accurate frequency domain modeling of ltcc solid-gridded plane structures

5. CONCLUSION

In this study, an optimization approach is used to synthesize asteerable array pattern with non-uniform spacing. Not only toovercome the scanning problem of a non-uniform linear arraypattern, but also to reduce the side-lobe level, the Gauss–Newtonmethod is applied to adjust the locations of array elements. Resultsshow that the proposed method for array pattern synthesis is ableto significantly reduce the first side-lobe level without patterndistortion of a steerable linear array.

ACKNOWLEDGMENTS

This work was supported by the Electronics and Telecommunica-tion Research Institute research grants in 2002.

REFERENCES

1. R.F. Harrington, Sidelobe reduction by nonuniform element spacing,IRE Trans Antennas Propagat (1961), 187–192.

2. F. Hodjat and S.A. Hovanessian, Nonuniformly spaced linear and planararray antennas for sidelobe reduction, IEEE Trans Antennas PropagatAP-26 (1978), 198–204.

3. R.E. Wiley, Space tapering of linear and planar arrays, IRE TransAntennas Propagat (1962), 369–377.

4. C.-C. Yu, Sidelobe reduction of asymmetric linear array by spacingperturbation, Electron Letts 33 (1997), 730–732.

5. J.-S.R. Jang, C.-T. Sun, and E. Mizutani, Neuro-fuzzy and soft com-puting, Prentice-Hall, Inc., 1997.

6. P.Y. Zhou and M.A. Ingram, Pattern synthesis for arbitrary arrays usingan adaptive array method, IEEE Trans Antennas Propagat 47 (1999),862–869.

© 2003 Wiley Periodicals, Inc.

ACCURATE FREQUENCY DOMAINMODELING OF LTCC SOLID-GRIDDEDPLANE STRUCTURES

Guang Chen,1 Andrej Jancura,2 Kathleen L. Virga,1

Gert Winkler,2 and John L. Prince1

1 CEPRECE Dept.University of ArizonaTucson AZ 857212 Technische Universitat IlmenauFachgebiet KTEPostfach 10056598684 Ilmenau, Germany

Received 5 September 2002

ABSTRACT: This paper presents a modeling approach for solid-grid-ded power-ground plane structures in low-temperature co-fired ceramic(LTCC) modules. The approach uses a two-dimensional transmissionline approach and uses a new physical-layout-based cell-dividing model-ing method to expedite the simulation process. The approach is verified bycomparing the S11 parameters obtained from simulation and measurement.© 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 367–371,2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10766

Key words: LTCC circuits; power/ground structure simulation; solid-gridded plane pair modeling; 2D transmission line model

1. INTRODUCTION

Low-temperature co-fired ceramic (LTCC) technology offers de-signers the possibility to realize low-cost electronic modules in awide frequency range, up to several GHz, and to integrate passivecomponents, like embedded resistors, inductors or capacitors, onseveral layers. This technology also opens a number of possibili-ties for realization of different connecting structures and multi-transmission lines.

One interesting class of geometries is gridded planes utilized inLTCC power-ground structures, as shown in Figure 1. For LTCCcircuits, solid-gridded or gridded plane pairs are used if one ormore of power/ground planes are embedded within the LTCCdielectric layers. The LTCC fabrication process causes this limi-tation. A higher percentage metalization inhibits the lamination ofstacked layers and causes edge bending, the metalized area of theembedded layers must be less than 70% of the overall layout area,and the metalization should also be evenly distributed over the areain order to minimize the fabrication defects during the LTCCsintering processes [1]. Therefore, gridded structures are used forembedded densely metalized areas, such as embedded power-ground structures.

TABLE 2 Comparison of Several Linear Array Arrangements

Items Array Geometry Case 1 Case 2 Case 3 Case 4 Case 5 Case 6

Maximum radiationangle, �0

�30° Maximum sidelobe level �13.08 dB �12.35 dB �16.55 dB �13.16 dB �11.9 dB �16.6 dB3-dB Mainlobe beamwidth 9.04° 9.09° 9.27° 6.90° 6.94° 7.03°

�10° Maximum sidelobe level �13.08 dB �17.45 dB �16.55 dB �13.16 dB �17.39 dB �16.6 dB3-dB Mainlobe beamwidth 7.94° 7.98° 8.13° 6.06° 6.09° 6.17°

0° Maximum sidelobe level �13.08 dB �17.45 dB �16.55 dB �13.16 dB �17.39 dB �16.6 dB3-dB Mainlobe beamwidth 7.82° 7.87° 8.0° 5.97° 6.0° 6.09°



MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 36, No. 5, March 5 2003 367

The main task of power-ground plane structures is to deliverclean power for circuits. The design process of power-groundstructures must consider the highest operating frequency, supplyvoltage, amplitude of currents flowing in the structure, layoutgeometry, and material properties. The materials together with thelayout geometry define specific properties of the structure, such asoverall impedance and resonant frequencies, while the operatingfrequency, supply voltage, and current amplitudes are parametersused for functionality analysis. When the electrical wavelength ofthe operating frequency is comparable to the layout dimensions orthe distance between contact points used for delivering power, thepower/ground structure should be considered as a system withdistributed parameters.

The electric characteristics of a gridded plane structure aremore complex than those of a solid plane structure. A griddedstructure has lower capacitance and higher inductance per unitarea. When the grid density is close to the operating wavelength,radiation in the power distribution network can no longer beneglected. The measured S11 data of a 40 mm � 40 mm solidplane pair structure and a solid-gridded ground plane structurewith a 2.5-mm trace pitch are presented in Figure 2. Figure 2shows some differences in the S11 of the solid and gridded groundplane structures. The resonant frequencies of the solid-griddedstructure are slightly lower than those for the solid plane pair. Thesolid-gridded structure also shows higher loss due to coupling andradiation at higher frequencies. This figure shows that models

developed specifically for gridded ground plane structures areneeded for accurate results.

Previous research regarding the gridded power-ground refer-ence planes primarily focused on the interference between griddedplanes and other structures. The signal propagation and signalcoupling behavior between transmission lines and perforatedgrounds was investigated in [2] and [3]. In [4], the inductance inthe presence of three-dimensional mesh structures used for on-chippower supplies was analyzed and ways of designing a power/ground mesh that reduce inductance were shown.

This paper presents a method to efficiently and accuratelymodel the resonant frequency behavior of gridded ground planestructures. Section 2 discusses a new modeling method for solid-gridded plane pair structures that is derived from a two-dimen-sional transmission line (2D TL) approach originally developed forsolid plane pairs [5]. The new approach incorporates a physical-layout-based cell-dividing method to expedite the modeling pro-cess for solid-gridded plane pair structures. This approach is usedto simulate the frequency characteristics of a benchmark solid-gridded plane structure and the simulation results are verified withcomparisons to measured results in section 3. Conclusions arepresented in section 4.

2. MODELING METHODOLOGY

The frequency domain characteristics of solid or gridded planestructures can be analyzed using full-wave numerical simulators,such as those based upon the method of moments, the finitedifference time domain method, or the finite-element method.Full-wave methods have been used to predict performance forarbitrary geometries over a wide frequency range for solid-planestructures [7, 8]. However, accurate solutions using such methodsoften require long simulation times and extensive computationalcapabilities. Full-wave models of gridded structures typically re-quire a mesh that is finer than what is needed for solid-plane pairs.

The frequency domain characteristics can also be simulatedwith the partial equivalent electrical circuit method (PEEC) [5, 9].In this approach the geometry is divided into small equivalentcircuit cells. Basic cell models incorporate mutual capacitance,inductance, resistance, dielectric loss, radiation loss, and skineffects. One advantage of the PEEC method over alternate numer-ical approaches is the capability to reduce the order of circuitdescription equations and to derive simple SPICE-compatible cellmodels [5, 6]. For gridded planes, a mismatch between the PEECcell size and the plane gridding leads to non-uniformity in thePEEC cell layout. This, along with the geometry of the gridded

Figure 1 Meshed plane structure

Figure 2 Measured results for 40 mm � 40 mm solid-solid and solid-gridded plane structures

Figure 3 Cell dividing method

368 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 36, No. 5, March 5 2003

plane structure, makes it very difficult to define a suitable PEEC-based equivalent circuit.

An efficient 2D-TL-based approach for the analysis of solid-plane pairs was presented in [5] and verified in [6]. In this ap-proach, the entire solid plane pair was divided into successivesquare resistive, inductive, and capacitive cells, each with the samesize. A slightly different pitch offset was used for the capacitivecells. The effective values of R, L and C were obtained from staticfield calculations of the respective unit cells. Transmission lineswere utilized to generate a 2-D mesh that represents the entireplane. The characteristic impedances and propagation constants ofthe transmission lines were computed using the calculated R, L andC values. For a good approximation of the distributed elements, itwas recommended that the size of discretized cells be about 10times smaller than the wavelength of the highest frequency ofinterest. It was also suggested that this approach may be used forgridded ground plane structures if the static capacitance calcula-tion incorporates the effects of fringing fields, but neither paperprovides details or examples.

The new work presented in this paper utilizes a cell-dividingmethod that is tailored for solid-gridded plane structures. In thisapproach, the solid-gridded plane structure is divided into unitcells according to the physical mesh of the gridded plane structure.Three types of cells, a center cell, an edge cell, and a corner cell,as shown in Figure 3, are utilized.

The transmission line equivalent circuit models for the unitcells are built using microstrip elements defined in Agilent Ad-vanced Design System (ADS) [11]. For example, the equivalentmodel for a center cell consists of four microstrip lines and amicrostrip “mcross” element at the intersection of traces. The

parameters of the transmission line elements used in the modelsare only defined by the physical dimensions of the cells. Thecalculated S-parameter matrices of the unit cell models are used toimprove the accuracy of the simulation results, especially in thehigher frequency range. The calculated S-matrix files from ADSare considered to be more accurate than lumped element counter-parts in describing the frequency characteristics of modeled cellsbecause the frequency dependent effects, such as dispersion, skineffects and dielectric loss, are taken into consideration in the ADSmodels. A 4-port S-matrix, a 3-port S-matrix and a 2-port S-matrixdescribe the frequency characteristics of the cells located at thecenter, the edge and the corner, respectively. The performance ofentire solid-gridded plane pair is computed by generating a 2-Dmesh of S-matrices.

Mutual coupling from nearby cells and traces will affect theelectrical characteristics of the gridded structures. Whether theseinterferences should be taken into considered in the basic cellmodel or not depends upon the layout geometry. Figure 1 showshow the density of gridded structures can be expressed usingaperture ratio. The coupling effect can be neglected if the aperture

Figure 4 Layout of benchmark structures

Figure 5 Measured and simulated results at point A for gridded groundplane with 2.5-mm grid pitch

Figure 6 Measured and simulated results at point B for gridded groundplane with 2.5-mm grid pitch

Figure 7 Measured and simulated results at point C for gridded groundplane with 2.5-mm grid pitch


ratio is high. If the aperture ratio is too low, additional couplingterms must be added to the cell models.

3. COMPARISON OF SIMULATED ANDMEASURED RESULTS

Two sets of benchmark circuits were fabricated on LTCC substrateusing the DuPont LTCC process [1]. The substrate material isGreen Tape DP951-A2, which has a nominal dielectric constant of7.8 and the single layer thickness of 140 �m. Figure 1 shows a topview of the square gridded plane layer. The backside has a simi-larly sized square solid metal plane. The overall size of thesolid-gridded plane pair is 40 mm � 40 mm and the gridded planeuses a 0.2 mm trace width. One benchmark circuit has a 2.5 mmtrace pitch and the other has a 1 mm trace pitch. Both structuresuse four layers of A2 tape, which results in a nominal 0.56 mmthick substrate thickness. The gridded planes and the solid planeswere fabricated with co-fired and post-fired process respectively.The solid plane was printed with a polymer-based conductingpaste, while the gridded plane utilized a silver-based conductingpaste. The frequency characteristics of the solid-gridded plane pairare measured through plated through hole (PTH) vias with circularpads on the solid plane side for probing. The vias are located in sixdifferent locations, labeled as A–F in Figure 4, in order to inves-tigate the influence of the excitation location on the resonantcharacteristics. After the structures were fabricated, the actualphysical dimensions were measured. The average height of thefabricated circuit is 0.53 mm, and the average trace width is 0.18mm. These values were used in the simulations, which werecarried out on a Sun Ultra5 workstation with 386-M RAM.

Measurements were performed with a HP8510C Network An-alyzer (ANA), that is connected to a Cascade Microtech Summit™On-Wafer Probe Station using ACP GSG-1000 probes. The ANAwas calibrated using the SOLT technique with an alumina imped-ance standard substrate.

The measured and simulated S11 parameters from 45 MHz to10 GHz for the solid-gridded plane structure with a 2.5-mm gridpitch are presented in Figures 5–10. There is good agreementbetween most of the measured and simulated results, since themagnitude of the simulated results are reasonably close to that ofthe measured data up to 9 GHz, and most of the measured resonantfrequencies are predicted by the simulation. Figure 11 comparesthe simulated and measured S11 results between 45 MHz and 18

GHz at point A. This figure shows that there is quite a differencebetween the measured and simulated results above 9 GHz. Thisdifference is primarily due to high frequency effects, such asline-to-line coupling and radiation, that are not considered in thetransmission line modeling approach. The 2.5-mm grid dimensionin LTCC is a quarter wavelength at 13.5 GHz, and thus it isexpected that there will be strong radiation and coupling betweenadjacent lines near and above this frequency. To investigate thisidea further, a comparison of the similar measured and simulatedresults on the split-ground plane structure with a 1-mm grid pitchwas made. This comparison shows that the smaller grid pitch hasreasonably good agreement up to 16 GHz.

4. CONCLUSION

In this paper, a method to model the frequency domain character-istics solid-gridded planes is presented. The method is based upona 2-D TL model and is applicable for gridded ground planestructures with thin conductor traces. Equivalent circuits of cellsare constructed using basic transmission line elements provided byAgilent ADS and the parameters for the transmission line elementsare defined based on the physical dimensions of unit cell struc-

Figure 8 Measured and simulated results at point D for gridded groundplane with 2.5-mm grid pitch

Figure 9 Measured and simulated results at point E for gridded groundplane with 2.5-mm grid pitch

Figure 10 Measured and simulated results at point F for gridded groundplane with 2.5-mm grid pitch

370 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 36, No. 5, March 5 2003

tures. The frequency domain behaviors of the unit cells are char-acterized using S-matrix files. Simulation results have been com-pared to measurements on a benchmark structure fabricated inLTCC. The transmission line approach requires 30 minutes withgood agreement between simulation and measurement results up to9 GHz for a 2.5 mm grid pitch and up to 16 GHz for a 1 mm gridpitch. A comparable full wave simulation using Ansoft’s HFSSrequires more than 100 hours to accurately model the frequencydomain behavior of the whole structure.

ACKNOWLEDGMENTS

This work was sponsored by Deutsche Forschungs-Gesellschaftunder grant GRK164-3 and Deutscher Akademischer Austauschdi-enst, National Science Foundation of the USA under grant NSF-INT-9910054, and the Semiconductor Research Corporation(SRC) under contract 2001.NJ.956.

REFERENCES

1. LTCC application manual at www.dupont.com/mcm/gtapesys/index.html

2. Y.L. Li, E. El-Sharawy, L. Polka, A. Madrid, J.C. Liao, and D.Figueroa, Modeling and experimental validation of interconnects withmeshed power planes, Proc of 47th Electronic Components TechnolConf (1997), 1158–1162.

3. H. Thust, K.-H. Drue, J. Muller, T. Thelemann, T. Tuschick, J. Chilo,C. Golovanov, and F. Ndagijimana, Coupling behavior between trans-mission lines with meshed ground planes in LTCC-MCMs, Proc 11th

Euro Microelectron Conf (1997), 92–99.4. A. Sinha and S. Chowdhury, Mesh-structured on-chip power/ground:

Design for minimum inductance and characterization for fast R, Lextraction, Proc IEEE Custom Integrated Circuits Conf (1999), 461–465.

5. K. Lee and A. Barber, Modeling and analysis of multichip modulepower supply planes, IEEE Trans Components Packaging Manufac-turing Technol Part B: Adv Packaging 18 (1995), 628–639.

6. H.H. Wu, J.W. Meyer, K. Lee, and A. Barber, Accurate power supplyand ground plane pair models, IEEE 7th Topical Meeting Elect PerfElectron Packaging (1998), 163–166.

7. W. Becker, B. McCredie, G. Wilkins, and A. Iqbal, Power distributionmodeling of high performance first level computer packages, IEEE 2nd

Topical Meeting on Elect Perf of Electron Packaging, (1993), 203–205.

8. G.-T. Lei, R.W. Techentin, P.R. Hayes, D.J. Schwab, and B.K. Gilbert,

Wave model solution to the ground/power plane noise problem, IEEETrans on Instrumentation and Measurement, 44 (1995), 300–303.

9. G.W. Peterson, J.L. Prince, and K.L. Virga, Investigation of power/ground plane resonance reduction using lumped RC elements, Proc of50th Electronic Components & Technol Conf (2000), 769–774.

10. L.D. Smith, R. Anderson, and T. Roy, Power plane SPICE models andsimulated performance for materials and geometries, IEEE Trans onAdvanced Packaging, 24 (2001), 277–287.

11. Agilent Advanced Design System User Manual

© 2003 Wiley Periodicals, Inc.

AN ANALYSIS OF THE KINKPHENOMENON OF SCATTERINGPARAMETER S22 IN RF POWERMOSFETS FOR SYSTEM-ON-CHIP(SOC) APPLICATIONS

Yo-Sheng Lin,1 and Shey-Shi Lu2

1 Department of Electrical EngineeringNational Chi-Nan UniversityPuli, Taiwan, R.O.C.2 Department of Electrical EngineeringNational Taiwan UniversityTaipei, Taiwan, R.O.C.

Received 4 September 2002

ABSTRACT: In this paper, the kink effect in scattering parameter S22

of RF power MOSFETs with drain-to-spacer offset is explained quanti-tatively for the first time. Our results show that for RF power MOSFETsthe output impedance can be represented by a “shifted” series RC cir-cuit at low frequencies and a “shifted” parallel RC circuit at high fre-quencies. The appearance of the kink point of S22 in a Smith chart iscaused by this inherent ambivalent characteristic of the output imped-ance. It is found that an increase of drain-to-spacer offset enhances thekink effect. In addition, the kink effect in S22 of RF power MOSFETscan also be interpreted in terms of poles and zeros. © 2003 Wiley Pe-riodicals, Inc. Microwave Opt Technol Lett 36: 371–376, 2003;Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.10767

Key words: RF power MOS; gate-drain resistance; kink effect; S22

1. INTRODUCTION

The kink phenomenon in scattering parameter S22 of FETs/BJTscan be seen frequently in the literature [1–4]. Up to now, twodifferent origins of the S22 kink phenomenon in deep sub-micronRF MOSFETs have been reported [5–6]. Hjelmgren, et al. attrib-uted the phenomenon to the small signal-substrate resistance [5],while Lu, et al. concluded that it resulted from the transconduc-tance and, consequently, the size of the transistor [6]. In this paper,based on the results of RF power n-MOSFETs for system on chip(SOC) applications, the third origin of the S22 kink phenomenon indeep sub-micron RF MOSFETs, that is, small-signal gate-drainresistance, is reported and explained quantitatively for the firsttime. It is found that an increase of drain-to-spacer offset enhancesthe kink effect. That is to say, for devices with higher effectivegate-drain channel resistance Rgd connected in series to gate-draincapacitance, the kink effect is more prominent.

The concept of dual-feedback circuit methodology [7] is usedto simplify the circuit analysis of the small-signal model of RFpower n-MOSFETs and then the output impedance of the devicesis derived. The formula shows that the output impedance of the RFpower n-MOSFETs follows a “shifted” constant resistance r circle

Figure 11 Measured and dimulated results up to 18 GHz at point A forgridded ground plane with 2.5-mm grid pitch


accurate frequency domain modeling of ltcc solid-gridded plane structures

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