic-Based Inductors for Hybrid RF/Microwave Applications,” IEEE Radio Frequency Integrated Circuits Symposium

Ansoft Ensemble Helical Inductor Design – Simulation
Frequency is swept from 100Mhz to 6Ghz using a fixed mesh at 6Ghz and the S-parameters are normalized to 50 The frequency is swept from 100Mhz to 6Ghz in steps of 20Mhz. The helical inductor is simulated using a fixed mesh at 6Ghz. The S-parameters are normalized to 50 ohm and are exported as Serenade (.flp) format. The port impedance, as the frequency is swept from 100Mhz to 6Ghz, varies from approx. 93 to 96.5 ohms.

Ansoft Ensemble Helical Inductor Design – Post Processing
Resonant Frequency = 3.64Ghz The plot shown above is the Imaginary part of Impedance showing the resonant frequency at 3.64Ghz.

Ansoft Ensemble Helical Inductor Design – Exporting S-parameters
Export S-parameters into Harmonica for the equivalent circuit model extraction using optimization Using the export feature in Ensemble, the normalized s-parameters are exported in Serenade format. An equivalent circuit model of the helical inductor will be created and optimized to the s-parameters exported from Ensemble.

Ansoft Harmonica Helical Inductor Design – Q of the Inductor
Ensemble S-parameters are read into Harmonica using a 1-Port black box and Q of the helical inductor is plotted. Qmax  102 at 1.62Ghz The 1 port circuit shown above reads in s-parameters using a black box in Harmonica and the Q of the helical inductor is plotted. This plot is created using equation feature within Harmonica report editor. The Q is calculated using the following equation: Q = Im(Z11) / Re( Z11) The maximum Q of the inductor is 102 at 1.62Ghz.

Ansoft Harmonica Helical Inductor Design – Equivalent circuit model
Cc = Coupling Capacitance Simplify the model by combining Cs // Cc = C The equivalent circuit model for the 1-port helical inductor is shown. The model consists of an ideal inductor L in series with a series resistor Rs and the following elements: Rp - Cs – substrate capacitance Cc – coupling capacitance The Cs is parallel to Cc and is combined to get C. The simplified circuit is also shown. Cs = Substrate Capacitance

Ansoft Harmonica Helical Inductor Design – Optimization Setup
1nH Values are initially guessed and constrained for optimizing 5pF 100K  5  Initially the values are guessed and constrained for optimization and are shown below: C :?0.1pf 5pf 5PF? L :?1nh 1nh 20NH? Rp :?1KOH 100KOH 100KOH? Rs :?0.3OH 50OH 10OH? The optimization is setup to optimize the equivalent circuit model to s-parameters.

Ansoft Harmonica Helical Inductor Design – Plot of S11
EM Simulation Our goal is to optimize the equivalent circuit model to EM simulation results in order to extract the equivalent circuit parameters. Based on initial guess, S11 of the circuit is plotted versus the s-parameters obtained from Ensemble. Our goal is to optimize the equivalent circuit s-parameters to match the Ensemble S-parameters. This will accomplish our objective of extracting the equivalent circuit model. Equivalent Circuit Model

Ansoft Harmonica Helical Inductor Design – Optimization results
The Random type optimization is ran with approximately 1000 iterations or until no better solution can be found and smith chart plot is shown as the circuit is being optimized. Random optimization is performed With 1000 iterations and it the optimization goals are achieved

Ansoft Harmonica Helical Inductor Design – Optimized values are shown
6.16nH 0.30pF 86.8K  0.45  The circuit is optimized and the optimized values are shown: C :?0.1pf pf 5PF? L :?1nh nh 20NH? Rp :?1KOH KOH 100KOH? Rs :?0.3OH OH 10OH? As it can be seen from the smith plot, the s-parameters of the equivalent circuit model and the ensemble results are in excellent agreement.

Mid - Summary MCM and LTCC substrate technology was discussed Helical Inductor model using Ensemble was created and simulated Results from Ensemble were imported into Harmonica using S-parameters and Equivalent Circuit Model was extracted Multi-layer capabilities of LTCC and MCM are demonstrated and a helical inductor is designed using Ensemble and its equivalent circuit is extracted using Harmonica. The inductance of the equivalent model is approximately 6.16nH and the resonant frequency is 3.68Ghz which are in good agreement with Ensemble results.

Design of a RFIC Spiral Inductor using Serenade Design Environment
Ansoft Serenade Design Environment Spiral Inductor Design Design of a RFIC Spiral Inductor using Serenade Design Environment A design of a RFIC spiral inductor is carried out using HFSS and Harmonica simulators present within the Serenade Design Environment. A 3D model of the spiral inductor is created and simulated using HFSS and the s-parameters are generated. The s-parameters are then imported into Harmonica and the equivalent circuit model is optimized to the s-parameters to extract the equivalent circuit model parameters.

RFIC Overview Radio Frequency Integrated Circuit Lossy substrate Lower Frequency range : below 5GHz High density circuits Cheap and widely used for Commercial Applications Technologies for RFICs Cap / Thin film resistors / Spiral inductors Silicon MOSFET / BJT / diode Larger diameter wafer ( inches) A brief overview of RFIC is discussed. There are something differences between RFIC and MMIC. The difference are type of the substrate, frequency range, density and applications. In this presentation, we will discuss about RFIC inductor.

MMIC Overview Monolithic Microwave Integrated Circuit Lossless substrate Higher Frequency : from 1GHz to 100GHz Low density circuits Expensive and widely used for Military Applications Technologies for MMICs MIM cap / Thin film resistors / Spiral inductors GaAs MESFET / HEMT / HBT Silicon bipolar / Silicon-germanium HBT Indium phosphide HEMT / HBT IMPAATT, Gunn and Schottky diodes Smaller diameter wafers (4-6 inches) A brief overview of MMIC is discussed.

RFIC / MMIC Inductor Type - Ribbon Inductor - Loop Inductor  There are four types in RFIC/MMIC inductor. That are ribbon, loop, meandered track and spiral inductor. We will discuss about the spiral inductor type. - Meandered Track Inductor - Spiral Inductor

Spiral Inductor Equivalent Circuits  - GaAs MMIC Spiral Inductor Ls : Series inductance of spiral Rs : Series resistance of spiral L1 : Series inductance of fed L2 : Series inductance of fed C1 : Series capacitance Cg : Capacitance of GaAs substrate Cg Cs C1 L2 L1 Ls Rs Cs Cox Rsi Ls Csi Rs - Silicon RFIC Spiral Inductor Cs : Series capacitance of spiral and underpass Ls : Series inductance of spiral and underpass Rs : Series resistance of spiral and underpass Cox : Oxide capacitance Rsi : Resistance of silicon substrate Csi : Capacitance of silicon substrate The equivalent circuit model for the spiral inductor are shown.

Spiral Inductor Design – What are the considered? Inductance Quality Factor Self-Resonance Frequency Design Goal Outer Dimension Metal Thickness & Metal Width Turn Spacing & Number of Turns Substrate & Oxide Thickness Parameter In spiral inductor design, inductance , quality factor and self resonance frequency have to consider as the goal. And outer dimension, metal thickness & width, turn spacing & number of turns and substrate & oxide thickness will be used for design parameters. Furthermore, skin depth and substrate resistivity field excitation have to consider for the simulation accuracy. Skin Depth of Conductor Substrate Resistivity Field Excitation (Port) Accuracy

Spiral Inductor Design – Procedure HFSS C / C++ 3D Model Building UDM Setup Material Harmonica Setup Boundary/Port Create Symbol for UDM Setup Solution Create Schematics The simulation procedure is as follow. RFIC spiral Inductor model using HFSS was created and simulated. Results from HFSS were imported into Harmonica using S-parameters and Equivalent Circuit Model was extracted. Solve Optimization S, Y parameter Equivalent Circuit

S-parameter Extracting of a RFIC Spiral Inductor
Ansoft HFSS Spiral Inductor Design S-parameter Extracting of a RFIC Spiral Inductor Title page

Ansoft HFSS Spiral Inductor Design – 3D Modeler

Ansoft HFSS Spiral Inductor Design – Library Macro
Library Macro allows the user to create the geometries automatically

Ansoft HFSS Spiral Inductor Design – Macro
A macro is a series of commands that are grouped such that they can be executed at once, just like a mini-program within HFSS. User change the dimension using Macro Wizard

Ansoft HFSS Spiral Inductor Design – Create a Model in 3D Modeler
Outer Dimension : 300um Metal Thickness : 1um Metal Width : 13um Turn spacing : 7um Number of Turns : 7 Oxide Thickness : 4.5um Silicon Substrate height : 600um

Ansoft HFSS Spiral Inductor Design – Macro Live Demonstration

Ansoft HFSS Spiral Inductor Design – Setup Material(1)
3D objects get material parameters Materials are valid in interior region of object No fields need be computed inside very good conductors (metals) Some possible materials Air, Vacuum Perfectly-conducting metal Non-perfectly-conducting metal Dielectrics, any permittivity, any conductivity Magnetic materials, any permeability, any magnetic losses Anisotropic materials Thin-film resistors, Bulk resistors Ferrites

Ansoft HFSS Spiral Inductor Design – Setup Material(2) Silicon Dioxide
Lossless Dielectric r = 4 Metalization : Aluminum Good Conductor Conductivity : 3.8e+007 S/m Solve Metal Inside Option Skin Depth mesh be requested Silicon Substrate Lossy Dielectric r = 11.9 R=200·Cm(Rsistivity) Conductivity =1/R = 0.5 S/m

Ansoft HFSS Spiral Inductor Design – Setup Boundaries/Sources(1)
Perfect E Perfect H/Natural Finite Conductivity Impedance Radiation Symmetry Perfect H Master, Slave Lumped RLC Perfectly-Matched Layer(PML)

Ansoft HFSS Spiral Inductor Design – Setup Boundaries/Sources(2) Port
Wave port Lumped Gap Source Incident wave Cartesian Spherical Voltage drop Current Magnetic bias Uniform Non-uniform

Ansoft HFSS Spiral Inductor Design – Setup Lumped Gap Source G S
Internal Lumped Gap source Port Port Impedance : 50 Ohm Good agreement with Air coplanar probe station G S Port Air coplanar probe Lumped Gap Source

Ansoft HFSS Spiral Inductor Design – Setup Boundaries
Air : Radiation Boundaries Outer : Perfect Electric Conductor Radiation Boundaries PEC

Ansoft HFSS Spiral Inductor Design – Setup Solution

Ansoft HFSS Spiral Inductor Design – Adaptive Solution

Ansoft HFSS Spiral Inductor Design – Skin Depth Skin Depth
The distance  through which the amplitude of a traveling plane wave decreases by a factor of or 0.386 Skin Depth of Various Materials Material (S/m) @60Hz @1GHz Silver 6.1e+7 8.32mm 2.04  m Copper 5.8e+7 8.53mm 2.09 m Gold 4.1e+7 10.15mm 2.49 m Aluminum 3.8e+7 10.54mm 1.83m

Ansoft HFSS Spiral Inductor Design – Skin Depth Meshing(Manual)
Number of Meshes Initial Meshes : 7650 Manual Meshes : (after Skin Depth Mesh) Adaptive Meshes : (after 6 passes)

Ansoft HFSS Spiral Inductor Design – Solve(1) ZERO_ORDER=1
Electrically Small Structure Linear Basic Function Default : 0 LAMBDA_REFINE_TARGET Seeding Wavelength Target Value : 0.05 Default : 0.25

Number of tetrahedra vs. Pass
Ansoft HFSS Spiral Inductor Design – Solve(2) Convergency (ZERO_ORDER=1) Number of tetrahedra vs. Pass Maximum Delta s vs. Pass Maximum Delta s = Number of tetrahedra vs. Pass Maximum Delta s vs. Pass

Ansoft HFSS Spiral Inductor Design – Solve(3)
Convergency (ZERO_ORDER=1) S-parameter vs. pass(magnitude,phase, real, imaginary) Zpi vs. pass Gamma vs. pass S11 |S11| |S21| S21 S-parameter(Magnitude) vs. Pass S-parameter(Phase) vs. Pass

Ansoft HFSS Spiral Inductor Design – Matrix Plot : S-parameter 500MHz
5.5GHz

Ansoft HFSS Spiral Inductor Design – Matrix Plot : Quality Factor

Ansoft HFSS Spiral Inductor Design – Post Process : Field

Ansoft HFSS Spiral Inductor Design – Post Process : Port Field

Simulation of a Equivalent Circuit Model
Ansoft Harmonica Spiral Inductor Design Simulation of a Equivalent Circuit Model

Ansoft Harmonica Spiral Inductor Design – Compiled User-Defined Models
Allow users to create custom models Linear, Nonlinear elements for Harmonica (Circuit UDMs) Functional, Electrical elements for Symphony (System UDMs) Model code compiled into a DLL Schematic symbol PDF documentation (optional)

Ansoft Harmonica Spiral Inductor Design – UDM process

Ansoft Harmonica Spiral Inductor Design – Linear Element UDM
Create Y-matrix based linear elements Full access to substrate and metalization Provide noise correlation matrix for active devices or let program compute it Model Input : Model Parameters Frequency, Temperature Substrate data (Optional) Model Output : Y matrix N matrix (optional)

Ansoft Harmonica Spiral Inductor Design – Nonlinear Element UDM
Create current-voltage based nonlinear elements DC IV curves supported Noise correlation matrix & flicker noise supported Model Input Model Parameters Voltage waveforms at each port Frequency(Tone 1), Temperature Flags for derivatives, noise, DC-IV Model Output : Current and Charge waveforms at each port Current and Charge derivative waveforms Noise matrix waveforms (Optional) DC IV data (Optional)

Ansoft Symphony Spiral Inductor Design – Functional Element UDM
Sources, I/Os, Probes Model Input (for I/Os and probes only) Model Parameters Input Signals Sampling Rate and Center Frequency State Variables (Option) Model Output (for I/Os and Sources only) Output Signals Sampling Rate (required for Sources) and Center Frequency

Ansoft Symphony Spiral Inductor Design – Electrical Element UDM
Model Input Model parameters Substrate parameters (optional) Analysis frequency Analysis temperature Model Output Y-parameter matrix Noise correlation matrix (optional)

Ansoft Harmonica Spiral Inductor Design – Create a UDM of the Spiral(1) Model Input Model Parameters : Cs, Ls, Rs, Cox, Rsi, Csi Frequency Model Output Y matrix Cs Cox Rsi Ls Csi Rs

Ansoft Harmonica Spiral Inductor Design – Create a UDM of the Spiral(2) #include "udm.h" #include <math.h> #define PI 4*atan(1.0) /* User Model function */ int UDM_DLL_EXPORT udmspFnc() { double *paramsPtr; double freq, Cs, Rs, Ls, Cox, Rsi, Csi; /* Get frequency value. */ freq = HudmGetFreq(); if (freq == 0.0) /* This model does not apply to DC analysis */ udmSendErrorMessage("udmsprFnc is not valid for DC analysis."); return (-1); } /* Pointer of parameter array. */ paramsPtr = HudmGetModelParams(); Cs = paramsPtr[0]; Rs = paramsPtr[1]; Ls = paramsPtr[2]; Cox = paramsPtr[3]; Rsi = paramsPtr[4]; Csi = paramsPtr[5]; Define State Variable User Model Function

Ansoft Harmonica Spiral Inductor Design – Create a UDM of the Spiral(3) ecomplex Ycs, Yrs, Yls, Ycox, Yrsi, Ycsi; Ycs.r = 0.0; Ycs.i = 2*PI*freq*Cs; Yrs.r = 1/Rs; Yrs.i = 0.0; Yls.r = 0.0; Yls.i = -(1/(2*PI*freq*Ls)); Ycox.r = 0.0; Ycox.i = 2*PI*freq*Cox; Yrsi.r = 1/Rsi; Yrsi.i = 0.0; Ycsi.r = 0.0; Ycsi.i = 2*PI*freq*Csi; ecomplex Y1, Yspiral, Ysi, Ysubstrate, Ytotal; double a, b, c, d; a = Yrs.r + Yls.r; b = Yrs.i + Yls.i; c = (Yrs.r * Yls.r) - (Yrs.i * Yls.i); d = (Yrs.i * Yls.r) +(Yrs.r * Yls.i); Y1.r = (a*c + b*d)/(a*a + b*b); Y1.i = (a*d - b*c)/(a*a + b*b); Yspiral.r = Ycs.r + Y1.r; Yspiral.i = Ycs.i + Y1.i; Ysi.r = Yrsi.r + Ycsi.r; Ysi.i = Yrsi.i + Ycsi.i; double e, f, g, h; e = Ysi.r + Ycox.r; f = Ysi.i + Ycox.i; g = (Ysi.r * Ycox.r) - (Ysi.i * Ycox.i); h = (Ysi.i * Ycox.r) + (Ysi.r * Ycox.i); Ysubstrate.r = (e*g + f*h)/(e*e + f*f); Ysubstrate.i = (e*h - f*g)/(e*e + f*f); Ytotal.r = Yspiral.r + Ysubstrate.r; Ytotal.i = Yspiral.i + Ysubstrate.i; User Model Function

Model Table Declaration
Ansoft Harmonica Spiral Inductor Design – Create a UDM of the Spiral(4) if ( HudmSetYmat(1, 1, Ytotal.r, Ytotal.i) != 0 || HudmSetYmat(1, 2, -Yspiral.r, -Yspiral.i) != 0 || HudmSetYmat(2, 1, -Yspiral.r, -Yspiral.i) != 0 || HudmSetYmat(2, 2, Ytotal.r, Ytotal.i) != 0 ) { udmSendErrorMessage("Set Y matrix error."); return (-1); } return (0); BEGIN_MODEL_TABLE LINEAR_MODEL ( "udmsp", udmspFnc, 2, SUBS_NOT_REQ, NO_NOISE_MAT, "Cs, Rs, Ls, Cox, Rsi, Csi" END_MODEL_TABLE Set Y matrix Model Table Declaration

Ansoft Harmonica Spiral Inductor Design – Create a Symbol for UDM
Creating a Symbol for UDM From the Draw menu, select “Create User Model Symbol”

Ansoft Harmonica Spiral Inductor Design – Create Schematics

Ansoft Harmonica Spiral Inductor Design – Optimization(S-parameter)

Ansoft Harmonica Spiral Inductor Design – Optimization(Quality Factor)

Ansoft Harmonica Spiral Inductor Design – Optimization Result
Equivalent Circuit Values Cs : 5.9nF, Ls : 8.5nH, Rs=11.8 Cox : 5.90pF Rsi : 1.68K, Csi=0.06pF Cs=5.9pF Ls=8.5nH Csi=0.06pF Rs=11.8 Cox=5.90pF Rsi=1.68K

Summary Helical Inductor model using Ensemble was created and simulated Results from Ensemble were imported into Harmonica using S-parameters and Equivalent Circuit Model was extracted RFIC Spiral Inductor model using HFSS was created and simulated Results from HFSS were imported into Harmonica using S-parameters and Equivalent Circuit Model was extracted

Reference Sutono A., Pham A., Lasker J., Smith W. R., “ Development of Three Dimensional Ceramic-Based Inductors for Hybrid RF/Microwave Applications,” IEEE Radio Frequency Integrated Circuits Symposium C.P.Yue et al., “Physical Modeling of Spiral Inductors on Silicon” IEEE Transactions on Electron Devices, VOL. 47, NO.3 MARCH 2000 Inder J. Bahl, “Improved Quality Factor Spiral Inductors on GaAs Substrates” IEEE Microwave and Guided wave letters, Vol.9, No.10 Octorber 1999

Extracting and Simulating Equivalent Circuit Models

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