Comparison of on-wafer calibrations using the concept of reference impedance

Compa ison o on-wa e calib a ions using he concep o e e ence impedance each o he as ollow: F ancesc Pu oy, Lluls P adell Uni e si a Poli ecnico de Ca olunyo, Depo men o signol heo y and communico ions, ETSE Telecomunicaci6. Ap. 30002 - 08080 Ba celona. Spoin Abs ac A no el me hod ha allows o compa e di e en calib a ion echniques has been de eloped. I is based on de e mining he e e ence impedance o a gi en Ne wo k Analyze calib a ion om he e lec ion coe icien measu emen o a physical open ci cui . The me hod has been applied o se e al on-wa e calib a ions. In oduc ion Many sel -calib a ion echniques o Ne wo k Analyze s ha e been p oposed o da e. A conside e o has been also de o ed o de elop me hods o compa e calib a ions. One way o do ha compa ison is measu ing a known s anda d and de ine an e o unc ion ha allow o compa e di e en echniques. Ano he way consis o compu ing a calib a ion e e ence impedance o each echnique, and compa e he di e en alues. Some au ho s [1] assume he e e ence impedance o a calib a ion based on lines (TRL) o be he cha ac e is ic impedance o hese lines, and he e e ence impedance o a calib a ion based on a ma ch (LRM) o be he ma ch impedance. Howe e his assump ion is no so ob ious as i seems, and less ob ious when a echnique like LRM(known- e lec ) is used. O he au ho s [2] ob ain di e en esul s compu ing he e e ence impedance om a benchma k TRILL calib a ion. In he line o he wo k p esen ed las yea [3] we p opose a no el me hod, consis en wi h he e e ence impedance concep , wi hou making any assump ions abou he e e ence impedance na u e. This me hod gi es a di ec way o compa e di e en echniques because i does no e e he e e ence impedance o any benchma k calib a ion. Re e ence Impedance Concep We de ine he e e ence impedance associa ed o a gi en calib a ion p ocedu e as he impedance o which he S- pa ame e s keep ac ually e e ed a e comple ing calib a ion. In consequence he measu ed (compu ed COmp ) e lec ion coe icien can be exp essed in e ms o a complex e e ence impedance 141 using he ollowing exp ession: ,.Mp = Zac Z e imp camp Z +Z,m ac .imp Eb=- a Ea-Eb=Ec(b- 1) Ea+Eb=Ec(b+l) (2) - Using (2) he compu ed e lec ion coe icien can be exp essed as ollows: z -Eb a 1 +Eb 'COW z l-Eb Z +ZO ac 1 +Eb (3) Z ac _Z COMP M ac Assuming ha ZMac is eal, his exp ession shows ha he e e ence impedance is he impedance o he ac ual ma ch. In addi ion i co ec s he e o s dues o inaccu a e knowledge o he load calib a ion s anda d. Al hough he meaning o he e e ence impedance is no clea and should be in es iga ed u he , i can be used as a es ima o o he goodness o a calib a ion me hod in o de o compa e di e en me hods. Compa ison Me hod The i s s ep is o pe o m he di e en calib a ions ha will be compa ed. Then he calib a ions a e used o measu e a known impedance. In o de o ha e an op imum compa ison he measu ed impedance should be he same o all calib a ions. A good choice is a physical open ci cui . The open ci cui can be modeled as a capaci o , wi h an unknown capaci ance. Fo on-wa e calib a ion we p opose o compu e he capaci ance alue by en o cing he e e ence impedance o a LRM (Ideal Ma ch) calib a ion a a gi en low equency o be exac ly 50 Q. This is jus i ied because he Ma ch s anda d in a LRM (Ideal Ma ch) calib a ion is a esis o immed o 50 Q wi hin a 0.3% e o . F om his assump ion and using (1) he e e ence impedance o any calib a ion can be compu ed om he nex exp essions: 1 1-1 e(z e )P= C m ) 1+Pcomp am(z ,e,@- 1( (1) Whe e (Zac ) is he ac ual alue o he load unde es , and (Z e .imp) is he e e ence impedance o he calib a ion. Al hough i is a widely used concep , i has no been ye shown ha he calib a ion e o s due o he incomple e knowledge o he calib a ion s anda ds can be ep esen ed by a change in he e e ence impedance. Suppose he simple case o a one po OSL (Open-Sho -Load) calib a ion pe o med using pe ec ly known and ideal open and sho s anda ds and a load s anda d no ideal whose e lec ion coe icien is no known ( Mac ). Th ee e o coe icien s: a',b' and c' a e ob ained wi h some e o : Ea=a-a', Eb=b-b' and Ec=c-c', whe e a,b,c a e he ac ual e o coe icien s (a=eloeol-eooell, b=eoo, and c=-ell). Suppose ha a=1, b=eoo and c=0. The e o s due o he inco ec knowledge o he load e lec ion coe icien (Ea = 1-a', Eb =b-b ', Ec = -c' ) a e ela ed (4) (5) - Whe e comp is he compu ed e lexion coe icien o he known es impedance, and i is assumed ha : Z e imp Z e /imp Expe imen al Resul s and Discussion In o de o es his me hod we applied his echnique o se e al on-wa e sel -calib a ion me hods, using a SUMMIT 9000 On-Wa e S a ion [5] p o ided wi h a LRM calib a ion subs a e. The di e en calib a ion echniques a e shown in he ollowing able. No e ha when an on-wa e calib a ion is pe o med wo di e en physical open ci cui s can be chosen: Fi s e lec is 857 NAM_: THRU: REFLECT: 3 h SlhML STANDARD: L_M I ps LINE AIR-OPEN/STUB-OPEN MATCH (KNOW MATCH) _ . LRRM AIR-OPEN,SHORT/ MATCH STUB-OPEN,SHORT TRL AIR-OPEN/STUB-OPEN 10&40ps LINE TAR 10 dB ooooo AT'ENUATO R LRM MATCH (KNOW-REFLE) -__-____-- _ _ __. done by lea ing he p obes in he ai ( e e ed o as ai -open), second is done using a lps open-ended s ub ( e e ed o as s ub- open). I a calib a ion using a s ub-open ins ead o an ai -open as he e lec s anda d is pe o med, he ip- o-subs a e ansi ions a e included in he e o e ms. In his case he ai -open can no be modeled as a capaci o , because ansi ion e ec s a e no included in i . The e o e, a s ub-open has o be used as he known es impedance in o de o compu e he e e ence impedance when a s ub-open is used as a e lec in a known ma ch LRM calib a ion. Howe e we es ed bo h possibili ies, which a e shown in Fig 2, and Fig 3. In Fig 2 he compu ed e e ence impedance using a s ub-open as a e lec , excep o he LRM(Known- e lec ) calib a ion whe e an ai -open has been used as he e lec s anda d, has been plo ed. In Fig 3, an ai -open has been used as he e lec s anda d. I he e e ence impedance o TRL, when a ai -open has been used as a e lec Fig 3., is examined and compa ed wi h Fig 17 whe e he cha ac e is ic impedance o a 40 ps line is plo ed, a simila equency beha iou is obse ed. On he o he hand i he compa ison is done be ween Fig 1 and Fig 3 he beha iou is mo e di e en . The low- equency inc emen due o he loses e ec can be minimised i we use a s ub-open as e lec s anda d, because losses a e included in all he s anda ds and hus co ec ed by he calib a ion (Fig 2). Ano he impo an poin is ha he 'o e lap' e ec [61 can be co ec ed simply by using a s ub-open as he e lec s anda d. This can be seen in Fig. 1 whe e LRM (Known-Ma ch) and LRRM calib a ions, ha has been de eloped o o e come he 'o e lap' e ec , gi e a e y simila e e ence impedance alue. I is impo an o obse e ha he TAR calib a ion exhibi he wo s e e ence eac ance beha iou (Fig 2.) due o he ac ha he a enua o impedance is much less ideal han he Ma ch o Line s anda d impedances. Conclusions In his pape he e e ence impedance concep has been de ined as well as an easy way o compu e i unde some hypo hesis. This me hod has been used o compa e di e en calib a ion echniques. I has been shown ha he low- equency beha iou o he ansmission lines cha ac e is ic impedance can be co ec ed by he calib a ion i a s ub-open is used ins ead o an ai -open as he e lec s anda d. Ano he impo an esul is ha he 'o e lap' e ec is co ec ed by he calib a ion i a s ub-open is used as he e lec s anda d gi ing a simila esul o LRRM. Re e ences [1] F. Williams. "Cha ac e iza ion o Thin-Film Calib a ion Elemen s.". ARTFG Con e ence Diges , pp 25-35. Win e 1991. [2] D.F. Williams, R.B. Ma ks. "Compa ison o On-Wa e Calib a ions". 38 h ARTFG Con e ence Diges , pp 68-81. Win e 1991. [3] Ll. P adell, M. Cace es, F. Pu oy. "De elopmen o Sel - Calib a ion Techniques o On-Wa e and Fix u ed measu emen s: A no el app oach". 22 h Eu opean Mic owa e Con e ence, pp 919- 924. Helsinki. Sep . 1992 [41 K. Ku okawa. "Powe Wa es and Sca e ing Ma ix". IEEE T ans. Mic owa e Theo y and Tech., ol MUT-13, pp 194-202, Ma 1965. [5] CASCADE MICROTECH. "SUMMIT 9000. Analy ical p obe s a ion. Ins uc ion Manual" [6] A. Da idson, K. Jones, E. S id. "LRM and LRRM Calib a ions wi h au oma ic de e mina ion o load induc ance". 36 h ARTFG Con e ence Diges , pp 57-63. No embe 1990. Real{ C.impedance } - 20 30 40 GHz Imag{ C.impedance } - - J-T I- - - - 2 0 -2 -4 -6 L. 0 10 20 30 40 GHz Fig 1.- Cha ac e is ic impedance o a CPW line. 858 60 55 50 45 40 35 301- 0 10 Real( Re e ence impedance) 60 - 55 50 ,- _ 1.J? ;.- ,< 45 0 40 35 30 3 2 1 0 -2 5 10 15 20 25 30 35 20 GHz Imag{ Re e ence impedance} GHz Fig.2.- Re lec =s ub-open, o all calib a ions Real{ Re e ence impedance) ~~~-T-- GHz Imag{ Re e ence impedance) 3' i IL IN ,CA %° 0 5 10 15 20 25 30 35 40 GHz Fig 3.- Re lec -=ai -open excep :LRM(Known-Re lec )7Re lec - ai -open (*) LRM(Known-Ma ch)[--l,LRRM[i,TRL- .],TAR[ooI,LRM(KnowC- xiii )[-I 859