interactive coupling to each other, as well as consideration of thelossy element. The equivalent circuit parameters of single-cellCSRR have been also successfully extracted. The promising ap-plications of these characteristics of CSRR can be easily designedto construct metamaterials that substitute for EBG structures insize reduction. The measured results of the experimental CSRRagree well with the simulation results.

ACKNOWLEDGMENT

The authors wish to acknowledge National Nano Device Labora-tories for supporting the equipments and the financial support ofthis study by the National Science Council of the Republic ofChina under Grant NSC 94–2622-E-492–001-CC3.

REFERENCES

1. R. Qiang, Y. Wang, and D. Chen, A novel microstrip bandpass filterwith two cascaded PBG structure, IEEE Antennas Propag Soc IntSymp 2 (2001), 510.

2. H.Y.D. Yang, R. Kim, and D.R. Jackson, Design consideration formodeless integrated circuit substrates using planar periodic patches,IEEE Trans Microwave Theory Tech 48 (2000), 2233.

3. F.R. Yang, R. Coccioli, Y. Qian, and T. Itoh, Analysis and applicationof coupled microstrips on periodically patterned ground plane, IEEEMTT-S Int Microwave Symp Dig 3 (2000), 1529–1532.

4. M.H. Weng, R.Y. Yang, C.Y. Hung, H.W. Wu, W.N. Chen, and M.P.Houng, A dual-mode bandpass filter with a wide stopband, MicrowaveOpt Tech Lett 43 (2004), 177.

5. D. Ahn, J.S. Park, C.S. Kim, J. Kim, Y. Qian, and T. Itoh, A design ofthe low-pass filter using the novel microstrip defected ground struc-ture, IEEE Trans Microwave Theory Tech 49 (2001), 86.

6. R.Y. Yang, M.H. Weng, H.W. Wu, H.D. Hsueh, and M.P. Houng,Dual-mode ring bandpass filter using defected ground structure with awider stopband, IEICE Trans Electron E87-C (2004), 2150.

7. F. Martın, F. Falcone, J. Bonache, R. Marques, and M. Sorolla, A newsplit ring resonator based left handed coplanar waveguide, Appl PhysLett 83 (2003), 4652.

8. F. Falcone, T. Lopetegi, J.D. Baena, R. Marques, F. Martın, and MarioSorolla, Effective negative-� stopband microstrip lines based on com-plementary split ring resonators, IEEE Microwave Wireless ComponLett 14 (2004), 280.

9. J. Garcıa-Garcıa, F. Martın, E. Amat, F. Falcone, J. Bonache, I. Gil, T.Lopetegi, M.A.G. Laso, A. Marcotegui, M. Sorolla, and R. Marques,Microwave filters with improved stopband based on sub-wavelengthresonators, IEEE Trans Microwave Theory Tech 53 (2005), 1997.

10. G.V. Eleftheriades, A.K. Iyer, and P.C. Kremer, Planar negative re-

fractive index media using L-C loaded transmission lines, IEEE TransMicrowave Theory Tech 50 (2002), 2702.

11. J.D. Baena, J. Bonache, F. Martın, R. Marques, F. Falcone, T. Lope-tegi, M.A.G. Laso, J. Garcıa, I. Gil, and M. Sorolla, Equivalent circuitmodels for split ring resonators and complementary split ring resona-tors coupled to planar transmission lines, IEEE Trans MicrowaveTheory Tech 53 (2005), 1451.

12. H.W. Wu, M.H. Weng, Y.K. Su, C.Y. Hung, and R.Y. Yang, Improvedstopband of the dual-mode ring bandpass filter using periodic comple-mentary spilt-ring resonators, IEICE Trans Electron Lett, in press.

13. D.M. Pozar, Microwave engineering, 3rd ed., Wiley, Hoboken, NJ, 2005.14. K.C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip lines and

slotlines, 2nd ed., Artech House, Boston, 1996.15. J.S. Park, J.H. Kim, J.H. Lee, S.H. Kim, and S.H. Myung, A novel

equivalent circuit and modeling method for defected ground structureand its application to optimization of a DGS low pass filter, IEEE IntMicrowave Symp Des 1 (2002), 417.

© 2006 Wiley Periodicals, Inc.

SINGLE FIELD-BASED EQUIVALENTCIRCUIT FOR STRIPLINEDISCONTINUITIES AND ITSAPPLICATIONS

Cheng Lu, Wanchun Tang, and Puke ZhouNanjing University of Science and TechnologyNanjing, Jiang Su Province 210094, China

Received 20 May 2006

ABSTRACT: A single field-based equivalent circuit model for differentstripline discontinuities has been constructed and applied to commonlyencountered stripline discontinuities, such as: open-circuit, step, right-angle bend, and T-junction. Also, a low-pass filter and a branch linecoupler are analyzed by using this field-based equivalent circuit. Com-pared with numerical results, the average errors of S parameters areless than 2%. © 2006 Wiley Periodicals, Inc. Microwave Opt TechnolLett 49: 234–237, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22082

Key words: stripline discontinuity; synthetic asymptote

1. INTRODUCTION

The packaging technology, low temperature cofired ceramic(LTCC), is now widely used in various microwave systems frontends to reduce the circuit size and lower the cost. As a transmissionline, stripline (symmetrical or asymmetrical) is often used inLTCC. The analysis of the stripline is thus of much importancesince a complicated circuit is realized by interconnecting circuitcomponents with striplines and their line discontinuities.

Different circuit models have been developed for differentcircuit discontinuities. Such complexity makes interpretation forimproved design of a total circuit of many discontinuities difficult.The authors have obtained a single field-based equivalent circuitmodel in solving many microstrip line discontinuities [1] that arerelated to the joining of half-lines of different widths. In thisarticle, this equivalent circuit model is applied for the analysis ofstripline discontinuities and practical circuit components, such as:low-pass filter and branch line coupler. Compared with IE3D, theaverage errors of S-parameters are less than 2%.

2. FIELD-BASED EQUIVALENT CIRCUIT

The field-based equivalent circuit has been obtained by the authorsfor microstrip discontinuities in Ref. 1 under the quasi-static con-

Figure 4 Simulated, measured, and extracted frequency responses of thesingle-cell CSRR

234 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 49, No. 1, January 2007 DOI 10.1002/mop

dition, assuming that the metal is a thin copper of thickness 2 �m.In this article, however, this equivalent circuit model is used forstripline discontinuities and two practical components (low passfilter and branch line coupler). Figure 1 shows the structure of astripline, where b and �r are, respectively, the distance betweentwo ground-plates and dielectric constant. W is the width of thestripline. Only TEM mode is considered in this article, just likethat in Ref. 1. Also we assume that the stripline is in the middle ofthe two ground-plates.

First of all, we analyze the open-end of stripline. The open-endof stripline is equivalent to an excess capacitance because of thefringe field at the open-end. For the open-end of the stripline, theexcess capacitance Cexcess can be taken directly from the accurateformula [2] as follows:

Cexcess ���l

�Z0(1)

with

��l � tan�1� � � 2W

4� � 2Wtan����� (2)

Figure 1 Structure of a stripline

Figure 2 A T-junction of stripline and its corresponding equivalentcircuit model

Figure 3 Stripline low-pass filter: (a) layout; (b) comparison of S11; and(c) comparison of S21. [Color figure can be viewed in the online issue,which is available at www.interscience.wiley.com]

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 49, No. 1, January 2007 235

Figure 4 Stripline branch line coupler: (a) layout; (b) magnitude of S11; (c) magnitude of S21; (d) magnitude of S31; (e) magnitude of S41; (f) phase of S21;and (g) phase of S31. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com]

236 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 49, No. 1, January 2007 DOI 10.1002/mop

� � b ln2/� (3)

� and Z0 are the propagation constant and the characteristic im-pedance of the stripline, respectively. The characteristic imped-ance can be computed by the following equation:

Z0 � ��0�0

CC0(4)

where C and C0 are, respectively, the distributed capacitance ofstripline with dielectric and air. The distributed capacitance can beobtained by synthetic asymptote of [3–5]:

C � �Cnear1.2 � Cfar

1.2�1/1.2 (5)

with

Cnear � 2��0�r

W

b/2(6)

Cfar � 2��0�r�1

ln�8

�

b

W� 1�

�W

8b � (7)

Cnear and Cfar are the two regular asymptotes of the distributedcapacitance at b3 0 and b3 �, respectively.

Just like that described in Ref. 1, two or three open-ends can beconnected together to construct other stripline discontinuities, suchas: step, right-angle bend, and T-junction, etc. As an example,Figure 2 shows a T-junction of stripline and its correspondingequivalent circuit model. All the parameters except Cexcess can becalculated by formulas in Ref. 1.

3. NUMERICAL RESULTS

To check the validity of the field-based equivalent circuit, twosimple practical components are taken as examples. The results bythe equivalent circuit and the transmission line theory are com-pared with those of IE3D. For the IE3D computation, each mea-suring port at the discontinuity is assumed, not at the equivalentcircuit boundary at length z � b from the discontinuity junction,but further along the connecting striplines to a port distance zp, asshown in Figure 2. The load connected to each port is taken to be50 .

For a low-pass filter shown in Figure 3(a), the distance betweentwo ground-plates and dielectric constant are 2.0 and 2.2 mm,respectively. Figures 3(b) and 3(c) show, respectively, the magni-tude of S11 and S21 by IE3D, equivalent circuit model, and trans-mission line theory. One can see that the S11 by all the threemethods agree very well below 10 GHz. However, the S21 bytransmission line theory has a deviation beyond 7 GHz because thediscontinuities are not considered in the conventional transmissionline theory.

The second example given in this article is a branch linecoupler. The structure is shown in Figure 4(a). The distancebetween two ground-plates and dielectric constant are 2.0 and7.8 mm, respectively. Figures 4(b)– 4(e) show the amplitudes ofS11, S21, S31, and S41 of the stripline branch line coupler by allthe three methods above. As can be seen, the amplitudes agreewell for the three methods. For the branch line coupler, how-ever, the phase of S21 and S31 are very important. As shown inFigures 4(f) and 4(g), one can see that the phase of S21 and S31

by conventional transmission line theory (without discontinui-

ties) deviate from those by IE3D and the equivalent circuitbeyond 2 GHz for S21 and 1 GHz for S31.

4. CONCLUSIONS

The field-based equivalent circuit model has been successfullyapplied in two practical components of stripline, i.e., a low-passfilter and a branch line coupler. With this equivalent circuit modeland transmission line theory, the analysis and design of the prac-tical components or circuits can be done very easily, even forcomplicated circuits. Compared with IE3D, the maximum errors ofS-parameters are less than 5% and the average error is less than2%. The equivalent circuit model can also be applied to CPWcircuits with some minor improvements and will be given in afuture article.

ACKNOWLEDGMENT

This article is supported by Natural Science Foundation (no.60371002) of China and Jiang Su Natural Science Foundation(no. BK2005129) at Nanjing University of Science and Tech-nology.

REFERENCES

1. W. Tang, Y.L. Chow, and K.F. Tsang, Different microstrip line discon-tinuities on a single field-based equivalent circuit model, IEE ProcMicrowave Antennas Propag 151 (2004), 256–262.

2. K.C. Gupta, R. Darg, and R. Chadha, Computer-aided design of micro-wave circuits, Artech House, Boston, 1981.

3. W. Tang and B. Jiang, CAD formula of asymmetric stripline viasynthetic asymptote, Microwave Opt Technol Lett 47 (2005), 143–145.

4. W.C. Tang and Y.L. Chow, Inverse of exact solution by syntheticasymptote—an example of stripline, IEEE Microwave Guided WaveLett 10 (2000), 454–456.

5. Y.L. Chow and W.C. Tang,“Development of CAD formulas ofintegrated circuit components—fuzzy EM formulation followed byrigorous derivation, J Electromag Waves Appl 15 (2001), 1097–1119.

© 2006 Wiley Periodicals, Inc.

A NOVEL MULTIBAND DIPOLEANTENNA WITH A MICROSTRIP LOOPFEED

Wen-Jiao Liao, Yu-Cheng Lu, and Hsi-Tseng ChouThe Department of Communication EngineeringYuan Ze University135 Yuan-Tung Rd.Chung-Li 320, Taiwan

Received 22 May 2006

ABSTRACT: A novel microstrip antenna applicable for multiband useis proposed in this work. The design was evolved from a conventionalparallel stripline dipole with modifications in the dipole geometry andfeeding structure. Those measures help introduce new resonant modesand increase bandwidths in the radiation spectrum. Fundamental an-tenna parameters including reflection coefficients, antenna gains, radia-tion patterns, and efficiency are measured. The results suggest that theproposed dipole provides roughly omni directional patterns at 1.8 to2.4, 3.6, and 5.8 GHz bands with 0 dBi gain on the H-plane of thedipole. Such a planar antenna is of low cost and can be used on per-sonal portable communication devices such as the smart phones to

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 49, No. 1, January 2007 237