Incomplete 2-Port Vector Network Analyzer Calibration Methods

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1 Incomplt -Port Vctor Ntwork nalyzr Calibration Mthods. Hnz, N. Tmpon, G. Monastrios, H. ilva 4 RF Mtrology Laboratory Instituto Nacional d Tcnología Industrial (INTI) Bunos irs, rgntina 4 bstract iffrnt typs of incomplt -port vctor ntwork analyzr (VN) calibration mthods ar xplaind. ll of thm ar particular cass of th - trm rror modl and a comparison, including advantags and disadvantags, btwn thm and a Full -Port mthod, such as TOM, is mad. Rsumn En l prsnt inform s xplican los distintos tipos d calibración incomplta d un VN d purtos. Todos llos son casos particulars dl modlo d términos d rror, y s raliza una comparación, incluyndo vntajas y dsvntajas, ntr llos rspcto a un método Full -Port como l método TOM. I. INTROUCTION Whn calibrating a -Port VN, Full -Port calibration is usually mployd []. Thr ar diffrnt typs of mthods dpnding on th rror modl to b considrd. Th most common calibration mthod usd for coaxial systms is TOM (also known as OLT) which uss th - trm rror modl []. Howvr, this mthod rquirs an 8- stp procdur to gt both ports calibratd. Whn is not ncssary to masur all four scattring paramtrs (i..,, and ) of th vic Undr Tst (UT) or uncrtaintis ar not ncssary to b as small as possibl, altrnativ calibration mthods may b mployd. dvantags and disadvantags must b prviously considrd in ordr to dtrmin which on will b th bst option for ach particular cas. II. TOM CLIBRTION Bfor masuring any UT -paramtrs, both VN s ports must b first calibratd in ordr to calculat systm rrors. Most common mployd mthod is TOM. It consists in calculating 6 forward (F) and 6 rvrs (R) rror trms as shown in figurs and. whr whr forward rror trms ar : : : : : : Fig. irctivity (F) Port- ourc Match (F) Rflction Tracking (F) Transmission Tracking (F) Lakag (Crosstalk)(F) Port- Load Match (F) Rvrs -trm rror modl flow chart whr rvrs rror trms ar : irctivity (R) : Port- Load Match (R) : Rflction Tracking (R) : Transmission Tracking (R) : Lakag (Crosstalk) (R) : Port- ourc Match (R) olving masurd -paramtrs from figurs and [] M M M M b a b a b a + + ( ) + + ( ) () () ' + () + b + (4) a + Fig. Forward -trm rror modl flow chart xxm : Masurd, i.. uncorrctd, -paramtrs xx : Corrctd -paramtrs (5)

2 . VN Calibration Calibration procdur consists in masuring 7 diffrnt rfrnc standards ( Opns, horts, Matchs and a Thru) with known rflction and/or transmission valus from a TOM calibration kit. In this papr rfrnc standards ar considrd to hav idal valus as follows Γ OPEN (6) Γ HORT (7) Γ MTCH (8) (9) THRU To prform a complt -Port calibration, an 8-stp procdur must b don as follows tp : Connct Opn to Port tp : Connct hort to Port tp : Connct Match to Port tp 4: Connct Opn to Port tp 5: Connct hort to Port tp 6: Connct Match to Port tp 7: Connct Match Port / Match Port tp 8: Connct Thru btwn Port and Port ) Port Calibration: Making stps to, an OM calibration [] to Port is prformd and th following forward rror trms ar calculatd from () ( ) M () match M ( opn ) + M ( short) () ( opn ) ( short ) M M [ ( opn ) ] [ ( short ) ] M M () ( opn ) ( short ) M M TBLE I PORT CLIBRTION UMMRY Rfrnc Error to b corrctd scription Opn ourc Match (F) hort Rflction Tracking (F) Match irctivity (F) ) Port Calibration: Making stps 4 to 6, an OM calibration to Port is prformd and th following rvrs rror trms ar calculatd from () ( ) M match () M ( opn ) + M ( short ) (4) ( opn ) ( short ) M M [ ( opn ) ] [ ( short ) ] M M (5) ( opn ) ( short ) M M TBLE II PORT CLIBRTION UMMRY Rfrnc Error to b corrctd scription Opn ourc Match (R) hort Rflction Tracking (R) Match irctivity (R) ) Isolation Ports Calibration: tp 7 is optionally mad only whn vry low transmission paramtrs must b masurd. In most cass this rror trm is nglctd. (, ) ( ) M (6) match (7) M match, Rfrnc Match Match TBLE III IOLTION PORT CLIBRTION UMMRY Error to b corrctd scription Crosstalk (F) Crosstalk (R) 4) Calibration btwn Ports: Whn making stp 8 both Load Match and Transmission Tracking rror trms ar calculatd from (), (), () and (4) as follows M (8) M [ Thru) ] ( ) M (9) ( whr M M [ Thru) ] ( ) ( () M () (). () Rfrnc Thru. TBLE IV CLIBRTION BETWEEN PORT UMMRY Error to b corrctd scription Load Match (F) Load Match (R) Transmission Tracking (F) Transmission Tracking (R) Equations () to () rprsnt th rror trms to b calculatd.

3 B. UT -Paramtrs Masurmnt olving quations () to (4), corrctd -paramtrs of th UT can b xprssd as follows [] [4] ( + ) [ + ( )] ( + ) [ + ( )] whr (4) (5) (6) (7) N M (8) M N (9) N M () M N () ( + ) ( + ) () whr N xx ar normalizd -paramtrs [4]. C. Full -Port: dvantags and isadvantags ) dvantags: Provids low uncrtaintis as all rror trms ar calculatd and all four UT -paramtrs ar masurd. ) isadvantags: Nds an 8-stp procdur calibration. It is always ncssary to masur all four UT - paramtrs vn if only on is ndd to b corrctd. III. INCOMPLETE -PORT VN CLIBRTION In th past, VNs had only a transmission/rflction (T/R) tst st. This allowd only forward paramtrs to b masurd, sinc Port actd as a sourc and Port as a load. Thn, calibration mthods usd wr: Transmission Rspons (TR) -Port + Normalization (-P+N) Enhancd Rspons(ER) On-Path -Port (-P -P) Nowadays, most VNs hav a full -paramtr tst st. This allows th sourc to b switchd to both ports, hnc it is abl to masur all four -paramtrs and a TOM, i.. complt, calibration can b don. Howvr, whn it is not ncssary (or convnint for som rason) to masur all four UT -paramtrs or, uncrtaintis ar not ncssary to b as small as possibl, abov mntiond incomplt calibration mthods can b usd [5]. ll of thm ar partial calibrations basd on TOM mthod dscribd in sction II. To simplify mathmatical xprssions, crosstalk rror trms will b considrd null valud for all cass () (4) IV. TRNMIION REPONE It is th simplst -Port calibration mthod and is usd whn only (or ) paramtr is of intrst. Thru rfrnc lmnt is connctd btwn ports for th calibration, so only transmission tracking rror trm is partially calculatd. This causs th highst uncrtaintis in transmission -paramtr masurmnts.. VN Calibration (btwn Ports) From () and (): M pplying (9) in () M ( Thru ) ( Thru ) ( Thru ) + ( Thru ) (5) (6) s nithr nor ar calculatd, th corrction trm rlatd to thm is considrd null valud. (7) Rplacing (7) in (6) (8) M imilar considrations ar applid for th rvrs transmission tracking trm (9) M B. UT (or ) Masurmnt s only paramtr is masurd and rror trm is calculatd, quation (5) is rducd to ( UT ) M (4) imilar considrations can b applid for ( UT ) M (4)

4 C. Transmission Rspons: dvantags and isadvantags ) dvantags: Vry fast on-stp calibration procdur. Only nds to b masurd in ordr to gt its corrctd valu, so a good option for unidirctional dvics. ) isadvantags: Only for transmission ( or ) paramtrs. s Transmission Tracking rror trm is not calculatd corrctly, this mthod is not vry accurat with lossy UTs. On th othr hand, it is rcommndd only for insrtabl dvics as in practic this mthod always considrs idal Thru valus as in (9). V. -PORT + NORMLIZTION This mthod prforms a -Port calibration (at Port or Port ) and, sparatly, a transmission rspons. This is usually mployd whn only forward paramtrs ( and ) or rvrs paramtrs ( and ) ar rquird.. VN Calibration ) Port (or Port ) Calibration: Procdur is applid in th sam mannr as in ction II. (or sction II.). ) Calibration btwn Ports: Procdur is applid in th sam mannr as in ction IV. B. UT Forward (or Rvrs) Paramtrs Masurmnt s UT rvrs paramtrs ar not masurd, and all rvrs rror trms ar not calculatd, hnc all corrction trms rlatd to thm in (4) and (5) ar considrd null valud. can b xprssd as follows M ( UT ) (4) ( UT ) M s OM and transmission normalization calibrations ar prformd sparatly, corrctd valu rmains th sam as in sction IV B. M ( UT ) (4) imilar considrations ar applid for rvrs paramtrs M ( UT ) (44) ( UT ) M ( UT ) M (45) C. -Port + Normalization: dvantags and isadvantags ) dvantags: Corrcts dirctivity, rflction tracking and sourc match of Port (or Port ). ) isadvantags: imilar as in Transmission Rspons mthod. VI. ENHNCE REPONE It is an improvmnt of th -P+N mthod for masuring Forward (or Rvrs) -paramtrs. It nds th sam four stps as bfor to calibrat th VN but, in this cas, it also calculats Load Match rror trm. This allows Transmission Tracking rror trm to b corrctly calculatd.. VN Calibration ) Port (or Port ) Calibration: Procdur is applid in th sam mannr as in ction II. (or sction II.). ) Calibration btwn Ports: Procdur is applid in th sam mannr as in ction II.4. B. UT Forward (or Rvrs) Paramtrs Masurmnt lthough is calculatd in this cas, UT rvrs paramtrs ar not masurd and non of th rvrs rror trms is calculatd. Hnc, all corrction trms rlatd to thm in (4) and (5) ar considrd null valud and and can b drivd as follows M ( UT ) (46) ( UT ) M M ( UT) M ( UT) (47) imilar considrations ar applid for rvrs paramtrs M M ( UT ) (48) ( UT ) M ( UT ) M ( UT ) C. Enhancd Rspons: dvantags and isadvantags (49) ) dvantags: Calculats Transmission Tracking rror trm corrctly. ) isadvantags: s only Forward (or Rvrs) - paramtrs ar masurd, Load Match valu can not b usd for corrcting UT -paramtrs. VII. ONE-PTH -PORT Originally namd On-Path Full -Port, was introducd to T/R VNs in ordr to masur all four -paramtrs. Howvr, UT must b manually rvrsd to masur Rvrs -paramtrs. t prsnt most VNs hav this calibration option, but spcial car must b takn as som manufacturs considr ER mthod as -P -P.

5 . VN Calibration This mthod considrs Forward and Rvrs modls th sam as follows (5) (5) (5) (5) (54) (55) Hnc, it nds th sam four stps as in th prvious mthods to calibrat th VN and only 6 forward rror trms ar ndd to b calculatd using (), (), (), (6), (8) and (9). B. UT Paramtrs Masurmnt Whn masuring UT dvic, forward paramtrs ar masurd first, and thn UT is connctd backwards and rvrs paramtrs ar masurd. This allows quations (4) to (7) to b usd with no corrction trms null valud. C. On Path -Port: dvantags and isadvantags ) dvantags: ll four UT -paramtrs can b masurd. s Forward and Rvrs rror trms hav sam valus, only a four-stp procdur is ndd to calibrat th VN. ) isadvantags: Not rcommndd for VNs using any combination of coaxial sxd port connctors du to th ncssity of adaptrs. sris of singl swp and UT manually chang procdur must b prformd in ordr to gt all four -paramtrs. In practic, uncrtaintis may b highr that Full -Port du to connctor mchanical rpatability or cabl flxibility. Fig. maximal dviation for -Port + Normalization and Enhancd Rspons with rspct to TOM mthod. B. viation Rsults iffrnt maximal dviations of for TR and ER mthods rspct to TOM ar shown in figurs 4 and 5 rspctivly for a UT having a nominal attnuation valu of db. VIII. IMULTION sris of comparisons btwn incomplt calibrations mthods rspct to TOM wr carrid out. and masurmnts wr simulatd and maximal dviation rsults ar shown in figurs to 6. Fig. 4 db maximal dviation for Transmission Rspons with rspct to TOM mthod whn masuring a valu of db.. viation Rsults iffrnt maximal dviations of for -P+N and ER mthods rspct to TOM ar shown in figur. s in both incomplt mthods, has th sam valu (s quations (4) and (46)), such dviations rspct to TOM ar th sam. Ths dviations dpnd on Port Load Match, i.. valu, and UT s attnuation, i.. valu. For xampl, if th UT consists of a 6-dB attnuator and., thn maximal dviation rspct to TOM mthod will b.6. If now th UT consists of a coaxial cabl with nominal db attnuation valu, and rmains in., thn maximal dviation rspct to TOM mthod ariss to.. Fig. 5 db maximal dviation for Enhancd Rspons with rspct to TOM mthod whn masuring a valu btwn db and 6 db.

6 For xampl, if UT s paramtrs., and VN s rror trms., thn maximal dviation rspct to TOM mthod will b.7 db for TR mthod and.9 db for ER mthod. ccording to figurs 5 and 6, if now th sam UT has an attnuation valu of 6 db and all othr valus rmain th sam, thn maximal dviation rspct to TOM mthod ariss to.4 db for TR mthod and rmains in.9 db for ER mthod. Fig. 6 db maximal dviation for Transmission Rspons with rspct to TOM mthod whn masuring a valu of -6 db. IX. CONCLUION iffrnt typs of incomplt -Port VN calibrations mthods ar xplaind in this papr. Each on of thm has its own advantags and disadvantags rspct to a complt -Port mthod as TOM. In practic, if VN s rror trms and/or UT s mismatchs ar quit low, thr will b no significant dviation btwn incomplt and complt calibration mthods whn masuring or. On th contrary, if VN s sourc and load match rror trm valus ar considrabl and also UT is lossy, thn incomplt mthods ar not suitabl du to th significant dviations thy may hav. REFERENCE [] N 87-, pplying rror corrction for VNs, nd. Ed., anta Clara, C: gilnt Tch.,. []. Rytting, Ntwork analyzr rror modls and calibration mthods, Palo lto, C, Hwltt Packard Inc., 998. [] B. Hall, VN rror modls: Commnts on EURMET/cg-/v., NMET Rport 5, Masurmnt tandards Laboratory of Nw Zaland Lowr Hutt, Nw Zaland,. [4] J. unsmor, Handbook of microwav componnt masurmnt, gilnt Tch., John Wily & ons, Ltd., UK,. [5] M. Hibl, Fundamntals of vctor ntwork analysis, Rohd & chwarz GmbH & Co. KG, 5 th Ed.,. [6] G. Wübblr, Clmns Elstr, Thomas Richl and Rolf Judaschk, trmination of th complx rsidual rror paramtrs of a calibratd on-port vctor ntwork analyzr, IEEE Transactions, Vol. 58, No. 9, 9. [7] N 87-, pcifying calibration standards and kits for gilnt vctor ntwork analyzrs, gilnt Tch.,.

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