transition characterisation for de-embedding purposes

7/28/2019 Transition Characterisation for de-embedding Purposes

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TRANSITION CHARACTERISATION FOR DE-EMBEDDING PURPOSES

S . R . Pennock*, C . M . D . Rycroft**, P . R . S he phe rd * a nd T . Rozzi*

ABSTRACTA technique for characterising tran s ition s b etwee n different transmissionline media i s examined. Applications include development of novel circuitmedia and use as a de-embedding measurement tool. The technique r e q u i r e smeasurement of only two sets of back to back t r a n s i t i o n s , separated b ydifferent, known, electrical l e n g t h s , and i s therefore simple to i m p l e m e n t .Both theoretical and measured results are p r e s e n t e d .1 . INTRODUCTIONA commonly encountered p roblem i n microwave measurements results from thefact that measurement equipment exists i n the s tan da rd tran s mi s s io n mediaof waveguide or co-axial cable, while the device to be measured exists i nsome other transm is si on m ed ium ( t h e device m e d i u m ) . I n order to performthe desired measurements, either the measurement equipment has to be cali-brated onto the de vic e m ed iu m [ 1 , 2 ] , or the transition onto the devicemedium must be characterised sufficiently to allow a d e-em bedd ing calcula-tion to be performed. This characterisation has often been done in thepast by mathematically modelling the transitions. These models may be ofdubious q u a l i t y , and are often very limited i n frequency range.Calibrating onto the device medium can present difficulties i n that stand-ards (open/short/offset/match) have to be constructed, and this can beparticularly difficult when dealing with novel transmission media. Highlyreflective loads can often be fabricated quite easily, but in order to givethe measurement system good dynamic range high quality matched loads areneeded. Fabricating a ma tc he d l oad r eq uir es either a prior knowledge ofcharacteristic impedance, or well matched transitions onto the novel mediumso that the quality of a matched load fabricated on that medium may bemeasured. However, high quality transitions need to be tested, usuallyrequiring a matched load on the n ov el m ediu m, hence we are in an unbreakablecircle.The f ir st p ar am et er of a novel medium that i s most accessible, bo th t he or et -i c a l l y an d experimentally, is the g uide wav elength . Characteristic imped-ance measurements need good transitions, even using time domainreflectometry. In this paper we describe a procedure that us es measure-ments of pairs of back to back tra ns itio ns to evaluate the scatteringparameters of the transitions. Hence the quality of the transitions maybe t e s t e d , and de-embedding calculations can then be performed to allowevaluation of components formed i n the novel transmission medium.The technique presented here relies on fabricating back to back transitionswith two different electrical separations. The accuracy of the resultsobtained must depend upon the repeatability of transition construction,but repeatability i s a problem in every measurement method i n this field.The technique i s based on that shown by Gupta et a l [ 3 ] , but that work was* University of Bath, U K . ** Marconi Research C e n t r e , Chelmsford, U K .

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restricted only to identical, reciprocal transitions where S 2 2 < < 1 (goodmatch onto novel medium). In this paper we show that it i s only the casew he re t ra ns i ti on s are identical that this procedure will evaluate thescattering parameters of the transitions exactly. In the more generalcase of non-identical transitions, various multiples and ratios of thetransition scattering parameters may be calculated. This information issufficient to allow nearly complete de-embedding calculations to beperformed. The S 1 2 and S 2 1 of the embedded device can be found exactlywhile the S , j and S 2 2 are found multiplied by ratio of the S12Is of thetransitions ( S i z c / S l 2 d ) C This ratio i s n ot e xpe ct ed to be too far removedfrom unity for reasonable transitions.2 . THEORYWith reference to the ca sc ade s how n in Figure 1 , the measurable wave trans -mission matrix of the complete circuit [M] may be written in terms of thetransmissi on matrices of the i nd iv id ua l e lement s. The transitions arerepresented as [ C ] a n d [ D ] , and if their matrices are known, device perform-ance on the novel media may be measured through

[ M ] = [ C ] . [ X ] . [ D ] [ X ] [ C ] - 1 . [ M ] I DThe transmission and scat teri ng m at ri ce s are uniquely related [ 4 ] , and sodetermining the transition scattering parameters will allow thede-embedding to be performed in this manner. To determine the transitionscattering parameters we examine what may be deduced from two measurementsof the transitions with different, k n o w n , electrical separations.( a ) Characterisation procedureW it h r ef er en ce to Figure 2 , the circuit may be analysed using Mason'srules to give the S-parameters of the complete circuit - the measurableS-parameters of the circuit. The equations f o r two such circuits withdifferent electrical s e pa ra tion s b etwe en the transitions may be manipula-ted to g iv e s ev era l combinations of the transitions S-parameters, as wellas Sl and S ' ' d

F 1 = S 2 2 d S l 2 C / S l 2 d ; F 2 = S 2 2 c S 2 1 d / S 2 1 cP i = S 2 2 c S 2 2 d ; P 2 S 1 2 d S 2 1 C P 3 = S 1 2 c S 2 1 d '=4 S 22S 12 d S 2 / d / 12lc c S 2 2 d S 1 2 c S 2 1 c / S 1 2 d S 2 d

P 6 = S 1 2 c S 2 l c S 2 2 d P 7= S 1 2 d S 2 1 d S 2 2 cThese factors d o not allow unique determination of the entire S-matrix ofeach t r a n s i t i o n , but are sufficient to allow d e - e m b e d d i n g of the S-matrixof a device measured through these transitions. O n l y in the c a s e ofidentical transitions can S 2 2 and S 2 2 d be u n i q u e l y determined as F 1 andF 2 , and hence the S 1 2 S 2 1 multiples also follow e x a c t l y .( b ) De-embedding calculationThe d e-em bedd in g ca lc u l at ion requires the inverses of the wave trans-mission m a t r i c e s :

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AS c- S i I -

S 2212c)

1D = s 2 ' d

A S d SI 1- S 2 2d 1

bearing in mind the switch in port definitions for transition D . Theelements of the transmission matrix of the device under test ( D U T ) maybe expressed in terms of the measured transmission matrix [ M ] , and theparameters deduced from the characterisation procedure:

+ m i 2 1 ) + M 1 l ( P 2 P 3 - P 6 S 1 d )- m l 2 ( S i I P i - P 6 )

= ( S c P 1 - P6)(Slldrnrl + M l n 2 )= ( SL d P i -P 7 ) ( m 2 1 - S l ml1 )

- S t lm 2

+ P L ( S l l d m 2 l + M22 )- P1(m22- m12S1l1)

The extra S-parameters in the LHS of these expres sions have been intro-duced to enable calcu lation in terms of known quantiti-es. The conversionto scattering matrix fo rm gives:Sii -- , [ I X 2 1 S 2 2 C ] / ( X 1 l S 1 2 cS21dS2 2 C )

S1 2 = X2 2 - [ X 1 2 S 2 2 d][x21S22C] /(XlPl)S 2 2 =[ X 1 2 S z 2 2 d]/(XX512 d S 2 1 c S 2 2 d )

( S 1 2 d / S 1 2 C ) [ X 2 l S 2 2 C ] / ( X 1 1 P 7 )

) / P3

= ( S 1 2 c / S 1 2 d ) [ x 1 2 S 2 2 d]/(xlP 6 )so the O U T S-matrix is determined to within a mu ltiple of ( S 1 2 /Sl2d) onS l l a nd S 2 2 . F or reasonable quality transitions the individuaiS 1 2 S o f the transitions would be expected to be near unity, as in de e dw o u l d the r a t i o of t h e s e quantities.3. EXAMPLES(a) TheoreticalTo illustrate the technique we consider the case of identical transitionsconsisting of a 3nH series inductance and a l pF shunt capacitance. Thetransmission line characteristic impedance is 50 Q a nd it s phase constanti s that of free s p a c e . Separations of 5 and 6cm are used to generate theS-parameters of the two c a s c a d e s , but these data are then rounded tointerval s of 0.2dB in modulus and 1 of phase t o indicate the sensitivity ofthe procedure to finite accuracy measurements. In addition, when dealingwith a novel medium, its phase c o n s tan t may not be known exactly. In thisc a l c u l a t i o n a deliberate 5% reduction in phase constant for one line is usedto indicate t he effect of such errors.

357

1C =

1 2 C

X 1 2 S 2 2d

x 2 i S 2 2X =2 iM 2 2 + S 1 l dM 2 1 - S i lc S l ldm l l

x i i = ( S "d P i -P 7 ) ( M i l s i l c

S 2 1 " " : P 3 / X l 1


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Figure 3 shows the perfect S of the transition ( s m o o t h c u r v e ) andthat calculated by the charaUcerisation procedure with the abovementioned errors. Clearly errors are large near 1 5 G H z , where the lcmdifference in transition separation corresponds to half a wavelength( X / 2 ) . The regular period t o the error i s caused by the 5% reductionin phase constant, while the more general ' r o u g h n e s s ' of the data isthe result of the finite accuracy we imposed on the S-parameters ofthe complete circuits (corresponding to finite measurement accuracy).Figure 4 shows the ratio of calculated to perfect d a t a , and e rro rsare typically no more than 5% below 15GHz and 10% above.Most of the parameters i n the calculations are evaluated by differentroutes - the final answers being the average of the calculations.The total modulus of the data spread ( t h e ' v a r i a n c e ' ) i s shown i nFig. 5 . Where the difference in separation equals X / 2 ( 1 5 G H Z ) . thedata i s clearly suspect. It i s also apparent that using a s e p a r a t i o ndifference of less than X / 2 gives the m os t a cc ur at e results. I n d e e d ,Gupta et a l indicated an optimum difference of X / 4 to minimise er r or sdue to inaccurate electrical length data.Figure 6 shows the comparison for the S 1 2 S 2 1 m u l t i p l e . Again the data isworse above 15GHz than below and highly variable at 15GHz. The regularperiod to the error results from the phase constant error, while the' r o u g h n e s s ' caused by the i na cc ur ac y i mp os e d on the input data is clear lyapparent below 15GHz.( b ) MeasuredA pair of back to back tr ans ition s b et we en coax and microstrip were con-structed, the transitions being SMA/microstrip launchers and the microstripbeing made on Duroid 5880 with E r = 2.2 and Z0=50. Figures 7 , 8 and 9show the S-parameters of the transitions. The S I , and S 2 2 of the transitionsare g ener al ly b el ow -30 dB, and the calculation is somewhat prone to calib-ration errors as the measured devices are 'non-insertable' giving the sharpresonances. The transmission characteristic shows the insertion loss ofeach transition exceeding 0.5dB for frequencies above 9GHz. With nocorresponding rise in transition reflection at this frequency, the lossmechanism appears to be a combination of resistive losses at the l a u n c h e r /microstrip contact and radiation at the launcher ( a s these are opend e v i c e s ) .4 . CONCLUSIONSWe have presented an analysis that uses two measurements of pairs of sep-ar ated back to back transitions to evaluate the performance of thosetransitions. All that need be known i s the phase constant of the trans-mission line between the transitions, and that the transitions can beconstructed repeatabl y. Whil e unique determination of the transitionS-parameters i s only possible i f al l four transitions are identical,sufficient information may be extracted to allow de-embedding of devicesmounted between dissimilar transitions.5 . ACKNOWLEDGEMENTWe are g r a t e f u l to the SERC for supporting this w o r k , in part, u nder Gr an tN o . G R / C / 8 4 1 7 0 "Finline Components for Millimetre Wave Applications".

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6 . REFERENCES[ 1 ] D.E. C a r l t o n , K.R. Gleason & E.W. Strid, "Microwave Wafer ProbingMicrowave J . vol. 2 8 , p . 1 2 1 - 1 2 9 (1985).[ 2 ] P.R. Shepherd & R.D. Pollard, "Direct Calibration and Measurement ofMicrostrip Structures on Gallium A r s e n i d e " , IEEE MTT-34 ( 1 9 8 6 ) p . 1 4 2 1 .[ 3 ] K.C. Gupta, Ramesh Garg & Rakesh Chadha, "Computer Aided Design ofMicrowave Circuits", Artech H o . 1981.[ 4 ] R.E. Collin, "Foundations for Microwave E n g i n e e r i n g " , M c G r a w - H i l l 1 9 6 6 .

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transition characterisation for de-embedding purposes

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