Appliction Note Multiport Vector Network Anlyzer Mesurements An nlysis of different rchitectures nd impcts on uncertinties nd pplictions Introduction An incresing number of multiport devices, whether they be multibnd wireless phone components, bckplne blnced trnsmission lines or clssicl devices such s power dividers, re being chrcterized in the RF, microwve nd millimeter-wve frequency bnds. -prmeter mesurements re often needed nd ordinry vector network nlyzer (VNA) mesurements must be modified in order to perform these mesurements quickly nd ccurtely. This ppliction note will look t number of hrdwre rchitectures nd clibrtion procedures for multiport mesurements nd their impcts on flexibility nd uncertinties. Appendix A will concentrte on rchitecture impcts on smll but incresing portion of ll microwve multiport pplictions, blnced devices. Appendix B will describe simple test to see wht rchitecture our DUT needs. Multibnd nd multifunction phones re prime consumer exmple of product requiring multiport devices. Often in such phone front-ends, the filters nd switching re integrted in single module to reduce cost. Hence, the mesurement problem becomes multiport. Blnced trnsmission structures re incresingly common in both the digitl nd nlog worlds for efficiency, noise nd crosstlk immunity, bndwidth nd other resons. These structures intrinsiclly hve 4 or more ports. Clssicl multiport devices such s couplers, power dividers, nd circultors re dditionl exmples. While these devices could be chrcterized by series of two-port mesurements (with remining ports terminted in something known or derivble), this cn be very time consuming nd cn led to incresing mesurement errors. There re vriety of wys to form multiport VNA, rnging from using the two-port VNAs with some dditionl switching ll the wy to structures with N sources nd N receivers (e.g., []-[]). Whtever structure one selects fter looking t the trde-offs, there re implictions to the clibrtion procedures to be used. Mny of the concepts for two-port mesurements tht users re fmilir still pply but re simply extended to more ports. In multiport system, there re still the fmilir concepts of source mtch, directivity, frequency response, nd isoltion. The difference is tht there re now more pths tht need to be chrcterized nd some ssumptions tht need to be mde bout their interdependence. Of prticulr importnce re how one hndles the termintions presented to the unused ports of the device nd how one chrcterizes the myrid of possible signl trnsmission pths. To further complicte things, the choice of hrdwre nd clibrtion procedures will hve vrying impcts on uncertinty. ome of the impcts will be discussed, long with some exmples, to help understnd the scope of interctions tht exist in this clss of mesurements.
Multiport -prmeters To begin, we should be cler bout the prmeter definitions tht will be employed. The mening of multiport -prmeter is simple nd is included in the bsic definition [3] with the nottion of Fig.. Multi-port VNA Port b N port DUT Port b Port n n b n Figure. The nottion for multiport -prmeter definitions is shown here (n ports). Clssiclly, bi ij, q 0... j q k The requirement of terminting ll device-under-test (DUT) ports is n importnt one nd will influence the multiport design nd the clibrtion pproches. A slight vrint on these concepts hs proven very useful for blnced devices, termed mixed-mode -prmeters. Discussed in detil elsewhere (e.g., [3]-[4]), the mixed-mode prmeters re liner trnsformtion of the stndrd -prmeter set tht describe the differentil nd common-mode responses to differentil nd common-mode excittions. As would be expected, these re intended for use with blnced devices nd cn be derived from single-ended -prmeters (under linerity ssumptions, ppendix A). The incident nd reflected/trnsmitted wves re expressed s sum or difference (depending on if it is commonmode or differentil wve being discussed) of the single-ended wves. The resultnt -prmeters end up being liner combintions of the single-ended -prmeters. ome of the relevnt expressions re shown below. d c d c ( ) b ( b b ) ( + ) ( + ) ( ) 3 ( + ) 3 4 4 d b c b d b c ( b + b ) ( b b ) 3 ( b + b ) 3 4 4 dd dd d d d d ( + ) 3 ( + ) 3 ( + ) Here dd describes pure differentil trnsmission from port pir to port pir. imilrly cc would describe pure common mode trnsmission from port pir to port pir. cd would describe mode conversion reflection t port pir ( differentil signl is incident, the common-mode signl is being mesured). ome of these mixedmode prmeters will be used in lter exmples. The mesurement nd interprettion of mixed-mode -prmeters under nonliner or true-drive conditions is subject of current interest (e.g., [5]-[7])) nd will not be discussed in detil here. The clibrtions required to enble such mesurements re somewht more complicted nd interprettion of the results is more chllenging. 33 3 4 43 4 3 34 4 4 44
Hrdwre Options Historiclly, one could mesure multiport devices of the type listed bove with just two-port VNA. If ll of the pths re firly well isolted (e.g., if the DUT is switch), then one does not need to worry much bout the other DUT ports. For mesuring multiple pths, simple switch fbric like tht shown in Fig., elimintes multiple connection nd throughput issues. Two Port Bse VNA Port Port Custom switch-fbric Port Port Port 3 Port 4 Figure. One of the simplest possible wys to mke multiport VNA mesurement is shown here. Not ll prmeters cn be mesured nd only set of two-port clibrtions re used. For simple, restricted-pth devices, this my be dequte. Flexibility my be n issue, however, in tht one my wnt to ccess vrious ports on DUT without reconnecting. The switch fbric could then expnd ll the wy to its most completely reconfigurble (or flexible) form suggested in Fig. 3. To VNA Port To VNA Port Port Port Port 3 Port 4 Ech box represents terminting switch Figure 3. A more complete switch fbric is shown here; still using full two-port VNA s the bse. Flexibility is improved but the insertion loss nd dynmic rnge re worsened, nd there re potentil stbility issues. everl trde-offs should be considered s one increses switch fbric complexity to crete more complete fbric, flexible enough to mesure ll ij prmeters using ny clibrtion routine: ) More insertion loss in the switch fbric, less dynmic rnge for trnsmission mesurements nd less isoltion between ports ) More expensive hrdwre 3) More complex softwre 3
As frequencies increse, this firly simple pproch becomes more pinful since the loss in front of the couplers gets very high. This leds to poor mesurement stbility s well s clibrtion complexity. The next evolution is to multiport VNA in which reflectometers follow the fbric (see Fig. 4). VNA Direct Access Loops Direct Access Loops b ource b ource Port Port Port Port Port 3 Port 4 Figure 4. A more complete rrngement is shown here in which the test couplers hve been moved out to the ports. One cn think of there being one receiver per port. This increses flexibility (in clibrtions nd mesurement) nd removes some mesurement side-effects such s stbility. The fbric-completeness issues re the sme lthough it is fr esier to mesure every -prmeter ij. There re still some complictions in how clibrtions re performed (minor lgorithmic modifictions required to void uncertinty degrdtion) but these re generlly subtle (e.g., [8]). A next evolutionry step is to use source nd receiver pir per port (see Fig. 5). While very flexible, this cn be n expensive solution t higher frequencies. ources VNA 3 4 b b b 3 b 4 Port Port Port 3 Port 4 Figure 5. The source/reference/test per port multiport structure is shown here in which sources nd receivers re segregted by port. This cn get complex t higher frequencies. ome of the trde-offs mongst these vrious hrdwre configurtions re summrized in the tble below. Ntive VNA w/ switching fter couplers (like Fig. 3) witching before couplers (like Fig. 4) imple fbric Inexpensive; evere clibrtion nd flexibility limits; tbility issues Moderte expense; ome clibrtion nd flexibility limits Complex fbric Moderte expense; Good flexibility; Moderte clibrtion limits; tbility nd dynmic rnge issues High expense; Good flexibility; ome dynmic rnge issues t high frequencies One source nd receiver per port (like Fig. 5) N/A Highest expense; Best flexibility 4
Multiport Clibrtion Implictions Intrinsiclly tied to the choice of the physicl mesurement structure is how the clibrtions will be performed. VNA clibrtion hs been discussed in the literture (e.g., [8]-[8]) for decdes nd will not be reviewed in detil here. The bsic principle is tht structurl fults in the mesurement system re chrcterized by the mesurement of known or prtilly known stndrds. These chrcterized fults re then fed bck into the mesurement to de-embed their effects from those of the DUT. In the simplest sense, one could pursue ll clibrtions s two-port clibrtions s lluded to erlier nd illustrted in Fig. 6. Here one simply reclls given two-port clibrtion dictted by wht pth is of interest. Indeed if the DUT ports re ll reltively well-isolted, this is not bd choice since the nture of the termintion or levels of correction t the other ports will be irrelevnt. VNA Port Port Port 3 Port 4 If for exmple -4 pth mesurement is being mde, two port clibrtion between ports nd 4 would suffice. Figure 6. The simplest clibrtion pproch, which is pproprite for some DUTs, is to consider ech mesurement s just two-port mesurement. If the "unused" ports ( nd 3 in this exmple) re well-isolted within the DUT from the "used" ports ( nd 4 here), the pproch cn work well but my not be the most efficient. But consider wht hppens when the other DUT ports re not so well isolted. The mesurement error induced by n unterminted third port reltive to low insertion loss min pth is shown in Fig. 7. Uncertinty with n unterminted & uncorrected 3rd port vs. isoltion of tht port 0 Trnsmission Uncertinty (db) 0. iso0 db iso0 db iso30 db iso40 db 0.0-00 -80-60 -40-0 0 (db) Figure 7. The effect on trnsmission uncertinty of ignoring DUT s third port termintion is shown here. is the pth being mesured but DUT port is left open nd ignored (nd its isoltion from the pth given by the vlue "iso"). The plot shows tht if is greter thn -40 or -50 db, the third port hd better be isolted by t lest 30 db for miniml uncertinty impct. 5
One could, of course, terminte the unused ports in qulity lods per the -prmeter definition. In switch ssemblies, prticulrly t higher frequencies, this gets to be incresingly difficult (which is one reson why we hve corrections for two-port VNAs). Mintining better thn 5 db return loss through switch over lrge bndwidth usully proves chllenging. The impct of performing the sme mesurement s in Fig. 7 but with vrying qulity lods is shown in Fig. 8. Low insertion uncertinty with prtilly terminted 3rd port Trnsmission uncertinty (db) 0. 0.0-40 -30-0 -0 0 Reflection coefficient of termintion (db) iso0 db iso0 db iso30 db Figure 8. The uncertinty of mesuring smll insertion loss when third port (isolted from the desired pth by the vlue "iso") is terminted in lod of vrying reflection coefficient is shown here. For low isoltion, the termintion needs to hve better thn 30 db return loss to void significnt uncertinty impct. This leds quickly to the conclusion, tht for generl mesurements, full correction of lod reflections (in ddition to other trditionl VNA correction prmeters such s directivity) would be desirble so tht lod mtch on ll of the unused ports would be corrected to within the cpbilities of the correction (usully 35-45 db t RF or microwve frequencies). To be ble to process the lod mtch informtion, ll -prmeters of the DUT must be mesured nd corrected becuse, in generl, there is no priori knowledge of the internl pths nd ports of the DUT tht my be ffected. Consider first the cse where receivers re not vilble on per-port bsis (i.e., where coupling is behind the switching s shown in Fig. 3). In this sitution, mesurements re still done on two-port bsis but with knowledge tht the other ports of the DUT re terminted in some non-perfect mtches. If these lod mtches were ll known, there is enough informtion to solve the problem (nd they cn be mesured bsed on single two-port clibrtion by sequentilly connecting thru from clibrted port to ech dectivted port). Ech of the two-port mesurements (involving ll ports) cn be normlized to common reference impednce frmework (tht of the off-stte ports), combined into single NxN -prmeter mtrix, nd then renormlized to the desired reference impednce (e.g., 50 ohms, see [9]). This process is illustrted in Fig. 9 (e.g., [5], [30]). 6
tep : Perform first two port clibrtion. Normlize the results to the off-stte impednces of ports nd. 3 4 tep : Repet until ll trnsmission pths hve been covered t lest once. In ech cse, renormlize to the off-stte impednces. 3 4 X X X X X X X X X X X X X X X X tep: Combine results into n NxN -prmeter mtrix bsed on the ports involved. Then trnsform the results bck to 50 ohms. Figure 9. The renormliztion clibrtion process is illustrted here. The off-stte impednce here refers to the impednce of given port when its nerest switch is "off" or in terminting stte. Consider now the sitution like tht described in Fig. 4, in which receivers re vilble on per-port bsis (indicted in tht figure by the couplers fter the switching). A simplified wy of looking t the multiport error model is shown in Fig. 0 (e.g., [9]). Associted with ech port is set of error coefficients describing the reflectometer. Associted with ech pth between ports is set of coefficients describing the frequency response of the pth. There re mny wys of pproching this composite clibrtion: two simple ones re: ) trt performing two-port clibrtions until ll ports hve been ddressed t lest once. This mens tht ll reflectometer behviors hve been determined long with some of the trnsmission pths. Line interconnects between some remining port pirs re then needed to complete the model. ) trt performing one-port clibrtions (three known stndrds) until ll ports re done. Then strt going through the possible port interconnects with known thrus/lines. e physicl port Perfect VNA e physicl port e3 physicl port 3 e4 physicl port 4 Figure 0. A simplified wy of looking t multiport error model is shown here for four ports. Associted with ech port is n error box describing reflectometer errors for tht port. Also for ech pth, there is trnsmission frequency response nd isoltion term (only three pth pirs of six re shown for clrity). Not ll of these terms re independent. 7
The former is more generl nd covers ll common clibrtion lgorithms while the ltter is somewht more specific to the fmily of entirely known stndrds clibrtions. One compliction tht my occur is tht good thru line my not be vilble between some port pirs. This issue cn be ddressed with the firly powerful concept of clibrtion hybridiztion where different lgorithms re used for different ports nd pirs depending on their chrcteristics. Ech lgorithm hs its strengths nd weknesses in terms of wht it requires from the stndrds (in terms of perfection or in terms of ccurcy of chrcteriztion). ince multiport clibrtion is somewht comprtmentlized bsed on the vrious interconnects, one cn choose vrious clibrtions t different points bsed on which fits best to the stndrds vilble t tht point. While the subject cnnot be covered in depth here (for more thorough tretments, see, e.g., [0], [3]), it cn be illustrted with n exmple. Consider four-port on-wfer differentil mesurement to high frequency (>40 GHz). uppose further tht two ports re close together on one side of the DUT nd the remining ports re close together on the other side (bsed on the probe ssembly). ince it is trditionlly difficult to ccurtely chrcterize on-wfer stndrds but the trnsmission lines re good, clibrtions dependent on the good qulities (such s Thru-Reflect-Line (TRL)) would be desirble for the bse. Unfortuntely from our lyout, shown in Fig., we my only hve fith in the trnsmission line qulity on pths -3 nd -4. ince those pths cn be used to fully determine reflectometer coefficients, we hve some lgorithmic freedom on hndling the remining pth(s). Fully-known-stndrds lgorithms (like hort-open-lod-thru (OLT)) my be rejected since it would require chrcteriztion or idelity of the sme lines which my be difficult to get. ome other prtilly-known stndrds lgorithms (like hort-open-lod-reciprocl (OLR)), on the other hnd, mke few ssumptions bout the port interconnect (e.g., [5]-[8]) nd might mke good choice for hndling the remining pths. As in mny clibrtion scenrios, these use redundncy of informtion to mke certin steps simpler. Port Port Port 3 Port 4 Port Port Port 3 Port 4 Port Port Port 3 Port 4 Figure. A possible wfer lyout sitution, in which not ll lines re likely to be of equl qulity is shown here. The port -3 nd -4 thrus re fine but the bends in the other combintions my led to rdition, loss, nd/or mismtch nd cuse clibrtion issues. 8
The effect of hybridiztion is illustrted in Fig., where the potentilly poor thrus of Fig. re hndled by number of different pproches. In this cse, cquiring only the trnsmission coefficients using n unknown-thru pproch like OLR for this pth produced the best results. This concept cn be generlized to the growing concept of sttisticl clibrtions (e.g., s in [3]) where more stndrds thn necessry re mesured nd lest-squres problem is solved bsed on uncertinty estimtes of the vrious quntities. Liner mgnitude of differentil dely line mtch reltive to tht from good line cl 0. 0.09 0.08 0.07 delt (unitless) 0.06 0.05 0.04 0.03 0.0 0.0 0 0 0 0 30 40 50 60 70 Frequency (GHz) cse cse cse 3 Figure. The dely line mtches for blnced dely line obtined with severl clibrtion schemes (ll reltive to good line clibrtion) re shown here. Cse uses known-stndrd pproch nd ssumes the line to be idel. Cse tries to obtin both mtch nd trnsmission behvior through the poor line. The best one, cse 3, uses lod mtch obtined from previous clibrtion steps nd trnsmission trcking obtined from n unknown-thru nlysis on the questionble line [3]. Uncertinties nd Exmples The pth to mesurement uncertinty hs lredy been briefly discussed (see lso [9], [30], nd [3]). For given trnsmission prmeter, the error is tht of the bsic two-port mesurement plus tht from residul lod mtch contributions from the vrious other ports. This is obviously multi-lyer effect since ny port cn interct with every other port, requiring complete informtion bout the DUT. For simplified clcultion, we will ssume low-loss DUT (such tht signl-to-noise rtio effects re smll nd instrument compression cn be ignored) with vrible mtch on ll ports (ssumed equl for convenience). Isoltion will be prmeterized nd will be ssumed equl for ll pths. An eight-port construct will be ssumed. This nlysis will be repeted for three clsses of clibrtion pproches ) Two-port-only clibrtions where 0 db termintions re ssumed for remining test set ports ) Multiport clibrtions bsed on re-referencing 3) Direct multiport clibrtions (s would typiclly hppen if t lest one receiver per port is vilble) A somewht idel setup will be considered for ech with 45 db residul directivities, 40 db residul mtches (on clibrted ports), 0.005 db trnsmission trcking error nd 60 db connector repetbility. Drift is not included but would certinly penlize the first two pproches listed bove more thn the third. The clculted uncertinties for trnsmission nd reflection re shown in Fig 3 for isoltion levels of 30 db nd 0 db. 9
Trnsmission mgnitude, low loss, 8 port, 30 db isoltion Reflection mgnitude, low insertion loss, 8 port, 30 db isoltion 0 Est. mgnitude uncertinty (db) 0. port cls N port with trnsform full N port Est. mgnitude uncertinty (db) port cls N port with trnsformtions full N port 0.0-30 -5-0 -5-0 -5 0 DUT mtch (db) 0. -30-5 -0-5 -0-5 0 DUTmtch (db) () (b) Trnsmission mgnitude, low loss, 8 port, 0 db isoltion Reflection mgnitude, low insertion loss, 8 port, 0 db isoltion 0 00 Est. mgnitude uncertinty (db) 0. port cls N port with trnsformtions full N port Est. mgnitude uncertinty (db) 0 port cls N port with trnsformtions full N port 0.0-30 -5-0 -5-0 -5 0 DUTmtch (db) 0. -30-5 -0-5 -0-5 0 DUT mtch (db) (c) Figure 3. Trnsmission ( nd c) nd reflection (b nd d) uncertinties for low loss DUT with eight ports re shown here s function of isoltion within the DUT (30 db for nd b, 0 db for c nd d) nd clibrtion pproch. The two N-port pproches show similr uncertinties but gin the trnsformtion pproch hs slightly higher uncertinties in prt becuse more mesurement steps re required (nd uncertinties re llowed to compound). The two-port clibrtion pproch produces reltively minor penlties with 30 db isoltion in the DUT (prticulrly on trnsmission) but mjor penlties when the isoltion flls. This is expected bsed on the erlier nlysis of the trnsmitted lod mtch effects. To estblish confidence in these methods, some multiport mesurements were mde nd compred to twoport mesurements in which the unused ports were terminted in vriety of different lods (if the lods re metrology-grde, the lod mtch terms should become very smll). The results re shown for high frequency dely line in Fig. 4, for six-port dul coupler in Fig. 5, nd for blnced dely line in Fig. 6. (d) Dely line trnsmission comprison 3 (db) or <3 devition (deg).0 0.8 0.6 0.4 0. 0.0-0. -0.4-0.6-0.8 -.0 0 0 0 30 40 50 60 Frequency (GHz) 4 3 0 - - -3-4 3 -ts 3 -p <3-ts <3-p Figure 4. A dely line mesurement is shown here compring four-port mesurement to very well-terminted two-port mesurement. As expected, the results essentilly coincide [8]. 0
Dul coupler input mtch vs. cl method -0 (db) -5-0 -5-30 full 6 port 4 port cl (uncorrected LM) 4 port cl (good termintions) -35 0 3 Frequency (GHz) Figure 5. The mtch of six-port coupler is shown here mesured with full six-port clibrtion nd with two different four- port clibrtions. As might be expected when poor termintions re not corrected, substntil ripple results [30]. Dely line mtch behvior: isolted p vs. full 4p cl 0 ii (db) -0-40 -60 p 4p -80 0 5 0 5 0 Frequency (GHz) Figure 6. The mtch on one port of blnced dely line is shown here. A full four-port clibrtion ws used for one trce while resonbly well-terminted two-port mesurement ws used for the other. The two-port termintions set floor for mesurble mtch over prt of the frequency rnge. To show the limits of correction, isoltion of the six-port coupler ws mesured for Fig. 7. Here the more limited four-port clibrtion with metrology-grde termintions ctully does little better thn the full six-port clibrtion. The termintions hd return loss of bout 50 db in this frequency rnge while the residul lod mtch from the clibrtion ws only in the 45 db rnge. At higher frequencies, this type of overlp becomes less likely nd the full clibrtion more esily wins out. -0 Coupler isoltion vs. cl method Isoltion (db) -5-30 -35-40.5.5 3 Frequency (GHz) full 6 port 4 port cl 4 port cl w/ metrology-grde termintions Figure 7. An isoltion mesurement of six-port coupler is shown here with full clibrtion nd with prtil clibrtions relying on well-terminted unused ports [30].
Finlly, mny of the cvets tht pply in two-port clibrtions lso pply to their multiport brethren. OLT clibrtions require firly precisely defined stndrds which cn led to errors, prticulrly high frequencies where these chrcteriztions weken. The TRL fmily of clibrtions (including Line-Reflect-Mtch (LRM)) is much less sensitive in tht regrd nd cn produce better results under most circumstnces (well-behved trnsmission lines being key ssumption). A comprison of four-port blnced dely line mesurement using OLT nd LRM is shown in Fig. 8 nd illustrtes the need to py ttention not only to the multiport extension process but lso to the ssumptions of the underlying clibrtion. 0-0. Blnced dely line: differentil trnsmission dd (db) -0.4-0.6-0.8 LRM OLT - 0 0 40 60 Frequency (GHz) Figure 8. The differentil trnsmission chrcteristics ( dd defined erlier) of blnced dely line re shown here, mesured with OLT nd LRM-derived multiport clibrtions. The stndrds chrcteriztion for OLT ws less precise t higher frequencies leding to some dditionl, though still smll, ripple. Conclusion This ppliction note discusses the different multiport rchitecture choices nd impcts to clibrtion, mesurement ccurcy, nd system cost. Anritsu VNAs use the Fig. 4 rchitecture s the best compromise between flexibility, ccurcy, nd cost. While it cn mesure ll single-ended ij prmeters nd ll blnced -prmeters (Appendix A), it offers optimum ccurcy nd system cost. Its only restriction is in the lck of LRL-clss of clibrtion between ports nd, or 3 nd 4, cused by the fct tht these two pirs of ports shre the sme reference receiver in the bse VNA. ince LRL/LRM nd reciprocl clibrtions re still vilble between.3;.4;.3;.4; the Anritsu rchitecture is indeed the idel choice.
Appendix A- Architecture impcts on mesurements of blnced devices As discussed erlier under Multi-port -Prmeters, single-ended mesurements cn be used for blnced devices mesurements, s long s the DUT stisfies the Linerity Assumption. In this ppendix, we will discuss the Linerity Assumption to see how it pplies to different devices, nd relte it to multi-port rchitectures. It is importnt to remind everybody tht this discussion only pplies to blnced devices. All single-ended multiport devices which still comprise of the vst mjority of microwve components, cn be mesured with ll previous rchitectures. Previous rchitectures re lso perfectly vlid for blnced mesurements, if the DUT response behves linerly. It is only when the blnced DUT s response exhibits non-liner behvior, tht the lterntive nd significntly more expensive rchitecture, where minimum of dul sources re needed, is required. Appendix B shows simple test tht determines if the DUT requires n lternte pproch. For blnced mesurements on devices whose response behves linerly, two seprte single-ended mesurements re performed, nd the dt super-imposed by the VNA to disply common-mode (0 degrees offset) or differentil-mode (80 degrees offset) responses to common-mode or differentil-mode stimuli. The following re the equtions used for the super-position. Notice tht this mthemticl eqution is only vlid under the Linerity Assumption. Differentil-to-Differentil terms: dd dd d d d d ( + ) ( + ) 3 ( + ) 3 ( + ) 33 3 4 43 4 3 34 4 4 44 Differentil-to-Differentil terms: dc dc d c d c ( + ) ( + ) 3 ( + ) 3 ( + ) 33 3 4 43 4 3 34 4 4 44 Common mode-to-common mode terms: cc cc cc cc ( + + + ) ( + + + ) 3 ( + + + ) 3 ( + + + ) 33 3 4 43 4 3 34 4 4 44 Common mode-to-common mode terms: cd cd cd cd ( + ) ( + ) 3 ( + ) 3 ( + ) 33 3 4 43 4 3 34 4 4 44 3
Wht Blnced Devices fll under this Linerity Assumption? All Pssive Devices - Pssive devices such s Trnsmission Lines (coxil, on printed circuit bord, on substrtes or otherwise), connectors, filters, ttenutors, bluns, combiners, splitters behve linerly under both smll nd lrge signl conditions. This ppliction note does not ddress pssive intermod (PIM) testing under multiple wtts input conditions tht re not supported by VNAs. All Active Devices tht re operting in their liner regions, typiclly under smll signl conditions. All multi-stge Active Devices whose output my indeed be driven into sturtion nd whose input remins in the liner region. All Active Devices whose input stge is driven into sturtion, yet the input non-linerity is blnced non-linerity. For ll the blnced devices bove, nd for ll single-ended multi-port devices, simple rchitectures tht rely on super-position of single-ended mesurements provide s ccurte results to more expensive rchitectures [33]. The ltter re only needed for the remining blnced ctive devices whose input exhibit unblnced behvior under lrge signl input. True-mode or Pure-mode rchitecture for the remining non-liner devices: True or Pure mode does not use single source to drive the DUT twice but uses two coherent source to drive the device s blnced port with two signls simultneously, in either differentil or common mode. Phse coherence between the sources is necessry to ensure perfect 0 degrees or 80 degrees offset for common or differentil stimulus respectively. In ddition, sophisticted clibrtion is necessry to ctively control the mgnitude nd phse of ech source s the DUT s mtch chnges with frequency. Notice tht nother source of error tht needs to be hndled is cused by the mtch of the DUT tht is lso chnging with power. If such pure or true-mode solutions ssume tht the mtch of this non-liner device under smll signl conditions is the sme s under lrge signl conditions, their results will not be s pure or true. Figure 5 shows complete rchitecture with single source per port tht cn ccomplish True Blnced- Differentil mesurements. Alterntively, only two switched sources could be used to sve cost. 4
APPENDIX B Mesurements of Norml -port Blnced Circuits using 4-port unblnced VNA cn be mde with ccurcy comprble to true-mode differentil mesurements systems. The Norml -port Blnced Circuit is circuit which stisfies the following chrcteristics: 3 If device is norml differentil device: Either liner DUT (pssive or mplifier in liner mode) Non-linerity occurs fter blnced stge - or- If the non-linerity t the input is blnced non-linerity Then: True-mode nd single-ended mesurements re identicl. Reference [33] Unblnced: ports referenced to ground (-prmeters) 4-Port VNA Test et 3 4 3 4 Blnced Amplifier ingle ended Mtrix qk b q, i 0 i k k -prmeters of Multi-port 3 4 3 3 3 33 4 34 4 4 43 44 Mixed Mode -Mtrix 34 b b b b d d c c dd dd cd cd dd dd cd cd dc dc cc cc dc dc cc cc d d c c dd cd dc cc d d c c If the device stisfies the chrcteristics of Norml differentil device described bove (which includes ll pssive devices operting in VNA environment), the - prmeters cn be ccurtely mesured nd displyed using the Mixed Mode -Mtrix. 5
If the user is not sure tht the device is Norml device operting in liner region, simple mesurement check cn help to confirm this. The simplest test is to look t the mount of compression occurring in the device. This cn be done with simple swept power dd mesurement. If there is less thn ~0.5 db of compression by the power level desired for mesurement, the superposition pproch should work without ny impct on uncertinty. After performing clibrtion t frequencies of interest over possible drive powers of interest, the differentil trnsmission coefficient dd cn be plotted. In Figure is such plot for pssive network over the power rnge of -5 to +0 dbm. ince the trnsmission is completely invrint (to within.0 db) over this rnge, one cn conclude it is liner nd norml per the bove definition. The smll mount of ripple in this plot is trce noise from the very low power levels being used nd this cn be reduced with verging if desired. Figure. The power sweep of differentil trnsmission for pssive network is shown here. ince this prmeter is flt with power, the device is liner nd norml nd superposition will produce the correct result. Next consider differentil mplifier. The sme power sweep ws performed on this device nd the result is shown in Fig.. For drive levels below +5 dbm, there is no devition nd the device is operting linerly nd norml. There is smll mount of gin expnsion between +5 nd +0 drive but only bout 0. db. Even t this drive level, the use of superposition would not dd to uncertinty. 6
Figure. The power sweep of trnsmission for differentil mplifier is shown here. For drive levels below bout +5 dbm, the device is liner nd norml nd superposition will produce the correct result. Even between +5 nd +0 dbm drive, the mount of gin expnsion is smll enough tht there would be negligible effects on uncertinty. Even if this level of compression is exceeded, which will only occur for ctive structures, the superposition pproch my lso work dequtely if the compression occurs t non-input stge. It is lso likely to hve miniml impct on uncertinty if the common-mode return loss is not very low. This cn be checked with quick mesurement of cc. If this is lower thn bout -5 db, compression levels higher thn the 0.5 db discussed bove cn likely be tolerted depending on the DUT internl topology. 7
Figure 3. The power sweep of common-mode return loss is shown here. The return loss is not extremely smll so superposition-bsed mesurements will likely be ccurte even for reltively high levels of compression (higher thn those shown here). Thus, in generl, if one cn quickly confirm linerity, the mesurement cn be mde directly. A single swept power sweep mesurement is enough to estblish this behvior. Depending on the bndwidth of the device, it my be desirble to repet t few frequencies of interest. 8
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