Multi-Port Calibration Techniques for Differential Parameter Measurements with Network Analyzers

Transcription

1 ROHDE SCHWARZ WORKSHOP, EUMC 2003,, OCTOBER Multi-Pot Calibation Techniques fo Diffeential Paaete Measueents with Netwok Analyzes Holge Heueann, Coittee Mebe, IEEE, MTT-11 Abstact Two geneal ethods of ulti-pot netwok analyze calibation ae descibed using the classical SOLT odel espectively the 7-te T odel which includes all linea eos of the netwok analyze test-sets. The GSOLT-pocedue suppots vecto netwok analyzes with n1 easueent channels only to easue n-pot devices with high accuacy. The GT-pocedue equies netwok analyzes with 2 n easueent channels and less calibation standad easueents. The eo coection algoiths ae both out-standing egading the siplicity and nueical obustness. The algoiths also allow an easy pogaing of the calibation and enable the eocoected easueent of any device iespective of the nube of pots (1 to n. Results of nueical expeients attest the excellent pecision of the GSOLT and the GT eo pocedue. The atheatical pocess to calculate fo the ulti-pot easueents the diffeential ode paaete is shown. The liitations ae discussed. Index Tes Netwok analyze, calibation, eo-coection, ulti-pot, ulti-ode, scatteing paaete. I. INTRODUCTION ON the one hand RF-electonics consue poducts with ulti-band applications ae a gowing aket and on the othe hand diffeential systes ae coing up due to bette noise and powe behaviou. Both syste tends esult in the fact that the nube of RF-pots is inceasing. E.g., a standad antenna switch odule fo GSM-tiple band applications has 9 RF-pots altogethe. To easue these ulti-pot poducts with an adequate accuacy, a ulti-pot vecto netwok analyze is needed. Twopot netwok analyzes ae well established. The hadwae expansion to ealize a ulti-pot netwok analyze based on the concept of a two-pot netwok analyze is well known and poduced by ost anufactues. Two-pot vecto netwok analyzes (VNAs ae ealized as a thee o a fou easueent channel (so-called double eflectoete concept. Fo ulti-pot VNAs based on double eflectoetes, calibation pocedues to coect all linea eos of the ipefect hadwae set-up ae well known [1]. Howeve, the GSOLT calibation pocedue is the fist one fo ulti-pot VNAs based on the cheape thee-channel concept. In pactice, netwok analyzes with no exact woking eo coection pocedue ae useless. This pape pesents the genealization of the classical SOLT two-pot pocedue, which is the standad eo coection fo thee-channel VNAs and double eflectoetes, too. This This wok was suppoted by Rohde Schwaz, Munich. Pof. H. Heueann is with the Univ. of Applied Sciences Aachen, Institute of High Fequency Technology. GSOLT-pocedue 1 allows accuate n-pot easueents with vecto netwok analyzes having only n1 easueent channels. Additionally, this pape pesents a vey siple atheatical foulation to pefo a ulti-pot calibation based on double eflectoetes,the so-called GT-pocedue 2. This pocedue equies vecto netwok analyzes with 2 n easueent channels fo a n-pot easueent. This algoith ay include evey known 7-te T- o L-pocedue, e.g. TRL, LMR, o the geneal TAN ethod [2]. The way to pefo a VNA eo coection is: 1 Measueent of well-known calibation standads 2 Calculation of the eo-coefficients = Calibation of the netwok analyze 3 Measueent of an unknown device unde test (DUT 4 Eo coection calculation of the DUT aw data by using the eo-coefficients This aticle begins with a shot desciption of the classical SOLT -te calibation pocedue. The atheatical deivation of the GSOLT calibation pocess pesents the calculation of the n 3 eo coefficients by using the eflection standads easueents. The issing n (n-1 2 eo coefficients can be calculated by using the tansission easueents. The second pat of the atheatical deivation of the GSOLT-pocedue is the novel and vey siple eo coection pocess. This vey shot atheatical solution is the key to pefo ulti-pot eo coection fo 1 to n pots all with the sae atheatical algoith. The last theoy section pesents a vey siple atheatical deivation of the GT ulti-pot VNA calibation and eo coection by using the 2 n easueent channel pefoance. The excellent confoity of the scatteing paaetes of ulti-pot veification standads geneated by a vitual ultipot VNA shows the syste accuacy of both pocedues. II. MULTI-PORT THEORY Fo SOLT two-pot easueents, eo coection algoiths ae published beginning with the -te pocedue to detect and in an uni-diectional way up to the 22-te pocedue to detect all fou scatteing paaetes of a two-pot in a leakage-eo syste [3]. 1 The nae GSOLT is the abbeviation of Geneal SOLT. 2 The nae GT is the abbeviation of Geneal T.

2 ROHDE SCHWARZ WORKSHOP, EUMC 2003,, OCTOBER A. The -Te Model The hadwae test-set fo an uni-diectional VNA is shown in Fig. 1. Fig. 1. Block diaga of a vecto netwok analyze with thee easueent channels Moe than 20 yeas ago the SOLT-pocedue was intoduced (e.g. [4]. This theoy descibes how to educe the test-set to a so-called scheatic block diaga, as shown in Fig. 2. and the elation between and yields 7 $ %! $',# (4,"$( Afte a e-oganisation of these equations, the eo coefficients, and - ae obtained:, 8 9 ' $ $#!%$(%:8 9 ' ( $; and - 8 < : $',(=; (6 All five eo coefficients can be calculated. B. GSOLT Calibation of a N-Pot VNA The siple way to calibate a ulti-pot VNA with the GSOLT-pocedue is descibed by using a thee-pot VNA. It is easy to extapolate these esults to n-pot VNAs. The block diaga with the eo netwoks of a thee-pot VNA is shown in Fig. 3. Fig. 2. odel Scheatic block diaga of a vecto netwok analyze fo the -te The scheatic block diaga includes the device unde test (DUT in scatteing paaetes and the two eo netwoks (atices and with the - and -eo coefficients. These five eo coefficients ae siila to scatteing paaetes, including the physical non-idealities of the test-set. Based on this -te odel ( unknown eo coefficients a siple elation between the easueent values, and the eflective one-pot device (eflection value can be deived: "! $' $#% (1 ( * Measuing the thee known eflection standads: shot (S, open (O, and load (L, o atch M with the known values,, and, thee equations ae available to calculate the thee eo coefficients,#, and$(. This fist step is also called eflectoete calibation. This step is used in ost cases whee only eflection easueents ae pefoed. In this case it is called 3-te pocedue (SOL- o MSO-pocedue. The othe eo coefficients, and - can be calculated fo the easueent esults of a thu-connection (T with the scatteing atix:./ 102 (2 2 3 Fo the elation of the easueent values to esults - 4 $' (3,"$(6 Fig. 3. Block diaga of a vecto netwok analyze with thee pots and fou easueent channels The (eal switch can be isatched, but it needs an isolation in the ange of the easueent dynaic. The block diaga shown in Fig. 3 can be sepaated into thee scheatic block diagas fo the thee states of the switch. The Figs. 4 and illustate the scheatic block diagas fo the fist and second state of the switch with the included eo coefficients. The calibation pocess fist consists of n (hee n=3 eflectoete calibations. These thee eflectoete calibations bing up 9 eo coefficients?>,?> #,?> (,?>>,?>> #, ( 3. The second calibation step is based on the thu-connection easueents between all pots: Fo evey state of the switch, the second pat of the -te pocedue is used twice: The fist state of the switch delives A>, and A> - as well >, >- by using equations siila to ( and (6. The second state of the switch povides the calculation of?>>,,?>> - fo ( and (6 and the thid state helps to deteine, >>>, - >>>,, >>>, and - >>>. 3 The nube of pies stands fo the state of the switch.

3 9 E # 9 ROHDE SCHWARZ WORKSHOP, EUMC 2003,, OCTOBER Fig. 4. Scheatic block diaga of a thee-pot VNA fo the fist state of the switch GHD D D GH K K K K IJLGH B K K B B A thee-pot scatteing atix is defined as follows: (12 We have aleady calculated thee sets of eo coected (highly accuate incident and eflected wave values which each fit equation (12. Finally, we can cobine the thee sets of scatteing paaete equations to the atix equation GHD D > D >> D > D >> D >>> >>> D > D >> D >>> MNPO GH Q Q K K Q K MR S O GHB B > B >> B > B >> B >>> >>> B > B >> B >>> MT O (13 Fig.. Scheatic block diaga of a thee-pot VNA fo the second state of the switch Geneally, the nube of eo coefficients is 3 n fo the eflection calibation steps and 2 n (n-1 fo the tansission calibation steps, i.e. 2 n n eo coefficients altogethe. C. GSOLT Eo Coection Pocess 0 > B > 3 C0?>?>?> ( 3 Using Fig. 4, the scatteing paaete elation 0 > D (7 > 3 is valid fo the popeties at pot 1. The incident and the eflected wave at pot 1 of the DUT can be calculated fo equation (7: B > >!?> # > : > ' > > ; (8 D > # > : > ' > > ; (9 All othe elations between the easueent values of the fist state of the switch, the eo coefficients, and the waves at the pot 2 and 3 can be diectly picked up fo Fig. 4: D > > -> B > A>, > (10 -> D >F >- >F (11 >- The waves B >> D, >>, B >> D,... >>> can be calculated in a siila anne fo the second and the thid state of the switch. The eo coection equation is siply expessed in a atix foulation:.u V W (14 The obustness of an eo coection algoith is vey ipotant [2]. Please note, that the tace values of the atix WP ae neve low o zeo. This is an ipotant fact fo a vey good nueical quality of this siple GSOLT eo coection equation. D. GT Calibation of a N-Pot VNA The way to calibate and to eo-coect the ulti-pot VNA with the GT-pocedue is descibed by using a theepot tiple eflectoete VNA. These esults can easily be extapolated to n-pot VNAs. The block diaga with the eo netwoks of a thee-pot tiple-eflectoete VNA is shown in Fig. 6. Fig. 6. Block diaga of a vecto netwok analyze with thee pots and six easueent channels (tiple-eflectoete The (eal switch can be isatched and it does not need a pefect isolation [2]. The block diaga shown in Fig. 6 can be sepaated into two double-eflectoete VNAs: Using the fist and second state of the switch, the eo atices YZ and []\ can be calculated with a standad two-pot calibation T-pocedue. With the fist and thid state of the switch, the 7 paaetes of the eo

4 _ ROHDE SCHWARZ WORKSHOP, EUMC 2003,, OCTOBER boxes A and B^ ^ can also be calculated by using a Tpocedue. The notation is using the tansission paaetes àu YZ bu []c (1 with the easueent atix `du fo the DUT beu [2]. The nube of eo coefficients is 3 fo the eo box A and 4 (n-1 fo the tansission calibation steps, i.e. 2 (n-13 eo coefficients in total. E. GT Eo Coection Pocess It is useful to invet the eo atices fo the GT ultipot eo coection pocess. fz YZ gc []c :h ji i i ; (16 Refeing to Fig. 6, the elations 0 D B 3 fz 0 ( D B 3 g\ D B 3 g\ \ 0 < F (18 3 apply to evey state of the switch fo the inveted tansission paaetes. That eans that fo a thee-pot, all thee sets of eo coected incident and eflected wave values which each fit equation (12 can be calculated with high accuacy. Finally, we can cobine the thee sets of scatteing paaete equations to the atix equation (13 and use equation (14 to calculate the eo-coeted scatteing paaetes. III. A COMPARISON OF GSOLT AND GT The advantages of GT: k Less calibation easueents. k Many possible calibation standads. k Easy to ealize self-calibation standads can be used. k Switch can have poo isolation. The advantages of GSOLT: k Less easueent channels = cheape VNAs. k Based on the ost used SOLT-pocedue = calibation standads ae widespead. k Moe obust fo high dynaic easueents. IV. RESULTS OF NUMERICAL EPERIMENTS The GSOLT-pocedue is ipleented in the ulti-pot netwok analyze 4 [] since Oct and pefos in an excellent way as shown in [6]. The best way to ake a copaison between two calibation pocedues is the use of easueent data of a vitual VNA. The conditions of this softwae-vna ae well known. Thee ae no e-connection eos o othe unknown eos in the syste. To ealize a copaison between the GSOLT- and the GT-pocedue, the data of a vitual VNA wee used with 4 A siila softwae in special RS-ulti-pot-VNA solutions. typical values fo leakage and eflection coefficients of the test-set and the signal/noise atio of -9 db. Fo the GT-pocedue the geneal TAN-pocedue [2] with atch- and eflect-standads was used. The eflectstandad was a shot. The ostly used veification standad is a 20 db attenuato. Fig. 7 illustates that both pocedues wok vey accuately fo the tansission of this attenuato Magnitude S21 (db: GSOLT Magnitude S21 (db: GT Fequency (GHz Fig. 7. Eo coected ulti-pot scatteing paaetes of a 20 db attenuato pefoed by using the GT- (solid and the GSOLT-pocedue (dashed Howeve, the lagest agnitude of easueent eos fo eflection easueents appeas fo both pocedues at pot 3. But the eo coected esults ae vey siila as shown in Fig. 8 and they ae quite sall (exact value: -40 db. Magnitude S33 (db Fequency (GHz Fig. 8. Eo coected ulti-pot scatteing paaetes of the etun loss of a 20 db attenuato pefoed by using the GT- (solid and the GSOLTpocedue (dashed

5 J J ROHDE SCHWARZ WORKSHOP, EUMC 2003,, OCTOBER 2003 All investigations show that diffeences between both pocedues up to values of -0 db can be neglected. In a eal syste the non-pefect calibation standads ae the ain influence on the easueent accuacy. In pactise it should be easy to cay out the eo coection of the easueent data of a well-atched and high isolating device. Howeve, Fig. 9 shows that the GSOLT-pocedue is oe suitable in this case than the GT-pocedue. Magnitude S23 (db Magnitude S23 (db Fequency (GHz Fig. 10. Eo coected ulti-pot scatteing paaetes of the isolation between a is-atched device pefoed by using the GT- (solid and the GSOLT-pocedue (dashed Fequency (GHz Fig. 9. Eo coected ulti-pot scatteing paaetes of the isolation between a well-atched device pefoed by using the GT- (solid and the GSOLT-pocedue (dashed Nevetheless, in pactise high isolation devices ae isatched ones, e.g. filtes. The GSOLT-pocedue shows a bette pefoance than the GT-pocedue (Fig. 10 fo wost case conditions of high eflective devices. V. MULTI-MODE THEORY A device unde test with diffeential in- and output is shown in Fig. 11. This diffeential device unde test (DDUT can be discibed with the dual ode atix `d : lgh D D I n D D LopqZ st u lgh B B I n B B (19 A signal flow diaga of these M-paaetes is illustated in Fig. 12. The calculation of the M-paaetes fo ulti-pot S- paaetes is possible if: k the DDUT has gound-couple pots only and k the DDUT is a passive device o k with two 0v /180v hybids fo an active device. To deive the M-paaetes, the elations between the unsyetical waves and the diffeential and coon ode Fig. 11. Illustation of a diffeential device unde test (DDUT with ultiode paaetes waves ust be used. B w x :B P! B ; B y :B ' B ; (20 D w x :D! D ; D y :D ' D ; (21 B w x :B! B 9 ; B y :B ' B 9 ; (22 D w x :D P! D 9 ; D y :D ' D 9 ; (23 Afte a longe calculation we obtain: M-paaetes fo the diffeential ode: x : P!% ' ' ; (24 x :!% 9 ' 9 ' ; (2 x : P!% 9 ' 9 ' ; (26 x :!% 9 9 ' 9 ' 9 ; (27

6 ROHDE SCHWARZ WORKSHOP, EUMC 2003,, OCTOBER Additionally, a siple, obust, and easy to poga algoith fo the GT-pocedue has been discibed. This ulti-pot pocedue shows benefits egading the calibation standads and a dawback egading the use of expensive 2 n channel netwok analyzes. The ulti-ode M-paaetes have been intoduced. It was shown, that the linea elations between M- and S-paaetes hold fo a lot of devices. ACKNOWLEDGMENT The autho would like to thank the RF-devision of Rohde Schwaz, especially Chistian Eves, who ade it possible to publish this aticle. Fig. 12. Signal flow diaga of the ulti-ode paaetes M-paaetes fo the coon ode: x : P!%!"!% ; (28 x :!% 9!" 9!% ; (29 x : P!% 9!" 9 P!% ; (30 x :!% 9 9!" 9!% 9 ; (31 Convesion paaetes fo the diffeential into the coon ode: x : ' ' P!% ; (32 x : ' 9 ' 9!% ; (33 x : ' 9!% 9 ' ; (34 x : ' 9 9 ' 9!% 9 ; (3 Convesion paaetes fo coon into the diffeential ode: x : '!% ' ; (36 x : ' 9!% 9 ' ; (37 x : ' 9 ' 9!% ; (38 x : ' 9 9!% 9 ' 9 ; (39 VI. CONCLUSION A geneal calibation and eo coection algoith that can be ipleented in any vecto netwok analyze has been pesented. This so-called GSOLT-ethod woks fo 1-pot easueents as well as fo n-pot easueents. The novel eo coection algoith is obust and easy to poga. This well tested pocedue allows to pefo accuate n- pot easueents with a netwok analyze with only n1 easueent channels. REFERENCES [1] Feeo, A., Pisani, U., Kewin, K.J., A New Ipleentation of a Multipot Autoatic Netwok Analyze, IEEE Tans. Micowave Theoy Tech., vol. 40, Nov. 1992, pp [2] Heueann, H., Schiek, B., Robust Algoiths fo Txx Netwok Analyze Pocedues, IEEE Tans. Instu. Meas., Feb. 1994, pp [3] Heueann, H., Schiek, B., Results of Netwok Analyze Measueents with Leakage Eos Coected with Diect Calibation Techniques, IEEE Tans. Instu. Meas., IM-, Oct. 1997, pp [4] Hewlett Packad, Autoating the HP 8410B Micowave Netwok Analyze, Application Note 221A, Jun [] Heueann, H., Faby, H.-J., Ballann, R., Kalibievefahen zu Duchfühung von Mehtoessungen basieend auf den 10-Te- Vefahen, Invention P , , Aktenzeichen: [6] Heueann, H., GSOLT: The Calibation Pocedue fo all Multi-Pot Vecto Netwok Analyzes, MTT-S Intenational Micowave Syposiu, Philidelphia, 2003, pp Holge Heueann (M 92 was bon in Wagenhoff, Niedesachsen, Geany, in He eceived the Dipl.-Ing. (FH degee fo the Fachhochschule Baunschweig-Wolfenbuettel in 1988 and the degee Dipl.-Ing. fo the Univesity of Bochu 1991, both in electical engineeing. Fo 1991 to 199, he was a eseach assistant at the Univesity of Bochu, Geany, woking in the field of high-fequency easueent techniques and industial applications of icowaves. Fo 199 to 1998 he was woking at Rosenbege Hochfequenztechnik, Tittoning, Geany, whee he was engaged in the design of high fequency equipent, especially fo the calibation of netwok analyzes. In 1998, he joined Infineon Technologies, Munich, Geany, leading a developent goup fo wie-less font-end odules and cicuits. Since 2002, he has been with the Univesity of Applied Sciences Aachen, Geany, whee he is cuently a Pofesso, leading the Institute of High Fequency Technology. His cuent eseach inteests include passive and active high fequency coponents, design of RF font-end cicuits, as well as high pecision-, ulti-pot-, and ultiode-scatteing paaete easueents. He is ebe in the icowave easueents technical coittee MTT-11.