Equivalent length design equations for right-angled microstrip bends Visser, H.J.

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1 Equivaent ength design equations for right-anged microstrip ends Visser, H.J. Puished in: The Second European Conference on Antennas and Propagation,. EuCAP. - Novemer, Edinurgh, UK Puished: // Document Version Puisher s PDF, aso known as Version of Record (incudes fina page, issue and voume numers) Pease check the document version of this puication: A sumitted manuscript is the author's version of the artice upon sumission and efore peer-review. There can e important differences etween the sumitted version and the officia puished version of record. Peope interested in the research are advised to contact the author for the fina version of the puication, or visit the DOI to the puisher's wesite. The fina author version and the gaey proof are versions of the puication after peer review. The fina puished version features the fina ayout of the paper incuding the voume, issue and page numers. Link to puication Citation for puished version (APA): Visser, H. J. (). Equivaent ength design equations for right-anged microstrip ends. In The Second European Conference on Antennas and Propagation,. EuCAP. - Novemer, Edinurgh, UK (pp. -). London: Institution of Engineering and Technoogy (IET). Genera rights Copyright and mora rights for the puications made accessie in the puic porta are retained y the authors and/or other copyright owners and it is a condition of accessing puications that users recognise and aide y the ega requirements associated with these rights. Users may downoad and print one copy of any puication from the puic porta for the purpose of private study or research. You may not further distriute the materia or use it for any profit-making activity or commercia gain You may freey distriute the URL identifying the puication in the puic porta? Take down poicy If you eieve that this document reaches copyright pease contact us providing detais, and we wi remove access to the work immediatey and investigate your caim. Downoad date:. Oct.

2 EQUIVALENT LENGTH DESIGN EQUATIONS FOR RIGHT- ANGLED MICROSTRIP BENDS H.J. Visser* *Host Centre TNO P.O. Box KN Eindhoven, The Netherands E-mai: Keywords: Antenna feeds, discontinuities, microstrip, propagation, refection. Astract For printed antenna systems, microstrip feeding networks may ecome quite compex, incuding severa right-anged ends. In designing feed networks we have to consider refection eves at and eectrica engths of the ends. Removing a part of the area of metaization in the end s corner can compensate for the excess capacitance and reduce the refection eve of the end. Fu wave simuations have een performed for unmitered and (%) mitered right-anged ends in microstrip on FR and FR -ike sustrates in the frequency range MHz GHz. The simuations reveaed that for refection eves eow -db, up to GHz mitering is unnecessary. For refection eves eow -db, mitering must e appied for frequencies in excess of.ghz. A sight modification of the centreine approach for unmitered ends eads to an equivaent eectrica ength for unmitered ends with an asoute accuracy of ess than one degree for a frequencies and sustrates, where the reference panes may e rought ack a the way to the end. Appying this modification to %-s, having the reference panes at.λ g distance from the end, λ g eing the waveength in the sustrate, eads to an asoute error in eectrica ength of ess than two and a haf degrees for a frequencies and sustrates. Introduction Microstrip transmission ines are very popuar due mainy to their ease of integration with common Printed Circuit Boards (PCBs). For wireess devices, a components as we as the antenna (e.g. PIFA or monopoe) or part of the antenna (e.g. microstrip patch) can e mounted on top of the same PCB, the antenna eing interconnected to the (active) eements y microstrip transmission ines. The antenna feeding network may ecome quite compex, e.g. for a dua poarised antenna or a aanced antenna that needs to e connected to an unaanced ampifier. Such feeding networks usuay empoy severa right-anged ends that compicate the feeding network design. The compications incude refections at the ends and assessment of the ends eectrica engths. Refection Due to charge accumuation at particuary the outer corner of a end, an excess capacitance is created, whie current interruptions give rise to excess inductances, []. Figure a shows a right-anged end and the equivaent circuit is shown in figure, []. α L C Figure : Right-anged microstrip end a. Un, top view.. Equivaent circuit c. Mitered end, top view. Especiay the excess capacitance may give rise to high refection eves. Removing the area of metaization in the corner a process known as chamfering or mitering can compensate for the L a c Authorized icensed use imited to: Eindhoven University of Technoogy. Downoaded on January, at : from IEEE Xpore. Restrictions appy.

3 excess capacitance. The equivaent circuit shown in figure aso hods for s as shown in figure c. Vaues for L and C in figure d are given in [] for frequencies up to GHz. The design of a microstrip network may e accompished y empoying a fu-wave anaysis program, empoying a microwave circuit simuator (that uses amongst others, equivaent circuits for microstrip ends) or empoying inhouse written dedicated software for microstrip transmission ines and right-anged ends. However, fu-wave and/or microwave circuit simuators are not at everyone s disposa and the writing of dedicated software is a time-consuming process. Furthermore, accurate modes for frequencies in excess of GHz are not readiy avaiae. Even if software is avaiae, guideines are sti needed for a fast generation of initia designs. For an initia design it suffices to decide whether or not to appy a miter and to restrict ourseves to the α=, =. (or %) miter, see figure c. The α=, =. miter appears to e the optimum miter for wide ines and appears to improve the refection over the unmitered case for a widths, heights, permittivities and frequencies considered, []. Refection eves have een cacuated empoying a Method of Moments for unmitered and % mitered right-anged microstrip ends in Ω microstrip transmission ines. The microstrip parameters used in the simuations are shown in tae. Frequency Strip width Sustrate thickness MHz.mm..GHz.mm..GHz...GHz.mm..GHz.. ε r..... tanδ Tae : Microstrip and sustrate parameters used in fuwave simuations. The sustrate parameters used are ased on commerciay avaiae PCB materia (FR) and microwave aminate (Rogers ROB ), wherein the oss tangent (tanδ) has een set to zero. Thus, refection eve simuation resuts are not distured y oss effects. Refections (S ) have een simuated for the configurations as shown in figure, for severa vaues of microstrip transmission ine ength in frequency ands around the centra frequencies shown in tae. The non-excited port has een match-terminated. Figure : Dimensions of microstrip structure eing simuated. Frequency Length S unmitered S mitered MHz.GHz.GHz.GHz mm mm -db -db -db -db -db -db -db -db Tae : Refection eves for unmitered and % mitered right-anged ends in microstrip. (VSR.) are considered to e acceptae, up to GHz mitering is not necessary. If refection eves eow -db (VSR.) are needed, mitering shoud e appied for frequencies in excess of.ghz. These resuts agree with oservations in [,]. For a right-anged ends simuated, for a frequencies, the radiation oss is negigie. These resuts agree with [,], []. hether a miter is appied or not, a need exists for a simpe procedure to assess the eectrica ength of a microstrip path incuding a right-anged end. In the next section, equivaent microstrip transmission ine engths wi e derived for unmitered and % mitered right-anged ends. Equivaent ength The eectrica ength of a right-anged microstrip end may e determined y repacing the microstrip circuit containing the end with a straight piece of microstrip transmission ine having an equivaent ength, see figure. The refection eves for unmitered and % s are shown in tae for typica vaues of at the centra frequencies. Care has een taken to verify that these changes in refection eve are consistent with the oserved changes over the frequency ands around these centra frequencies. eq The simuations revea that if refection eves up to -db Figure : Dimensions of microstrip structure eing simuated. Authorized icensed use imited to: Eindhoven University of Technoogy. Downoaded on January, at : from IEEE Xpore. Restrictions appy.

4 In figure, the dotted ines indicate the termina panes of the right-anged end. The ength is the distance etween the termina panes and reference panes ess than one degree when is approaching zero, i.e. the reference panes are rought down to the termina panes of the end. =. () For practica reasons we want to design compact feeding networks we want to have the reference panes as cose as possie to the end termina panes.. Un In the centreine approach, as shown in figure a, the equivaent ength is taken as the ength of the centreine through the microstrip structure mm mm un centreine modified centreine Tae : Cacuated s for unmitered right-anged microstrip end and equivaent ength microstrip transmission ines at MHz. a mm mm mm mm mm un centreine modified centreine Figure : Determination of equivaent ength for unmitered right-anged end. a. Centreine approach.. Modified centreine approach. Tae : Cacuated s for unmitered right-anged microstrip end and equivaent ength microstrip transmission ines at.ghz. eq = +. () By sighty modifying the equivaent ength as shown in figure, we take the actua current fow etter into account. The equivaent ength is now given y eq = +. () To compare the equivaent engths of equations () and () with the actua structure, the signa transfer (S ) through the actua structure has een cacuated y a Method of Moments for different vaues of. The same has een done for straight pieces of microstrip transmission ine of physica engths eq and eq. The cacuated phases are shown in taes to for the frequencies MHz,.GHz,.GHz,.GHz and.ghz, respectivey. mm mm mm..mm.mm mm.mm.mm. mm un centreine modified centreine The taes ceary show the improvement of the modified centreine approach, equation (), over the traditiona centreine approach, equation (). The asoute phase error is Tae : Cacuated s for unmitered right-anged microstrip end and equivaent ength microstrip transmission ines at.ghz. Authorized icensed use imited to: Eindhoven University of Technoogy. Downoaded on January, at : from IEEE Xpore. Restrictions appy.

5 mm. mm....mm un centreine modified centreine into a path foowing the inner edge more cosey, equation (). / a Tae : Cacuated s for unmitered right-anged microstrip end and equivaent ength microstrip transmission ines at.ghz...mm mm..mm.. un centreine modified centreine Figure : Current path approximations. a. Shortest path.. Shortest path and modiefied centreine path. The shortest path ength, short, foows from figure a Tae : Cacuated s for unmitered right-anged microstrip end and equivaent ength microstrip transmission ines at.ghz.. Mitered end For the mitered right-anged end we foow the procedure as outined in [] for douy chamfered ends. As in [] we oserve that aso the current distriution through a rightanged end tends to concentrate aong the inner edge, see figure. short = +. () The equivaent ength of the % mitered right-anged microstrip end, eqmit, is now cacuated as eqmit eqshort =, () where eq is given y equation (). To compare this equivaent ength with the actua mitered right-anged end, the signa transfer (S ) through the actua structure has een cacuated y a Method of Moments for different vaues of. The same has een done for straight pieces of microstrip transmission ine of physica engths eqmit and eqmit. The equivaent ength eqmit is the equivaent ength ased on the unmodified centreine approach, [] eqmit eq short =, () where eq is given y equation (). Figure : Typica exampe of current distriution through a right-anged microstrip end, dark: ow current density, ight: high current density. The current path therefore is not foowing the centreine, ut deviates towards the shortest path, see figure a. For the unmitered right-anged end we corrected for the actua current path y modifying the centreine path, equation (), The cacuated phases are shown in taes to for the frequencies MHz,.GHz,.GHz,.GHz and.ghz, respectivey. The taes show that the equivaent ength ased on the modified centreine approach, eqmit, may generate resuts that reseme the actua structure more cosey than eqmit. The improvement, however, is not monotonousy increasing with decreasing ength as in the case of the un. Authorized icensed use imited to: Eindhoven University of Technoogy. Downoaded on January, at : from IEEE Xpore. Restrictions appy.

6 mm mm eqmit eqmit Tae : Cacuated s for mitered right-anged microstrip end and equivaent ength microstrip transmission ines at MHz. mm. mm....mm eqmit eqmit Tae : Cacuated s for mitered right-anged microstrip end and equivaent ength microstrip transmission ines at.ghz. mm mm mm mm mm eqmit eqmit Tae : Cacuated s for mitered right-anged microstrip end and equivaent ength microstrip transmission ines at.ghz. mm mm mm..mm.mm mm.mm.mm. mm eqmit eqmit Tae : Cacuated s for mitered right-anged microstrip end and equivaent ength microstrip transmission ines at.ghz...mm mm..mm eqmit eqmit Tae : Cacuated s for mitered right-anged microstrip end and equivaent ength microstrip transmission ines at.ghz. To derive practica guideines for using the new equivaent ength approximation, eqmit, the asoute phase differences etween the equivaent ength transmission ines and the actua structures have een evauated as function of the ength, normaised to the waveength in the sustrate, λ g. This waveength is given y λ λg =, () ε eff where λ is the free space waveength and ε eff is the effective reative permittivity, that is given y, [] ε r + ε r h ε eff = + +, () where ε r is the reative permittivity of the sustrate, h is the thickness of the sustrate and is the microstrip width. The resuts are shown in the figures to. The figures show that using the equivaent ength ased on the modified centreine approach eads to a etter accuracy for a smaer separation of end termina panes and reference panes. For.λg, the asoute phase error is ess than two and a haf degrees for a frequencies and sustrates considered. Authorized icensed use imited to: Eindhoven University of Technoogy. Downoaded on January, at : from IEEE Xpore. Restrictions appy.

7 MHz de MHz de..... /amdag Figure : Asoute phase differences at MHz..GHz de.ghz de..... /amdag Figure : Asoute phase differences at.ghz..ghz de.ghz de..... /amdag Figure : Asoute phase differences at.ghz..ghz de.ghz de..... /amdag Figure : Asoute phase differences at.ghz. deta (degrees) deta (degrees) deta (degrees) deta (degrees)..ghz de.ghz de... /amdag Figure : Asoute phase differences at.ghz. Concusions. Fu wave simuations for microstrip ends on FR (ike) sustrates, revea that mitering is necessary for frequencies in excess of (.GHz) GHz to otain refection eves eow (- db) -db. Equation () cacuates an equivaent ength for an un with an asoute error of ess than one degree, having the reference panes at the end termina panes. For % s, equations (), () and () cacuate an equivaent ength for.λg with an asoute error of ess than two and a haf degrees. References [] T.C. Edwards, Foundations of Microstrip Circuit Design, John iey & Sons, Chichester UK, ( ). [] M. Kirschning, R. H. Jansen and N. H. L. Koster, Measurement and Computer-Aided Modeing of Microstrip Discontinuities y an Improved Resonator Method, IEEE MTT-S Internationa Symposium Digest, pp. -, (). [] R. J. P. Douvie and D. S. James, Experimenta Study of Symmetric Microstrip Bends and Their Compensation, IEEE Trans. Microwave Theory and Techniques, Vo. MTT-, No., pp. -, (). [] T. S. Hong,. E. McKinzie and N. G. Aexopouos, Fu-ave Spectra-Domain Anaysis of Compensation of Microstrip Discontinuities Using Trianguar Sudomain Functions, IEEE Trans. Microwave Theory and Techniques, Vo., No., pp. -, (). [] A. J. Raina, Refections from Bends in Printed Conductor, IEEE Transactions on Components, Hyrids, and Manufacturing Technoogy, Vo., No., pp. -, (). [] J. X. Zheng and D. C. Chang, Numerica Modeing of Chamfered ends and Other Microstrip Junctions of genera Shape in MMIC, IEEE MTT-S Internationa Symposium Digest, pp. -, (). [] S. A. Bokhari, Precision Deay Matching y Trace ength Contro in Printed Circuit Boards, Canadian Conference on Eectrica and Computer Engineering, pp. -, (). [] D.M. Pozar, Microwave Engineering, nd edition, John iey & Sons, New York, (). deta (degrees) Authorized icensed use imited to: Eindhoven University of Technoogy. Downoaded on January, at : from IEEE Xpore. Restrictions appy.