TR///JT -Mode -Prmeter Chrcteristion of Differentil tructures W. Fn, A. C. W. Lu, L. L. Wi nd B. K. Lok Astrct Comined differentil-mode nd common-mode (mixed-mode) scttering prmeters (s-prmeters) re well dpted for ccurte mesurements of liner networks t RF nd microwve frequencies. The reltionships etween stndrd s-prmeters with twoport vector network nlyser () nd mixedmode s-prmeters with four-port re derived in this pper. A fricted differentil structure ws mesured with stndrd two-port nd mixed-mode four-port. The correltion etween stndrd s-prmeters nd mixedmode s-prmeters is presented s well. Keywords: -mode s-prmeter, Differentil structure, Blnce trnsmission line, Multiport BACKGROUND The differentil structures re widely used in RF, microwve nd high-speed rodnd pplictions. The evlution of differentil structures is necessry to ensure optiml circuit nd system performnce. Comined differentil-mode nd common-mode (mixed-mode) scttering prmeters (s-prmeters) re well dpted to ccurte mesurements of liner networks t RF frequencies. However, differentil structure mesurements with trditionl two-port vectornetwork nlyser () present mny chllenges [-]. The mjor ostcle in RF ppliction of differentil structures is tht most test equipment is intended for single-ended devices. The relted infrstructure is lso unlnced, such s clirtion stndrds, trnsmission lines nd connectors, nd even industry stndrd reference impednce [-]. This pper presents the trnsformtion etween stndrd s- prmeters nd mixed-mode s-prmeters. A fricted differentil structure is mesured with two-port nd four-port mixed-mode, respectively, nd the correltion dt is presented s well. Although the stndrd trnsformtion technique could idelly e used to llow trditionl two-port to crry out mesurements of mixed-mode s-prmeters, mixmode mesurement system is essentil to ccurtely chrcterize the effect of modeconversion in the rel differentil test structures ccurtely []. OBJECTIVE The min ojective of this work ws to uild up the in-house cpility in IMTech on development of techniques nd methodologies for multiport chrcteriztion up to GHz. METHODOLOGY. tndrd-mode nd mixed-mode - prmeter of differentil structure For single-ended devices, RF voltges nd currents reltive to common ground cn e defined t ech terminl of the device. From the voltge, current nd impednce definitions, normlized power wves cn e defined s stimulus nd response. timulus power wves propgte into the device-under-test (DUT), nd response power wves propgte wy from it. A lock digrm of four-port device is shown in Fig.. Port Fig.. Digrm of single-ended -port DUT. Port Port DUT Port () The reltionship etween the power wves is shown in Eq. () where B std std A std. B std. nd A std represents response nd stimulus wves mtrix respectively; wheres std is the stndrd four-port s-prmeters mtrix. The mtrix representtion is shown in () nd () respectively. 66
-Mode -Prmeter Chrcteriztion of Differentil tructures B std std A () std () For lnced devices, differentil- nd commonmode voltges nd currents cn e defined on ech lnced port. imilrly differentil- nd common-mode impednces cn lso e defined. A lock digrm of two-port differentil DUT is shown in Fig.. DUT Port Port Fig.. Digrm of differentil -port DUT. A mixed-mode s-mtrix in () cn e orgnized such tht it is similr to the single-ended s- mtrix, where ech column (row) represents different stimulus (response) condition. The mode informtion s well s port informtion must e included in the mixed-mode s-mtrix []. d d d d d d c c d c c d d d d d c d c d d c d c c c c c d c d d c d c c c c c c () didj nd cicj (i, j, ) re the differentil-mode nd common-mode s-prmeters respectively. dicj nd cidj (i, j, ) re the mode-conversion or cross-mode s-prmeters. Differentil response is represented y the prmeters didj (i, j, ) in the upper left corner of the mixedmode s-mtrix () due to differentil Conversion of common-mode (differentilmode) wves into differentil-mode (commonmode) wves is chrcterized y dicj ( cidj ) (i, j, ) prmeters.. Trnsformtion etween tndrdmode nd mixed-mode -prmeter The mixed-mode s-prmeters in () cn e directly relted to stndrd four port s- prmeters () if nodes nd in Fig. re pproximted s single differentil port. imilrly nodes nd re lso grouped s nother differentil port [5]. The reltionship etween the response nd stimulus of stndrd-mode nd mixed-mode re shown in (5) nd (6) respectively. i nd i (i to ) re the wves mesured t ports - in Fig.. d c d c d c d c ( ) ( + ) ( ) ( + ) ( ) ( + ) ( ) ( + ) (5) (6) The trnsformtion mtrix in () etween stndrd s-prmeters nd mixed-mode s- prmeters cn e derived from the following equtions: mixed-mode incident wves A mm in (7); mixed-mode response wves B mm in (8); mixed-mode s-prmeters mtrix mm in (); stndrd four port s-prmeters mtrix std in (); nd the conversion mtrix M in (9) nd M - in (). A mm MA std d d c c B mm MB std d d c c (7) (8) M (9) * M M () M 67
-Mode -Prmeter Chrcteriztion of Differentil tructures B mm mm A mm d d d d d d c c d c c d d d d d c d c d d c d c c c c c d c d d c d c c c c c c () d d d d mm M std M c d c d + + + + d d d d c d c d d c d c c c c c d c d c c c c c + + + + + + + + + + + + + + + + + + + + () REULT & DICUION The test vehicle is -lyer FR sustrte with coupled differentil structure design. The cross section nd fricted test ord re shown in Fig. nd respectively. The cross section illustrtes microstrip topology nd the test vehicle prmeters re shown in Tle. The test structure ws designed s tightly-coupled microstrip differentil structure nd its differentil impednce is Ohm. The MA connectors were used for the connection. Prepreg Cu Trce Ground Plne Fig.. Cross-section of test ord. The set up of single-ended two-port mesurement is shown in Fig. 5(). During the twoport mesurement, ny two ports on the DUT is connected to two-port respectively, nd the two remining ports were terminted with 5 Ohm. All comintions of four individul ports re mesured to get stndrd s- prmeters mtrix, i.e. P&P, P&P, P&P, P&P, P&P nd P&P. These two-port mesurement results cn e used to form stndrd four-port s-prmeters mtrix std in (). tndrd s-prmeters mtrix std will e converted into mixed-mode s-prmeters mtrix mm in (). The setup of differentil-ended fourport mesurement is shown in Fig. 5(). All four ports on the DUT re connected to mixedmode four-port. The clirtion method of short-open-lod-through (OLT) is used for oth two-port nd four-port. -Port < P Differentil P > -Port DUT 5 < P P > 5 () For single-ended -port. Fig.. Fricted test ord. -Port < P P Differentil DUT P -Port > P Copper (Cu) Prepreg Tle. Test ord prmeters. Thickness (µm).5 Line Width (µm) 9 pcing (µm) 5 Thickness (µm) 9 Dielectric Constnt, εr. Loss Tngent δ. () For differentil-ended -port. Fig. 5. etup of s-prmeters mesurement. In Figs. 6 to, the curves denoted s tndrd represent the mixed-mode s-prmeters converted from two-port mesurements, nd the curves denoted s represent the mixed-mode s-prmeters mesured with 68
-Mode -Prmeter Chrcteriztion of Differentil tructures mixed-mode four-port. In Fig. 6, the insertion loss dd of differentil response nd differentil stimulus hs very good greement etween tndrd nd. The curve denoted s ingle-ended is shown s reference for the insertion loss etween singleended port nd single-ended port. Return Loss (db). -. -. -. -. -5. Comprison of tndrd nd -Mode -Prmeters cc The insertion (return) loss of response nd stimulus with sme mode hs very good correltion etween tndrd nd mode s- prmeters in Fig. 7 to. For the response nd stimulus with different mode, there is slight vrition etween tndrd nd mode s-prmeters for oth insertion nd return loss shown in Fig. to. It cn e seen tht the mode conversion method etween stndrd nd mixed-mode s-prmeters cn e used to chrcterize the differentil structures for the users who only hve trditionl two-port.. -. Comprison of tndrd nd -Mode -Prmeters dd vs -6. -7. tndrd -8...8.6.6.8 6 Fig. 8. Return loss in common-mode of response nd. -. -. -. -. -5. -6. Comprison of tndrd nd -Mode -Prmeters dd -. -7. tndrd -. -. -5. -6. -7. tndrd ingle-ended -8...8.6.6.8 6-8...8.6.6.8 6 Fig. 9. Insertion loss in differentil-mode of response nd. -. Comprison of tndrd nd -Mode -Prmeters cc Fig. 6. Insertion loss in single-ended nd differentilended structure. -. -. -. -5.. Comprison of tndrd nd -Mode -Prmeters dd -6. -7. tndrd -. -. -8...8.6.6.8 6 Return Loss (db) -. -. -5. Fig.. Insertion loss in common-mode of response nd -6. -7. tndrd -8...8.6.6.8 6 Fig. 7. Return loss in differentil-mode of response nd Return Loss (db). -. -. -. -. -5. -6. Comprison of tndrd nd -Mode -Prmeters dc -7. -8. tndrd -9...8.6.6.8 6 Fig.. Differentil-mode response nd commonmode 69
-Mode -Prmeter Chrcteriztion of Differentil tructures return Loss (db). -. -. -. -. -5. -6. -7. -8. Comprison of tndrd nd -Mode -Prmeters cd tndrd -9...8.6.6.8 6 Fig.. Common-mode response nd differentilmode. -. -. -. -. -5. -6. Comprison of tndrd nd -Mode -Prmeters dc 5 CONCLUION Mode trnsformtion etween stndrd s- prmeters nd mixed-mode s-prmeters hs een presented in this pper. Chrcteriztion of fricted differentil structure hs demonstrted tht there is close correltion etween the mixed-mode s-prmeters converted from two-port nd mixed-mode four-port mesurements. The mixed-mode s-prmeters derived from the two methods hve good greement for the stimulus nd response with the sme mode (common or differentil), nd smll vrition for the stimulus nd response with different modes (common/differentil, differentil/common). In order to predict the ehviour of the mixed-mode s-prmeters using trditionl two-port, the mode trnsformtion technique cn e pplied, however, mixed-mode four-port system is still required to ccurtely mesure the impct of mode conversion in rel integrted differentil test structures. 6 INDUTRIAL IGNIFICANCE -7. -8. tndrd -9...8.6.6.8 6 Fig.. Differentil-mode response nd commonmode PCB mnufcturers, test service providers nd communiction trnsceiver mnufcturers will enefit from the techniques nd methodologies for multi-port chrcteriztion developed in this work. REFERENCE. -. -. -. -. -5. -6. -7. -8. Comprison of tndrd nd -Mode -Prmeters cd tndrd -9...8.6.6.8 6 Fig.. Common-mode response nd differentilmode [] D.E. Bockelmn nd W.R. Eisenstdt, Pure-Mode Network Anlyzer for On- Wfer Mesurements of -Mode - Prmeters of Differentil Circuits, IEEE Trns. Microwve Theory Tech., Vol., pp. 7-77, (997). [] D.E. Bockelmn nd W.R. Eisenstdt, Comined differentil nd common-mode scttering prmeters: Theory nd simultion, IEEE Trns. Microwve Theory Tech., Vol., pp. 5-59, (995). [] Appliction Notes: Blnced Device Chrcteriztion, Agilent Technologies, (). [] Appliction Note 7-: An Introduction to Multiport nd Blnced Device Mesurements, Agilent Technologies,(). [5] K. Kurokw, Power Wves nd the - ctering Mtrix, IEEE Trns. Microwve Theory Tech., Vol., pp. 9-, (965). 7
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