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ABSTRACT ADITYA P. GOSWAMI. Implementation of

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1. 49 Characteristic impedance magnitude calculated using the ETRL al LOFTS 4875 ein gab EA ld eee Ca e d a de La te dh BS ste 50 Characteristic impedance phase calculated using the ETRL algorithm 51 Propagation Constant magnitude using l m lines 52 Propagation Constant phase using l m lines 53 Error network S parameters magnitude using lom lines 54 Error network S parameters phase using l m lines 55 De embedded S parameters magnitude of the DUT 56 De embedded S parameters phase of the DUT 57 De embedded Medium line S parameters Magnitude using the long and medium line as the line and through standards 82 Final Front Panel for TL calibration 85 Chapter 1 Introduction 1 1 Motivation As clock speeds increase each year the accurate knowledge of transmission line ef fects is needed to successfully design and fabricate electronic systems There are two methods of determining these effects One these effects can be predicted by using electromagnetic field theory also known as analytical modelling and two these parameters can be measured experimentally leading to what is known as empirical modelling Discontinuities can be described by S parameters The Vector Network Analyzer VNA is used to measure S parameters whereby a single frequency sinusoid is applied to the network or Device under Test DUT and t
2. final_gamma k 1 int_gam k 1 L beta k 1 imag final_gamma k 1 if beta k 1 lt 0 amp adflag 0 amp abs beta k 1 gt twobetac 9 0 20 0 adjust twobetac adflag 1 elseif betam5 lt 0 amp betam4 lt 0 amp betam3 lt 0 amp betam2 lt 0 amp betami lt 0 amp beta gt 0 adflag 0 end betamb betam4 betam4 betam3 betam3 betam2 betam2 betaml betami beta k 1 g_ans k 1 real final gamma k 1 i abs beta k 1 adjust end gamma int cat 2 freq g ans retval gamma int 72 A 7 tl Purpose Calculates the error network parameters for the two port TL calibration Output Format Real Imaginary Array ordering freq S11 S21 12 22 Usage This routine is called internally from within the tl_calib routine Code function retval trl thru line rthru stor thru rline stor line freq vect xlsread freq xls rerror for idx 1 size thru 1 gammasc thru idx 2 thru idx 3 rt rthru idx 2 rthru idx 4 rthru idx 3 rthru idx 5 rl rline idx 2 rline idx 4 rline idx 3 rline idx 5 t rl inv rt tmpa t 2 1 tmpb t 2 2 t 1 1 tmpc t 1 2 al tmpb sqrt tmpb 2 4 tmpa tmpc 2 tmpa a2 tmpb sqrt tmpb 2 4 tmpa tmpc 2 tmpa if abs a2 gt abs al ac a2 b al else ac al b a2 end wi gammasc a wi b 1 0 1 0 w1 ac c a ac r22 s
3. 21f pem Similarly for an open circuit placed at the Port 1b of A gives the result 2 a oc 7 0 E 2 8 p 3 2 8 From Equations 2 6 2 9 the short circuit reflection coefficient and the open circuit reflection coefficients can be expressed as a function of the measured fixture S parameters as Pse Suf Soir 2 9 Poe Ouf Sap The above results are used in the later chapters while explaining the Through Line Calibration Algorithm in detail Compared to TRL TL reduces the number of standards needed and requires fewer connections to the microstrip ports and thus improves the repeatability of this connection Moreover ps and p can be derived for any fixture with a first or second order symmetry As these reflection coefficients are derived mathematically it is possible to insert an ideal open or an ideal short circuit within the non insertable medium like a dielectric loaded waveguide too 2 7 Summary In this chapter it is seen that in the TL calibration the reflection standard of the TRL calibration is synthesized from the through measurement by using a perfect short or 14 open Thus by using symmetric arguments it is possible to reduce the number of required calibration standards Chpater 3 discusses the TL algorithms as well as the procedural flow for the calibration and de embedding process 15 Chapter 3 Through Line Algorithms 3 1 Introduction This chapter explains the algorithms used in the Thr
4. 1 0 g d e 1 c ac b T GL E a bc f 1 b ac a b E 1 0 g lot a 2abc b r oc a 60 f 1 c2 b ac flac b a Equating both sides of 3 49 four equations are obtained r d 1 c e b ac r2 f ac b a b d ac b e a b f c ac b Substituting the value of d from 3 52 in 3 50 E g pare d ac b e a b 2 ee ME Cdi A NE L i a 2 S ac b Awe 2 n ge JU c ac 9 22 a bc ac b ue OS a b ate bic a c b 2abc 2 a bc ac b ge a bc ees a bc ac b 24 3 47 3 48 3 49 3 50 3 51 3 52 3 53 3 54 3 55 3 56 3 57 25 and finally rer 3 58 ac b As values of a b c and rs have been obtained the wave cascading matrix for error network A can now be built by finding T1 Tf X 3 59 T19 T22 X b 3 60 TN Toa XC 3 61 Hence following conversion of these wave cascading parameters to S parameters the S parameters of error box A are obtained 3 2 5 De embedding Algorithm As the error boxes A and B are assumed to be symmetrical the S parameters for error box B are obtained by reversing the S parameters of error box A Thus Serror A and Serror B are obtained We now put the two port network whose de embedded S parameters Sa are to be ob
5. S12 S21 J S11 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 Frequency Ghz x 10 Figure 6 14 Error network S parameters phase using l m lines 96 Derived Parameters 1 T T T i NetA results 0 9 M 4 11 0 8 S22 0 7 0 6 Th i J Magnitude o al T l 0 4 7 12 821 0 1 10 15 20 Frequency Ghz o9 o Figure 6 15 De embedded S parameters magnitude of the DUT Phase degree 57 Derived Parameters 200 150 100 50 100 150 NetA results 200 0 Figure 6 16 10 15 20 Freguency Ghz De embedded S parameters phase of the DUT 58 Chapter 7 Conclusion 7 1 Summary The objective of this study was to study symmetric methods of calibration and imple ment a Computer Aided tool NetA that can be used for the purposes of calibration and de embedding as well as S parameter processing This work consists of two parts Introduction of the symmetrical methods for calibration and then Novel implemen tations of these procedures In the first part of this study we discussed symmetrical calibration methods that have been developed before The symmetry condition helps us reduce the number of required standards for microwave calibration without physically inserting them Using properties of first order symmetry and by synthesizing the reflection standard the TL technique can be effectively use
6. 43 planarity of the contact pads with the result that probe contact could not be made with the probes operating in their normal range of operation The original design called for the ground and signal pads to be at the same level However this was not achieved Each set of measurements took two to three hours instead of the anticipated 15 minutes Measurements were made on structures where possible but it is difficult to determine the accuracy of the measurements However the measurements were repeatable 6 5 Transmission Line Characterization A standard transmission line characterization was performed using a microwave net work analyzer and microprobes as in Figure 6 2 Again severe problems were en countered with the measurements Measurements were made on structures where possible but it is difficult to determine the accuracy of the measurements However the measurements were repeatable Ground Pad C 1 50 microns 50 microns Signal L3 T 50 microns y 50 microns Ground Pad A 50 microns Y ka 50 microns Figure 6 2 Single line microstrip fixture As a result of the planarity problems it was not possible to use Cascade probes because they are ceramic and cannot flex The microprober used is shown in Figure 6 3 and a Hewlett Packard Automatic Network Analyzer ANA HP8510B connected to a HP workstation was used for data retrieval The microstrip fixture used is shown 44 Mirowave Measurements Automat
7. The FINAL sub routine function retval final dut for k 1 size dut 1 rawdut 1 1 ptor dut k 2 dut k 3 rawdut 2 1 ptor dut k 4 dut k 5 rawdut 1 2 ptor dut k 6 dut k 7 rawdut 2 2 ptor dut k 8 dut k 9 final_dut k dut k 1 rawdut 1 1 rawdut 2 1 rawdut 1 2 rawdut 2 2 end retval final_dut We first read the raw DUT S parameters and then convert them to the Real Imaginary format 65 A 3 tl calib Purpose Calculates the propagation constant characteristic impedance and the error matrix Output Format Real Imaginary Array Ordering freq 11 21 512 22 for the error network freq y for the propagation constant Ze for the complex characteristic impedance Usage serror gamma array zc tl_calib thru line freq_vect ldiff c0 thru_o line_o Code function serror gamma_array zc tl calib thru line freq vect ldiff cO thru o line o zc zo 50 gamma array cal gamma thru line freq vect ldiff for x 1 size thru 1 newzcelement gamma array x 2 i 2 0 pi freq vect x c0 zc cat 1 zc newzcelement sline_rev x stos line o x newzcelement zo sthru rev x stos thru_o x newzcelement zo end en trl sthru rev sline rev for x 1 size thru 1 serror x stos en x 50 zc x end gamma array zc We now have the error matrices propagation constant and characteristic impedance arrays built by using th
8. 1980 in Ahmedabad India He received a degree in Electronics and Communication Engineering in May 2001 from the Nirma Institute of Technology Gujarat India He was admitted to the Master s program at North Carolina State University in the Fall of 2001 His interests are in the fields of RF and Mixed Signal Circuit Design ACKNOWLEDGEMENTS I would like to thank everybody who has helped me during my graduate school years and while I was working on my thesis I would like to express my sincere gratitude to Dr Michael B Steer my principal advisor for his support and guidance during my graduate studies research work and thesis preparation This thesis would not have been possible without his continuous help I would also like to express my sincere appreciation to Dr Griff Bilbro and Dr Douglas Barlage for serving on my M S committee and providing me with valuable suggestions I would like to thank Steve Lipa and Jayesh Nath for helping me out on quite a few occasions Most of all I would like to thank my Mother and Father who have always stood by me and made it possible for me to pursue graduate studies My brother Siddharth has also been a constant source of motivation I would like to thank my good friends Shalin and Rachana who have constantly supported and encouraged me during my Masters I would like to thank the Lord for all his blessings To all of you I thank you Contents List of Figures 1 Introduction ET Mot
9. Measurements were made using the conventional contacting probes shown in Figure 3 There are two probes shown here each has three contacts a signal con tact and two guard contacts We use coaxial probes GGB Model 40 picoprobes which continue the coaxial probe to within 1 mm of the final test fingers The guard contacts are extensions of the outer conductor of the coaxial line On the chip a set of three probe pads are contacted The minimum dimension of the probe pads are 50 u on one side with the outer pads typically connected to the chip ground In previously reported measurements GSG probes were used Due to considerable probing difficulties encountered with the GSG probes however GS probes were used for the measurements reported here Except for there being only one ground contact the construction of the GS probes is identical to the construction of the GSG probes Sub picofarad capacitance measurements require a balanced probe system but the electrical balance must of course be disturbed at the probe resulting in a residual capacitance The residual capacitance of the microprobe and the probe pad is ap proximately 70 fF this must be subtracted out of the measurements This establishes a resolution of 4 fF Thus the resolution of the capacitance measurement is indepen dent of that of the capacitance meter provided that the meter s resolution is 1 fF or less Problems were encountered with the measurements The principal problem was
10. Re Dd A A leds AS FA R O MIO ccu ME PA MMOS PASS 27 5 ua AS S S EEA te da vil ATO Example nos e dap Ne Ha are ma min dd mir de re le dent 81 B LabVIEW User Manual 83 B 1 Installation Guide 84 List of Figures 2 1 2 3 2 4 2 5 2 6 2 7 3 1 3 2 4 1 9 1 5 2 9 3 5 4 Two port model for a fixture a fixture can be described by eight error terms Sija and 5 where Port 1 and 2 are the pre calibrated VNA measurement ports and b are the measured fixture S Para MeterS 2 5 m 404 x04 ag de ie a oU OA oct de dp RORIS eeu Two port error model for a first order symmetric structure Fixture error networks are described by three S parameters Sija Two port error model for a first order symmetric structure 5714 and Sa are measured fixture S parameters Two port error network for a second order symmetric structure Error network is described by two S parameters Sj and 91 Through Reflect Line Calibration Standards a Through Standard b Reflection Standard and c Line Standard Through Line TL Calibration Standards a through connection and b line connection The TRL reflection standard is synthesized Using Symmetry LS Aura ne Gt th tole Ge ie Braud ee for mc dote ae TL signal flow graphs a Measured fixture S parameters b Fixture described by parameters 6 a and y and c Signal Flow Graph with an ideal short placed at fixtu
11. calculation Likewise press the second button that reads Get error matrix It will turn green too and once the calculation will be com pleted it will turn off 4 Press the third button that reads Get_dut_param Include the file that has the raw data for the DUT to be de embedded 84 5 Finally press the TSL De embedding button and after calculation of the de embedded data it will turn off Data will appear after each of the four buttons turn off in their respective indicators 6 Also the arrow button that was pressed in the beginning will now indicate completion of execution Data is now ready to be examined in each of the indicators These indicators are just like two dimensional arrays B 1 Installation Guide The guidelines are as follows 1 All files for the LabVIEW Implementation have been zipped under the name TL Labview 2 Install a version of LabVIEW that supports MATLAB Scripts 3 You must have MATLAB and LabVIEW Installed on your workstation It will work only on a Windows Operating System 4 Unzip all files in your directory 5 All MATLAB Scripts that you extract must be included in the Matlab bin win32 directory These are internally called subroutines from the MATLAB scripts within LabVIEW 89 mp Jooo 0 00 40 001 th TETE C2 un Figure B 1 Final Front Panel for TL calibration
12. do o ba Gm pr 0m Gm gan Du Cm pom do Figure 5 4 Front Panel for VI in Figure 5 3 connector pane has been created for the VI so that it can be used as a subVI The front panel for this VI is given by Figure 5 4 5 3 3 Third Block The Third block is similar to the first VI It has the same structure and reads in the measured S parameters for the DUT The input data in the text file is in the magnitude angle format This data is converted into real imaginary format for all measurement frequencies and then fed to the output of the VI s block diagram An icon connector pane has been created for the VI so that it can be used as a subVI 39 MATLAB Script This Matlab Script performs the final de embedding after the availibility of the Error parameters and the DUT S parameters for idx 1 size final_dut 1 trerror idx tdut idx stottfinal dut idx 50 For idx 1 size final dut 1 A 1 1 idx terror idx 2 A 1 2 idx terror idx 4 A 2 1 idx terror idx 3 A 2 2 idx terror idx 5 Ar 1 1 idx trerror idx 2 Ar 1 2 idx trerror idx 4 Ar 2 1 idx trerror idx 3 Ar 2 2 idx trerror idx 5 dutparams tdut idx 2 tdut idx 4 tdut idx 3 tdut idx 5 Ainv inv AC idx Arinv inv Ar idx tmpt Ainv Y dutparams tdmb tmpi Arinv tdmblist idx final dut idx 1 tdmb 1 1 tdmb 2 1 tdmb 1 2 tdmb 2
13. procedure of finding the S parameters of error network A refer to Figure 3 2 a is explained below Error network determination begins by converting the S parameters of the through and the line calibration standards into wave cascading parameters or a wave cascading matrix by the following formula proposed by Engen and Hoer 1 b 1 A 1 LA EN 11 a2 3 24 ay SM 8 1 bo b x ag Non in where 511599 51259 and R is the wave cascading matrix Moreover an important Hence property of the R matrix is that the cascade of two or more two ports is merely the product of the individual R matrices Let us consider Ra and R to be the R matrices of the error networks A and B as shown in Figure 3 1 Now for the through connection R Ra Rp 3 26 where R is the R matrix for the through connection Similarly for the line connection Ra Ra Ra Ri Rp 3 27 where R represents the line that has been inserted Now from 3 25 and 3 26 Ra Ra R Re R 3 28 Ra R TR Ra R 3 29 22 Hence TR RAR 3 30 where T RaR 3 31 If we assume a non reflecting line with propagation constant y and length l then et 0 Ri 3 32 0 ev Since S11 0 and S22 0 using 3 30 and 3 32 tir t Tit r Tjj r e 0 k em d al i 3 33 toi ta ro T22 Tai T22 0 e where rjj is the wave cascading matrix Ra of error network A and t is the wave cascading matrix of the line Hence tai Tai
14. s21 s12 s11 Usage out_var sreverse A Code function retval sreverse A rev for idx 1 size A 1 rev A idx 1 A idx 5 Alidx 3 A idx 4 A idx 2 end retval rev A 14 stoh Purpose Converts the S parameters to the H parameters Output Format Real Imaginary Array Ordering freq h11 h21 h12 h22 Usage out_var stoh A z0 Code function retval stoh A z0 if nargin 1 error stoh two port s parameter list z0 end if nargin 2 zO 50 end z for idx 1 size A 1 v A idx s11 v 2 s21 v 3 s12 v 4 s22 v 5 79 d 1 s11 1 s22 s12 s21 h11 z0x 1 s11 1 822 s12x xs21 d h12 z0 s12 s12 d h21 z0 s21 s21 d h22 z0 1 s22 1 s11 s12 s21 d z idx A idx 1 h11 h21 h12 h22 end retval z A 15 magphase Purpose Converts data from Real Imaginary to Magnitude Phase degrees format Output Format Magnitude Phase degrees Usage out_var magphase input_arg Code function retval magphase A PX 57 2957795130823 if size A 2 1 for idx 1 size A 1 v A idx slim sqrt real v 1 real v 1 imag v 1 imag v 1 slip PX atan2 imag v 1 real v 1 y idx slim slip end retval y else if size A 2 3 for idx 1 size A 1 v A idx slim sqrt real v 2 real v 2 imag v 2 imag v 2 slip PX atan2 imag v 2 real v 2 80 y idx A idx
15. shows the flow chart for the Through Line de embedding algorithm 4 3 Utilities available in NetA In MATLAB for every command executed the resultant arrays or matrices are dis played with their name dimension and contents So any of the utility subroutines can be individually executed by passing the required data as input arguments Error display occurs in case there is a violation To understand the semantics of each com mand the user is directed to Appendix A Below is a list of the MATLAB utilities and a brief discussion of their function These utilities can be used to implement the TL and the TRL calibration procedures 10 11 12 13 14 15 16 17 18 Function GET MAG ANG TL TL CALIB TSL CAL GAMMA STOR RTOS PTOR STOZ SREVERSE ZTOS STOH HTOS STOY YTOS STOT TTOS MAGPHASE Purpose Input Data Error Matrix Calculation Through Line Calibration Routine Two port De embedding Calculates the Propagation Constant Converts S parameters to R parameters Converts R parameters to S parameters Converts Polar to Rectangular Converts S parameters to Z parameters Reverses the input S parameter network Converts Z parameters to S parameters Converts S parameters to H parameters Converts H parameters to S parameters Converts S parameters to Y parameters Converts Y parameters to S parameters Converts S parameters to T parameters Converts T parameters to S paramet
16. structures for all measurement frequencies 2 The second block performs the calculation of the propagation constant y com plex characteristic impedance Z and error network parameters for all measure ment frequencies 34 3 The third block reads in the S parameter data for the DUT that is to be de embedded 4 The fourth and final block performs the de embedding on the measured embed ded DUT S parameters Each of these above blocks is a subVI These subVIs are then combined on a separate VI block diagram to implement the Through Line De embedding procedure The next four sub sections explain the LabVIEW Implementation of each of the above mentioned four blocks in detail 39 This script coverts the MA data to RI data and also returns the thru and line s parameters of the two port network cO 1 621e 12 2500e 6 for k 1 size thru data val 1 v thru data valik ro til v 2 pli v 3 t21 v 4 pei v 5 t12 v 6 plz v 7 t22 v 8 p22 v 9 w line data valtk L11 w 2 Pil w 3 L21 w 4 paf P21 w 5 L12 w 6 P22 9 Figure 5 1 Block Diagram for the VI which reads in Through and Line Data 5 3 1 First Block The screenshot in Figure 5 1 is of the first VI This VI performs the function of reading in the S parameters for the Through and the Line calibration standards This data is read from text files and then fed in as an input to th
17. the LabVIEW environment must be included in the Matlab bin win32 directory 37 z0 50 Idiff 0 0005 cO 1 621e 12 25008 6 gamma array cal_gamma thru line Freq_vect Idiff for x 1 size thru 1 newzcelement array x 2 i 2 0 pi freq vect x c0 2c x newzcelement sline rev x stos line o x newzcelement zo Thus os T AA stos thru_o x newzcelement z0 Error matrix Line Uas en trl sthru_rev sline_rev freq_vect or k 1 size thru 1 RENI stos en k 50 zc k plotifreg vect gamma array error out 4 ATI Figure 5 3 Block diagram for the second VI 5 3 2 Second Block The VI in Figure 5 3 is the second block which contains the Matlab script for cal culation of the propagation constant y complex characteristic impedance Z and the error network parameters The structure and principles for the VI block diagram im plementation have been explained in the previous section The naming convention for the controls and indicators is the same through out the different VIs thus indicating which outputs of the previous VI serve as inputs for the next VI The S parameters for the through and line structures and T parameters for the same serve as controls or inputs and the complex characteristic impedance Z and the error network parameters are the indicators or outputs for this VI An icon 38 Gom a com m oz Gom
18. the transmission line and ca pacitance measurements made on a test wafer supplied by SEMATECH Transmission lines were characterized using a Hewlett Packard network analyzer 7 Capacitances were determined using conventional capacitance meter techniques 7 Details of these measurements are explained in the following sections and have been previously re ported 7 The results shown here have been obtained by using NetA tools for de embedding these microwave measurements for two port networks The measure ment set of one of the test wafer has been taken 6 2 Layers The IC had three metallization layers as shown in Figure 6 1 Passivation Metal 3 Metal 2 Metal 1 Substrate Figure 6 1 Cross section of test IC showing three metallization layers 42 6 3 Measurements The measurements performed are capacitance and resistance measurements and mi crowave transmission line characterization In general three forms of a structure were used to determine the characteristics of a measurement Raw measurements were made on a long line with the suffix 1 a medium length line with suffix m and a short line with suffix s All derived parameters are reported for two extractions designated by the source of the raw data Extractions with the suffix Is or l s were extracted using the long and short lines Extractions with the suffix Im or l m were extracted using the long and medium lines 6 4 Capacitance Measurement Capacitance
19. y for Sita Sora 12a and S224 respectively refer to Figure 2 6 The input reflection coefficient with an ideal short circuit placed at the Port 1b 10 Through Connection oo Port 1 A B Port 2 D r OO Q a Arbitrary Reflection m i b Line Connection A Line B Figure 2 5 Through Reflect Line Calibration Standards a Through Standard b Reflection Standard and c Line Standard 11 Through Connection D L 00 4 o O OO a Line Connection A Line A b Figure 2 6 Through Line TL Calibration Standards a through connection and b line connection The TRL reflection standard is synthesized using symmetry 12 Sot O AUG 0 Sait Sur Sar a Q 1 Qa 1 1 1 Qa Port 1b Port 2b b Figure 2 7 TL signal flow graphs a Measured fixture S parameters b Fixture described by parameters 6 a and y and c Signal Flow Graph with an ideal short placed at fixture Port 1b 13 of in Figure 2 6 c when calculated is o 12 Pse 0 2 6 Previously we used Mason s formula to derive 2 1 to 2 4 For the first order symmetric structure shown in Figure 2 6 b a S 2 7 uf p EF 2 7 2 a S
20. 0 521 3 3 To 1 su 1 522 812 821 2 521 3 4 3 2 1 Propagation Constant Determination This routine requires the T parameters of the through and line structures and differ ence in lengths of the through and the line structures Mondal and Chen 5 showed that the TRL Algorithm can be used to determine the propagation constant of the TRL Line Standard This is given by y In At T 5 Ij 3 5 where l length of the line calibration structure lg length of the through calibration structure and A in 3 5 is given by A Dion TiuTz2 Tu Toi TisiTou 3 6 where T and T in 3 6 are the chain scattering parameters for the through and line calibration standards respectively One of the most important parts of the algorithm is deciding the phase of the propagation constant The phase depends upon the difference in the lengths of the through and the line calibration standards However if the electrical length of the transmission line is 2 measurement errors are observed Reliable propagation 18 constant values can be extracted between 20 and 160 degree phase differences So the lengths should only be such that this problem is avoided over the entire measurement frequency range This appears to be particular to the TRL procedure However generally good results are obtained using the TL calibration procedure even when the phase is not in this range 3 2 2 Characteristic Impedance D
21. 1 slim stip end retval y else if size A 2 5 for idx 1 size A 1 y Alidx slim sqrt real v 2 real v 2 imag v 2 rimag v 2 slip PX atan2 imag v 2 real v 2 s21m sqrt real v 3 real v 3 imag v 3 imag v 3 s21p PX atan2 imag v 3 real v 3 s12m sqrt real v 4 real v 4 imag v 4 imag v 4 s12p PX atan2 imag v 4 real v 4 s22m sqrt real v 5 real v 5 imag v 5 imag v 5 s22p PX atan2 imag v 5 real v 5 y idx A idx 1 slim stip s21m s21p si2m s12p s22m s22p end retval y end end end 81 A 16 Example This section explains the stepwise execution of NetA for TL calibration and de embedding This example uses the long and short lines as line and through standards and de embedds the s parameters for the long line The commands to be executed at the MATLAB prompt are get_mag_ang thru line thru o line o touchstone thru data line data freq vect ldiff 0 006 cO 1 2e 10 serror gamma array zc tl calib thru line freq vect ldiff cO thru o line 0 dut xlsread long xls final dut final dut deemb tsl serror final dut This will obtain the de embedded result in the parameters deemb To further convert it to the Magnitude Angle format d_result magphase deemb Similarly other utility routines can also be used by assigning the result to any tem porary variable at the prompt and passing the r
22. 2 E n put idx ttos tdmblist idx 50 Figure 5 5 Block diagram for the fourth VI 5 3 4 Fourth Block The VIin Figure 5 5 is the fourth and final VI of the de embedding implementation It has the Matlab script that performs the final de embedding after the availability of the error network parameters and the measured DUT S parameters which are the controls of the VI on the front panel The output of this VI is the de embedded S parameters for the two port network DUT for all measurement frequencies which is an indicator on the front panel An icon connector pane has been created for the VI so that it can be used as a sub VI The front panel for this VI is given by Figure 5 6 40 Figure 5 6 Front Panel for VI in Figure 5 5 5 4 Summary In this chapter the implementation issues and details of the four main blocks for TL calibration has been provided The above explained four VIs are integrated in the same order to implement a larger VI that essentially performs the TL De embedding Moreover all the above VIs are used as subVIs in the final VI The final VI will have its own front panel The reader is directed to Appendix B for information about the LabVIEW user s manual along with a screenshot of the front panel of the final VI 41 Chapter 6 Results 6 1 Introduction In this chapter we discuss the results obtained using the Through Line algorithm for calibration and de embedding This report documents
23. 2 s21 r idx A idx 1 r11 r21 r12 r22 end retval r A 11 stoy Purpose Converts the S parameters to the Y parameters Output Format Real Imaginary Array Ordering freq y11 y21 y12 y22 Usage out_var stoy A z0 Code function retval stoy A z0 retval 0 if margin lt 1 error stoy s parameter list Zo end yO 1 z0 v A 1 s11 v 2 s21 v 3 s12 v 4 s22 v 5 for idx 1 size A 1 v Ads s11 v 2 s21 v 3 s12 v 4 s22 v 5 d 1 s11 1 s22 s12 s21 y11 yOx 1 sil x 1ts22 ts12xs21 d y12 yO 2 s12 d y21 yOx 2xs21 d y22 y0 1 811 1 s22 s12 521 d y idx A idx 1 y11 y21 922 5 end retval y 76 77 A 12 stoz Purpose Converts the S parameters to the Z parameters Output Format Real Imaginary Array Ordering freg z11 z21 z12 z22 Usage out_var stoz A z0 Code function retval stoz A z0 retval 0 if margin lt 1 error stoz two port s parameter list z0 end z for idx 1 size A 1 v A idx s11 v 2 s21 v 3 s12 v 4 s22 v 5 d 1 s11 1 s22 s12 s21 zii zO 1 s11 1 s22 s12 s 21 d z12 z0 s12 s12 d z21 z0 s21 s21 d z22 z0 1 s11 1 822 s12 s21 d z idx A idx 1 z11 z21 712 722 end retval Z 78 A 13 sreverse Purpose Reverses the input matrix Output Format Real Imaginary Array Ordering freq s22
24. 5 1 Brief Introduction to LabVIEW 52 gt Basic VL Structure Sou o is a A AA se 5 3 LabVIEW Implementation of NetA 5 dal a First Block lt 2 So ex ar Re L En el 5 32 Second Block 22 4 Las dE Sethe de Eden tes aan ee a 539 Lhird Block z ss ame sas ana MR RS EE LS a ed 53 4 Fourth Block teta A te S OUI el a Oh gs KIAT Shige oq acp den EDAN goth der SG AE er te Ach 6 Results 6 1 Introduction 2 ae clar eine Bt Da Se Rn 6 23 o as weer Rh ow ae See eo Be BE DAD he was 6 3 Measurements 64 Capacitance Measurement 1 34 ke Xue a du yos yum e Y s por 6 5 Transmission Line Characterization 6 6 Results using NetA rs 4 0 E A A A A A 6 6 1 Single Line with Ground Plane 7 Conclusion Cale Summary 2 e002 AA o A EE A RA 7 2 Future Work one Lu nat a ea Bibliography A NetA Programmer s Manual Aul Pen Le ur Cop de BA a a rs ER A2 d tandfinal se ee GRO a ue en dde Ne dE TE nts 3 9 seb salib nsr AN RS A oe ion Oe a La sr ia AA touchstone LS 4 orkid oat we end RE a ee SS ae wt Se aa ed Door ASL doc ae Da BA a A Daa Dee Pa eae AD cal AAA AAA AST Elks e DEN AA ees Sd ho Se bo SET r f AS BLOKS e ds A teh rho eco d RRA AA AAA AO SEDES od ce i Aen SOE e en est TEE a ae ve APT eae ik PT A ht LA Wa AIA a eo ee TRES TTE POI REGI Sete ps ag toe Ney sp Ne seem died O ad i DIO e RE D PR ES T a al ae TONI Seok
25. ABSTRACT ADITYA P GOSWAMI Implementation of Microwave Measurements using Novel Calibration Techniques Under the direction of Dr Michael Steer NetA Network Analysis tools for calibration of microwave measurements has been implemented NetA contains calibration and de embedding procedures as data analysis MATLAB routines The Through Line method for calibration of two ports has been used and the NetA process flow has also been explained Complex charac teristic impedance of the micro strip transmission line has been calculated using the ETRL Enhanced TRL technique Results have been simulated using NetA tools A LabVIEW Implementation of NetA has also been implemented so as to enhance the usability of NetA and also provide the capability of Real time microwave calibration and de embedding IMPLEMENTATION OF MICROWAVE MEASUREMENTS USING NOVEL CALIBRATION TECHNIQUES by Aditya P Goswami A thesis submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Master of Science Computer Engineering Raleigh May 2003 APPROVED BY Chair of Advisory Committee Dedication This thesis is dedicated to my parents Pramod Gosai and Jyoti Gosai who have worked so hard and always given me the best education They have raised me with a freedom of choice and presented me with boundless opportunities iii BIOGRAPHY Aditya P Goswami was born on 10 June
26. I receives instructions from the block diagram which you construct Ba 33 sically the block diagram is a pictorial solution to a programming problem It is the source code of the VI e VIs are hierarchical and modular You can use them as a top level program or as a subVI which is a subprogram within a program VIs can pass on data to subVIs Hence with the above features LabVIEW promotes and adheres to the concept of modular programming One can divide an application into a series of tasks and then subdivide it to decrease the complexity of the required application Hence a VI can be built to accomplish each subtask and then by combining all these subVIs on another block diagram a larger task can be accomplished Finally the top level VI contains a collection of subVIs that represent functions or tasks The above explanation aids us in understanding the LabVIEW implementation of NetA Moreover two major practical advantages of integrating NetA within Lab VIEW are e Usability of NetA is improved as it is used in conjunction with LabVIEW e LabVIEW can be interfaced real time with the Network Analyzer hence saving a lot of measurement and data analysis time 5 3 LabVIEW Implementation of NetA The LabVIEW implementation has been divided into four major blocks These four blocks perform the following functions respectively 1 The first block reads in the input S parameter data of the Through and the Line calibration
27. an view of the 20G structure The following graphs show results for the medium and long line used as the through and line calibration standards We have de embedded the S parameters for the long line Magnitude 46 Raw Long Line Scattering parameters 1 NetA results 0 9 i 4 0 8 H 0 7 H 0 6 0 5 0 44 4 0 3 mie S RL exa ag i Se Wm AR rate oar due De ea es Me D cA SIS AMP A och AA Na an DD ote npe dune TR a et 0 1 H2 UN S12 S21 0 LP 0 5 10 15 20 Frequency Ghz Figure 6 5 Raw S parameters magnitude for the Long line 47 200 150 100 50 Phase degree o 100 150 Raw Long Line Scattering Parameters T NetA results 12 821 200 0 10 15 20 Freguency Ghz Figure 6 6 Raw S parameters phase for the Long line Magnitude 48 Raw Medium line Scattering parameters 0 9 T T NetA results o e 0 1 0 5 10 15 20 Frequency Ghz Figure 6 7 Raw S parameters magnitude for the Medium line 49 Raw Medium line Scattering parameters T 30 T NetA results 20 A S22 A PEPE REESE SEES SES ae nea ae ee ee S11 i i M 40 ie I 50 0 5 10 15 20 Frequency Ghz Figure 6 8 Raw S parameters phase for the Medium line 90 Characteristic Impedance Zc using I m lines 500 I T NetA re
28. can be used for the purpose of data analysis are explained The routines that are to be executed at the MATLAB command prompt for the TL calibration are 1 GET MAG ANG 2 TOUCHSTONE 3 TL_CALIB 4 DUT and FINAL 5 TSL The usage and purpose of each of the above routines is explained in the coming sections 63 A l get mag ang Purpose Gets the raw S parameters of the through and the line calibration stan dards Output Format Magnitude and Phase Array Ordering freq S11 S21 S12 S22 Usage get mag ang Code thru data xlsread short xls line data xlsread long xls freq vect xlsread freq xls The raw data is now available in local variables These variables will be used to pass data to the next routine and will also show up in the Workspace area of MATLAB as an array with its dimensions The short xls long xls and freq xls are excel files When read into NetA the files must only contain numeric data The file freq xls contains just one column of all measurement frequencies Usage of this vector is minimum throughout the code and can be removed completely if needed as the frequency vector is the first column in all data arrays 64 A 2 dut and final Purpose We use this routine to read in the S parameters for the DUT to be de embedded Output Format Real Imaginary Array Ordering freq 11 21 12 522 Code dut xlsread long xls final dut final dut
29. d TL was also enhanced by calculating the complex characteristic impedance of the line standard For this the ETRL method was used Using the above two calibration techniques NetA tools for calibration of mi crowave measurements was developed NetA s process flow was also explained An extension to the implementation of NetA has been shown by implementing the cali bration in LabVIEW This implementation provides us with a capability of interfacing the calibration algorithm with the VNA and using it as a virtual instrument to cal ibrate and analyze data real time A previous measurement set has been taken and 99 simulated using NetA tools These results have been shown 7 2 Future Work Additional areas of study include 1 Analysis of the sensitivity of the TL calibration technique to randomness in transmission line parameters 2 Symmetry sensitivity for different kind of transmission lines 3 Further expansion of NetA to larger port devices 60 Bibliography 1 G F Engen and C A Hoer Thru reflect line an improved technique for calibrating the dual six port automatic network analyzer IEEE Trans Mi crowave Theory and Techniques pp 987 993 Dec 1979 M B Steer S B Goldberg G Rinne P D Franzon I Turlik and J Kas ten Introducing the through line de embedding procedure Int Microwave Symposium pp 1455 1458 June 1992 M B Steer S B Goldberg P D Franzon and J Kast
30. d Circuit Board PCB discontinuities The VNA calibration is done with coaxial standards but the PCB transmission line standards are microstrip and stripline This requires a fixture for conversion from coaxial to PCB structures This introduces systematic errors in the measurement The Through Line TL Algorithm determines this error and removes it Moreover a PCB is man ufactured such that without physically altering the board it is not possible to insert calibration standards This also enhances the need for Computer Aided Microwave Measurements 1 2 Thesis Overview This thesis talks about the Through Line TL calibration process and its imple mentation using MATLAB as the program NetA Network Analysis for Microwave Measurements and LabVIEW Chapter 2 reviews the basic arguments of symmetry that give rise to the TL calibration process for a non insertable medium like an Inte grated Circuit Chapter 3 discusses the TL calibration algorithms in detail along with the final de embedding process for a two port network DUT Chapter 4 discusses the MATLAB implementation NetA and flow of these TL algorithms for de embedding two port Microwave Measurements This chapter also redirects the reader to the Appendix A for further details regarding usage of NetA and its utilities Chapter 5 discusses the LabVIEW Implementation of NetA Chapter 6 includes the results obtained using NetA for a test wafer Finally we conclude with the summary of the wo
31. e Matlab Script arithmetic structure as can be seen in the Figure 5 1 The Matlab Script structure is an in built function within LabVIEW Within this Matlab Script structure the Matlab code is written Some changes are made in the basic NetA Code to successfully incorporate it within the LabVIEW environment The input data in the text file is in the magnitude angle format This data is first converted into real imaginary format and then converted to its equivalent 36 Line_s n r d 1000 0 fe i Thru s uU p r d 0 short A Jo long 4 A Thru t Jio No 00 0 frea f mi Lime_t J 0 00070 jo freq 4 Ye Mo 00 0 J 0 error out 2 Figure 5 2 Front Panel for the Block Diagram in Figure 5 1 T parameters for both the calibration standards for all measurement frequencies and then fed to the output of the VI s block diagram Each input to the block diagram is a control and each output of the block diagram is an indicator Each control and indicator is displayed on the front panel of this VI There is also an error out signal associated with each VI that displays the error if any during simulation The resultant front panel for the VI along with all controls and indicators is shown in Figure 5 2 We also prepare an icon connector pane for this VI so that it can be used as a subVI at a higher level of abstraction during implementation Note each separate Matlab subroutine that is called within the Matlab code in
32. en Experimental elec trical characterization of interconnects and discontinuities in high speed digital systems IEEE Trans Components Hybrids and Manufacturing Technology pp 761 765 Dec 1991 J S Kasten M B Steer and R Pomerleau Enhanced through reflect line characterization of two port measuring systems using free space capacitance calibration IEEE Trans Microwave Theory and Techniques pp 215 217 Feb 1990 J P Mondal T Chen Propagation Constant Determination in Microwve Fixture De embedding Procedure EEE Trans Microwave Theory and Tech niques pp 706 714 Apr 1988 J S Kasten Calibration of Automatic Network Analysis and Computer Aided Microwave Measurement Masters Thesis North Carolina State University 1992 61 7 M B Steer P D Franzon W J Ficken A W Glaser B Biswas and S Lipa Experimental Determination of On Chip Interconnect Capacitances 1998 SE MATECH Test Report 2nd Edition pp 4 7 pp 121 126 8 Applying Error Correction to Network Analyzer Measurements Application Note AN 1287 8 pp 1 15 Agilent Technologies 9 Matlab User Guide 10 LabVIEW User Guide 62 Appendix A NetA Programmer s Manual This appendix is a user s manual for NetA Firstly the user is informed about the command syntax to be used and the series in which the TL NetA routines are to be executed for calibration and de embedding Secondly all the utility routines that
33. ers Converts to Magnitude Angle degrees format 31 4 4 Summary MATLAB can be used to directly implement the TL calibration and de embedding process Various utility routines provided help for further two port network analy sis More information about the command line syntax and parameters required for implementation and usage of these routines has been provided in Appendix A The next chapter discusses the LabVIEW Implementation of NetA 32 Chapter 5 LabVIEW Implementation 5 1 Brief Introduction to LabVIEW LabVIEW is both an instrument control program and program development applica tion LabVIEW uses a graphical programming language G to create programs in a block diagram form LabVIEW is a general purpose programming tool but it also includes libraries of functions and development tools designed specifically for data acquisition and instru ment control LabVIEW programs are called Virtual Instruments VIs because their appearance and operation can imitate actual instruments 5 2 Basic VI Structure A VI consists of an interactive user interface a data flow diagram that serves as a source code and icon connections that allow the VI to be called from a higher level VI Vis are structured as follows e The interactive user interface of a VI is called a frontpanel because it simulates the panel of a physical instrument The front panel can contain knobs push buttons graphs controls and indicators e The V
34. etermination An inherent assumption of the TRL algorithm is that the characteristic impedance of the line calibration standard is either equal to the measurement system impedance or can be precisely determined A technique was proposed in 4 in which the character istic impedance is calculated using the Enhanced TRL Technique ETRL technique This is an enhancement to the TRL algorithm If the medium used is a dispersive medium like the microstrip line then the frequency dependence of Z characteristic impedance needs to be explored ETRL determines the complex characteristic impedance using the free space ca pacitance Co of the line and the propagation constant y a 6 determined in the standard TRL Algorithm This impedance is then used in the TRL algorithm to ob tain characteristic impedances of any arbitrary TEM transmission lines In the next subsection the calculation of the complex characteristic impedance of a microstrip transmission line is shown 3 2 3 Calculation of Complex Characteristic Impedance Many lines such as microstrip lines support a quasi TEM mode However the TL and the TRL algorithm require the equivalent TEM mode characteristic impedance as the reference plane is perpendicular to the direction of propagation and it is to this plane that the impedances are referred For a uniform TEM transmission lines the characteristic impedance I 1 RER Lk pc ang ee and where Up is the phase velocity L
35. he reflected and the transmitted energy determine the S parameters Measurements by the VNA must have a high degree of accuracy The are various sources of errors which may occur while doing measurements 8 Namely e Systematic error These are caused by imperfections in the test equipment and test setup If these errors do not vary over time they can be characterized through calibration and mathematically removed during the measurement pro cess Systematic errors encountered in network measurements are related to signal leakage signal reflections and frequency dependent loss of fixtures e Random errors These errors vary randomly as a function of time Since they are not predictable they cannot be removed by calibration The main contrib utors to random errors are instrument noise e Drift errors These errors occur when a test system s performance changes after a calibration has been performed They are primarily caused by temperature variation and can be removed by additional calibration By constructing a test environment with a stable ambient temperature drift errors can usually be minimized The VNA has the ability to remove the systematic errors by using known standards This process of using known standards to remove systematic errors is known as vector error correction or calibration or de embedding Here we discuss a procedure for calibration of the VNA with respect to its applica tion to the measurement of a Printe
36. ic Network Analyzer HP8510 a Device Under Test 1 Through Measurement O i O _ b O O 2 Line Measurement c A Reference Planes Figure 6 3 Microwave Measurement Set up in Figure 6 2 It was not possible to make coupled line measurements because these require that contact be made with five conductors and severe problems were found with just three 6 6 Results using NetA The following results have been obtained using NetA tools for de embedding two port microwave measurements The medium line and the long line have been used as the through and the line standards for calibration The results shown here are obtained 45 while using the long line as the DUT de embedded S parameters of which are ob tained using NetA The details of the structures used as calibration standards are as mentioned below These results have been matched with a previous characterization of the same structure in 7 6 6 1 Single Line with Ground Plane This structure is also known as the 20G S M L structure or Single Line with Ground plane and three difference lengths of line This is a unique name that has been provided at the time of measurements 7 e Index 20G S M L e Description M2 line over M1 ground plane e Dimensions Ls 400 um Lm 800 um L 6400 um W Wm 0 5 ym A Passivation Metal 3 Metal 2 Metal 1 Substrate Figure 6 4 Cross sectional and Pl
37. ight input argument 82 De embedded Medium Line S parameters 1 4 T T T T T T NetA results 12 821 Magnitude o 00 T o o 04r 4 0 Frequency Ghz Figure A 1 De embedded Medium line S parameters Magnitude using the long and medium line as the line and through standards The medium and long line have been used as the Through and Line calibration standards Raw parameters of the medium line have been used as the DUT The derived parameters show the characteristics of a Through connection 83 Appendix B LabVIEW User Manual This section is a user s manual for the LabVIEW Implementation of NetA Fig B 1 shows the front panel for the final VI that implements all of the four blocks explained in Chapter 5 in cascade 1 The menu of the screenshot shows an arrow As soon as you press that arrow button the VI starts running and passes data from the front panel to the VI 2 Press the first yellow button that reads Grab Data It will immediately turn green It will open up the current directory Select the right raw data text files i e long txt short txt and freq txt These are made available from the VNA After these files are included the button will turn off and will wait for you to press the next button 3 The interface between the modules in the VI is waiting for the user to ask it to perform the propagation constant characteristic impedance determination and error matrix
38. is routine All of these arrays will be produced in the Workspace area of MATLAB We have now completed the TL Calibration and can use the data for de embedding 66 A 4 touchstone Purpose Converts the raw data from Polar to Rectangular co ordinates symmetrizes the data and calculates the T parameters of the calibration structures Output Format Real Imaginary Array Ordering freq 11 21 12 522 Usage thru line thru_o line_o touchstone thru_data line_data freq_vect Code function thru line thru_o line_o touchstone thru_data line_data freq_vect z0 50 if nargin lt 3 error Input Arguments are less end for k 1 size thru_data 1 v thru data k tii v 2 p11 v 3 t21 v 4 p21 v 5 t12 v 6 p12 v 7 t22 v 8 p22 v 9 w line_data k L11 w 2 P11 w 3 L21 w 4 P21 w 5 L12 w 6 P12 w 7 L22 w 8 P22 w 9 sthru11 ptor t11 p11 ptor t22 p22 2 sthru12 ptor t21 p21 ptor t12 p12 2 67 sthru21 sthrui2 sthru22 sthruil sline11 ptor L11 P11 ptor L22 P22 2 sline12 ptor L21 P21 ptor L12 P12 2 sline21 slinei2 sline22 slineil thru o k freq vect k 1 sthru11 sthru21 sthru12 sthru22 line o k freq vect k 1 sline11 sline21 sline12 sline22 thru k stot thru o k z0 line k stot line_o k z0 end This routine produces the S parameters and the T parameters of the calibratio
39. is the series inductance per unit length and C is the shunt capacitance per unit length Now ee ells LC and so L 1 Zor a cL 2 where c is the velocity of light in free space C is the free space capacitance Hence T 1 eC In the dielectric medium the phase velocity v becomes 19 3 8 3 9 3 10 3 11 3 12 3 13 c v p Ver or c v FE Co where is the relative dielectric constant Now from 3 7 and 3 11 we have several expressions for the characteristic impedance 3 14 1 a cvCC 1 Ze cC amp Z Ze C Co and Zo Le Moreover the propagation constant y jwype ty JW Hopir otr jw c VPS and LEE de er Hence from 3 10 3 21 and 3 22 SJ Ze C we 20 3 15 3 16 3 17 3 18 3 19 3 20 3 21 3 22 3 23 The Through Line calibration algorithm like the TRL procedure requires a reflection less line So each calibration measurement is transformed from the system reference impedance to Ze The application of the TRL algorithm is then used to determine the S parameters of the error network which is referenced to Ze Now the S parameters of the error network are referred back to the system reference impedance which is usually 50 8 21 3 2 4 Error Network Determination As mentioned earlier the error network is determined using the TRL algorithm The
40. ivation a te sant SU ENG s SO ek ee Soh het a eet eds 1 2 Thesis Overview ora 4 o b e e Ae EE lies 1 3 Original Contributions So Eig bg iG Eae AE ek OPE SY RSS 2 Literature Review Desk Introductions naspa de ete S hg der na armate 2 2 Advantages of using a Symmetric Fixture Dod Symmetric PISDHEG do dise serit mem ead es de og da Bebe S as Bees 2 4 First Order Symmetric Fixture kcu toa rece dev ch wae pes 2 5 Second Order Symmetric Fixture 2 6 Through Line Using First Order Symmetry 2 6 1 Using Symmetry to Replace the TRL Reflection Standard 2 6 2 Synthesize Reflection Standards du ROUTIER LE REA ANA ANR a a ad ds SY 3 Through Line Algorithms JL Inttodmenon on AAA oe SS AS Len Lu Site da ANE 0 25 TEE ye oe a Cee Se Ud TT 3 2 1 Propagation Constant Determination 3 2 2 Characteristic Impedance Determination 3 2 3 Calculation of Complex Characteristic Impedance 3 2 4 Error Network Determination 44 4 La vus eee ha os 3 2 5 Desembeddine Algorithm 4 ali edo ey ata ee Seve 5 io wet AP este du oe eer Bs Oa Ne Ghe Bs a fete ae arte 4 NetA 4 1 Introduction to NetA es le aa Re Od ta 12 NetA Algorithm Flow A La gs GS AS 4 3 Utilities available in NetA HW ND HO Oo ON O ot EEB E 24 Dimana peee ENS dt an t neto e ge Mee MM ata Deed Teen Toc nls 5 LabVIEW Implementation
41. lp in the Microwave Measurement analysis for two port networks NetA has been written in MATLAB which is a programming language widely used by engineers It has been developed in a very structured format and is also upgradable Moreover other de embedding techniques can be included as MATLAB subroutines to enhance its capability while utilizing the same MATLAB routines for data analysis Each routine can be called through the command line in MATLAB Moreover these MATLAB routines have been used to develop a LabVIEW implementation which shall be explained in the following chapter 4 2 NetA Algorithm Flow As explained earlier the core de embedding algorithm has been divided into four ma jor parts Namely Start Repeat for all values of measurement frequency Y Get S parameter data for the Through and Line Calibration standards Get Propagation Constant Calculate Zc Convert the measured S parameters referenced to the calculated Zc Calculate Error Matrices A and B Get the measured DUT S parameters De embedd the measured DUT S parameters Figure 4 1 Flow Chart for the NetA Algorithm End 28 29 Propagation Constant Determination e Z characteristic impedance Determination e Error Matrix Determination De embedding Algorithm Each of the above mentioned algorithms was discussed in detail in Chapter 3 Figure 4 1
42. n standards and stores them in local variables At the command prompt also enter values for the difference in the line and through standard lengths as diff and the free space capacitance c0 The arrays produced by this routine diff and Co are used as input arguments for the TL calibration routine 68 A 5 tsl Purpose Performs the TL de embedding once the DUT S parameters and the error network parameters are available Output Format Real Imaginary Array ordering freq S11 21 12 22 Usage deemb_dut tsl serror final_dut Code function retval tsl serror final_dut if nargin lt 2 error Input arguments are less end for idx 1 size final_dut 1 srerror idx sreverse serror idx terror idx stot serror idx 50 trerror idx stot srerror idx 50 tdut idx stot final dut idx 50 end for idx 1 size final dut 1 A 1 1 idx terror idx 2 A 1 2 idx terror idx 4 A 2 1 idx terror idx 3 A 2 2 idx terror idx 5 Ar 1 1 idx trerror idx 2 Ar 1 2 idx trerror idx 4 Ar 2 1 idx trerror idx 3 Ar 2 2 idx trerror idx 5 dutparams tdut idx 2 tdut idx 4 tdut idx 3 tdut idx 5 Ainv inv A idx Arinv inv Ar idx tmp1 Ainv dutparams 69 tdmb tmpi Arinv tdmblist idx final dut idx 1 tdmb 1 1 tdmb 2 1 tdmb 1 2 tdmb 2 2 end end retval tto
43. oard measurements 2 5 Second Order Symmetric Fixture If each of the fixture halves are identical and symmetric as shown in Figure 2 3 the fixture is a second order symmetric fixture This implies that error network B is equal to error network A i e the reflection S parameters Siia or Si are equal to S11 and all transmission S parameters Sija or 5 j are equal to 551 In the next section we apply the first order symmetry to the microstrip fixture and synthesize the reflection standard from there on Sar 11f 11f O 21f b Figure 2 3 Two port error model for a first order symmetric structure 5714 and Sa are measured fixture S parameters A A 1 O O O Q i S5 i S5 i Port 1 Port 2 d Su Si S Su l eN i S S I 21 1 I 6 lt E lt 6 l Figure 2 4 Two port error network for a second order symmetric structure Error network is described by two S parameters 1 and 55 2 6 Through Line Using First Order Symmetry 2 6 1 Using Symmetry to Replace the TRL Reflection Stan dard For calibration of a planar measurement fixture e g microstrip or stripline we re quire distributed standards The traditionally preferred method for planar fixture de embedding is Through Reflect Line or TRL because the distributed standards can be easily modelled and constructed A typical microstrip fixture is a first order sym metric fixtu
44. ort error network B is the reverse of A i e B AF A B EE O 2 O Q Q Sota S21b Port 1 Port 2 Sita Sova i Sb Sb S122 i S425 O O 1 l 1 i i a Sort 11f 22f O 12f b Figure 2 1 Two port model for a fixture a fixture can be described by eight error terms Sija and Sije where Port 1 and 2 are the pre calibrated VNA measurement ports and b S are the measured fixture S parameters R A A 1 gt O 270 gt Q i Sora i Sora Port 1 Port 2 iil Sita Sova i S 22a Sita i S 422 S 12a O O O 1 i a Figure 2 2 Two port error model for a first order symmetric structure Fixture error networks are described by three S parameters Sija where A and B are network parameters Hence Siia S225 23 Sip and S2 S2 Moreover these conditions satisfy the symmetry condition in Equation 2 5 A coaxial to microstrip and microstrip to coaxial fixture is an example of first order symmetrical fixturing provided that the two adapters are identical Most importantly the signal flow graph also shows that symmetry reduces the number of error terms to three for the A network only In other words symmetry reduces the number of error terms for a two port fixture which is strictly a function of the manufacturing repeatability with direct application to printed circuit b
45. ough Line calibration procedure These algorithms have been implemented as MATLAB code This implementation enables raw S parameters of the through and the line calibration standards refer to Figure 3 1 to be read applies the various calibration procedures and hence obtains the de embedded result Moreover it has various utility routines that can be used for data analysis These calibration routines perform four main functions to obtain the de embedded result Namely e propagation constant determination e Z characteristic impedance determination e error matrix determination e de embedding algorithm Each of the above algorithms will be discussed in detail in the following sections 16 Through Connection D L 00 4 o O OO a Line Connection A Line A b Figure 3 1 Through Line TL Calibration Standards a through connection and b line connection The TRL reflection standard is synthesized using symmetry 17 3 2 Theory The first step in the algorithm is to read in the raw S parameters of the through and the line calibration structures These S parameters are then converted into T parameters or ABCD parameters The equations used for this conversion are Ti 1 51 1 522 S12 gt 521 2 551 3 1 To 20 1 811 1 522 812 821 2 S21 3 2 Ta 1 511 1 522 12 821 2 2
46. qrt thru idx 2 thru idx 3 a c b rerror idx freq_vect idx 1 a r22 c r22 b r22 r22 final_rerror idx rtos rerror idx end retval final_rerror 73 A 8 ptor Purpose Converts polar to rectangular Output Format Real Imaginary Usage out_var ptor mag ang Code function retval ptor x y r3 x cos y r4 x sin y final r3 r4xi end retval final A 9 stot Purpose Converts the S parameters to ABCD or T parameters Output Format Real Imaginary Array Ordering freq 11 21 12 22 Usage out_var stot input_arg z0 Code function retval stot A z0 retval 0 if margin lt 1 error stot two port s param list Zo end for idx 1 size A 1 v A idx s11 v 2 s21 v 3 s12 v 4 s22 v 5 d s21 s21 74 75 t11 1 s11 1 822 s12 s21 d t12 z0 1 s11 1 s22 s12 s21 d t21 1 s11 1 s22 s12 s21 zO d t22 1 s11 1 822 s12 s21 d t idx A idx 1 t11 t21 t12 t22 end retval t A 10 stor Purpose Converts the S parameters to the R parameters or wave cascading param eters Output Format Real Imaginary Array Ordering freq r11 r21 r12 r22 Usage out_var stor input_arg Code function retval stor A r for idx 1 size A 1 s11 A idx 2 s21 A idx 3 s12 A idx 4 s22 A idx 5 r22 1 s21 r21 s22 s21 r12 s11 s21 rii s12 s11 s2
47. r of required standards A symmetrical fixture reduces the number of required standards and hence increases certainty 2 3 Symmetric Fixture Let us consider a fixture containing two error networks as shown in Fig 2 1 a It has two error networks A and B with respective S parameters Sija and Sija The signal flow graph for one error network is shown in Fig 2 1 b The cascade of the two error networks is the fixture S parameter set which are designated by S A fixture is symmetric if the reflection coefficients are equal and the fixture is reciprocal i e if 9114 52 and Saf Sir Using Mason s non touching loop rule we see that the fixture S parameters are related to the individual error network parameters as follows u 521491209110 Sus Strat m Mm 2 1 Soga 95159 Soop Sox 1 7 5 2 2 S21a921b S 2 T 52245116 23 S12a 9126 S ES SE 2 4 A T 55245116 d Equating for Equations 2 1 and 2 2 and applying reciprocity we find one equa tion and six complex unknowns Sua 1 85245116 51165831 Sax 1 85245115 234521 2 5 The above equation is the symmetry condition As symmetry corresponds to the physical nature of the fixture the symmetric solutions are of two types first and second order symmetry as discussed below 2 4 First Order Symmetric Fixture A first order symmetric fixture as shown in Figure 2 2 has identical fixture halves that are asymmetric The two p
48. r ti9791 rue 3 34 to1711 tooTo1 re 3 35 turi tira rpe 3 36 to1rio togroy Trze 3 37 Dividing 3 34 by 3 35 and 3 36 by 3 37 2 2 ta 2 Dl 2 ee Tl 3 38 T21 T21 2 padan t21 2 too tu 2 te 0 3 39 2 23 It is assumed that a rj1 r22 b T12 T22 r21 r22 and ac r11 r21 Hence ac a c By solving 3 38 and 3 39 the values for the roots ac and b are obtained Now from Equation 38 of Engen and Hoer 1 Q1 b ms t 3 40 Pa T we Here T 1 as a perfect short is used and w1 ps see Chapter 2 Hence Psc b 1 1 Pscz As ac a c SC b EE AAB 3 42 1 1 Psc The main objective here is to find the S parameters of the error boxes A and B Using 3 26 and assuming that a 8 y and p are the wave cascading parameters for error box B and d e f and g are the wave cascading parameters for the Through a b a B d e mapa A be 3 43 As error box A and B are symmetrical it can be said that r22 po2 a a 8 c connection and y b Substituting these values in 3 43 yields Sd b a c 7 d e AA VA b b ac d e 3 45 r gr Pe T3 Let us assume that a b z b ac y ac b w and 1 c z and solving 3 45 further gives UE MA g d Zz w i leal E 4 2 Substituting back the values for x y w and z yields d e le ac b f 1 b ac a amp
49. re The coaxial to microstrip transitions and the microstrip line lengths must be symmetrical At low microwave frequencies these can be easily achieved and at higher frequencies achieved through careful design First order symmetry allows the fixture to be represented by three error terms 3 Symmetry permits synthesis of the TRL reflection standard thereby eliminating its need TRL standards are shown in Figure 2 4 a through connection a reflection standard and a reference transmission line of length The reflection is arbitrary and is typically a short circuit As will be shown for the symmetrical through connection we can calculate the reflection coefficient with the microstrip ports terminated in ideal open or short circuits Either of these synthesized reflection coefficients can replace the TRL reflection standard Thus we will refer to this method of using synthesized standards as Through Line or TL method for calibration 2 6 2 Synthesize Reflection Standards The Through Line TL standards are the thorough and the line connections as shown in Figure 2 5 Their results are based on low fixture return loss assumption We will now look at the derivation of the ideal open and short circuit reflection coefficients as previously presented in 3 and 6 As seen in the signal flow graphs of Figure 2 2 we consider the through connection S parameters Sip 525 and Sa Sig and the actual parameters of the error network A are 6 a and
50. re Port lb Through Line TL Calibration Standards a through connection and b line connection The TRL reflection standard is synthesized usine Symmetry sos utu is xs oto e LA edat ois a tit v esr dics Final De embedding of a Two port Device Under Test Simeas here are the measured S parameters for the cascade of error networks A B and theDUT 244 Kava d ba B bau d ie d le PAN Flow Chart for the NetA Algorithm Block Diagram for the VI which reads in Through and Line Data Front Panel for the Block Diagram in Figure 5 1 Block diagram for the second VI i ue ou dev ee spo Front Panel for VI in Figure Gi asf die nt due dran So es ferme pile viii 10 11 12 16 9 9 9 6 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 A 1 B 1 Block diagram for the fourth VI lt 4 3 cg v TRO RUP EO RP 39 Front Panel for VI in Figure 5 5 icu yeh ary Re tape wr arpes 40 Cross section of test IC showing three metallization layers 41 Single line microstrip fixture gado a ah 43 Microwave Measurement Set up 44 Cross sectional and Plan view of the 20G structure 45 Raw S parameters magnitude for the Long line 46 Raw S parameters phase for the Long line 47 Raw S parameters magnitude for the Medium line 48 Raw S parameters phase for the Medium line
51. rk accomplished and suggestions for future research work in Chapter 7 This report also includes two appendices One contains information regarding usage of NetA and each of its utilities The next is about the guidelines for using the LabVIEW implementation of NetA 1 3 Original Contributions The original contributions reported here include 1 NetA tools for TL calibration and de embedding of two port networks and results 2 LabVIEW Implementation of TL calibration and de embedding Chapter 2 Literature Review 2 1 Introduction There are a number of calibration theories that have been developed over the years These calibration theories help us determine network parameters and perform net work analysis which is fundamental to the understanding and design of all microwave components and systems This chapter discusses the fundamentals of a symmetric fixture advantages of using a symmetric fixture types of symmetric fixtures and the Through Line calibra tion process 2 using symmetric fixture This algorithm is built on the basic TRL calibration 1 process 2 2 Advantages of using a Symmetric Fixture In the case of calibration in Network Analysis there are two considerations Firstly there is a need to compensate for imperfections within the calibration standard and secondly calibration certainty Calibration certainty is dependent upon prior knowl edge of the calibration standards and the choice of a minimum numbe
52. s tdmblist 50 Now the TL de embedding is complete and the result is available as the variable deemb dut in the work space area of MATLAB The later sections will explain the utility routines that have been internally called within the above mentioned routines and which are also available for later usage A 6 cal gamma Purpose Calculates the complex propagation constant y Output Format Real Imaginary Array Ordering freq y Usage This routine is called internally from within the t _calib routine Code function retval cal gamma thru line freg L if nargin lt 4 error Input arguments are less end piby2 pi 2 Z0 50 c0 1 621e 12 2500e 6 twobetac 2 0 pi L adflag 0 adjust 0 betami 100 0 betam2 100 0 betam3 100 0 betam4 100 0 betam5 100 0 g_ans for k 1 size thru 1 A k 1 thru k 2 line k 5 line k 2 thru k 5 thru k 4 line k 3 thru k 3 line k 4 phase k 1 angle A k 1 A2m4 k 1 A k 1 2 4 ap k 1 A k 1 sqrt A2m4 k 1 2 an k 1 A k 1 sqrt A2m4 k 1 2 if phase k 1 gt 0 amp phase k 1 lt piby2 egamma k 1 ap k 1 elseif phase k 1 gt piby2 amp phase k 1 lt pi egamma k 1 an k 1 70 71 elseif phase k 1 gt pi amp phase k 1 lt piby2 egamma k 1 an k 1 elseif phase k 1 gt piby2 amp phase k 1 lt 0 egamma k 1 ap k 1 end int_gam k 1 log egamma k 1
53. sults 300 Magnitude Ohms o eo T T N e eo T 150r 100 50 4 0 5 10 15 20 Freguency Ghz Figure 6 9 Characteristic impedance magnitude calculated using the ETRL algo rithm 51 Characteristic Impedance Zc using I m lines T 0 T T NetA results nk 50 MM T 0 o 2 100 0 77 oO de a 150 200 l I l 0 5 10 15 20 Freguency Ghz Figure 6 10 Characteristic impedance phase calculated using the ETRL algorithm Magnitude 1 m 1600 1400 1200 1000 Co o o o o 400 200 92 Propagation Constant using I m lines NetA results o9 5 10 15 20 Frequency Ghz Figure 6 11 Propagation Constant magnitude using l m lines 93 65 T 35 Propagation Constant using I m lines T NetA results 0 5 10 Frequency Ghz Figure 6 12 Propagation Constant phase using 1 m lines 15 20 Error Network Parameters 54 1 T T NetA results 0 9 J 0 8 J 0 7 B S11 TD 2 E 0 6 ds A AA RS e ED A EA A AAA UR A ARE N n Mz ARES SEA AMA DAA ARAN 3 S22 0 5 0 43 12 921 7 0 3 PE ck eg ane TS ECCE I RM IEEE E M NE EQ race 0 2 l l 0 5 10 15 20 Frequency Ghz Figure 6 13 Error network S parameters magnitude using l m lines 99 Error network parameters 40 30 20 10 o 20 40 NetA results
54. tained and measure its S parameters which are inclusive of the assumed error boxes and are given by Seas Refer Figure 3 2 Thus Smeas Serror A Sdut Serror B 3 62 Saut Bea Smeas ae 3 63 Saut here is the de embedded S parameters for the measured two port network Here the above error matrices and measured parameters are first converted into T parameters de embedded results are now obtained in terms of T parameters and then converted back to S parameters 3 3 Summary In Chapter 3 we discussed the TL calibration algorithms in detail along with the final de embedding process for a two port network DUT The next chapter discusses 26 Oo Porti DUT O Figure 3 2 Final De embedding of a Two port Device Under Test Simeas here are the measured S parameters for the cascade of error networks A B and the DUT the MATLAB implementation and flow of these TL algorithms for de embedding two port microwave measurements 27 Chapter 4 NetA 4 1 Introduction to NetA NetA is a Computer Program developed to enhance the capability of Computer Aided Microwave Measurements NetA enables engineers to perform the Through Line TL calibration and de embedding procedure for two port networks NetA is a tool which is used for processing S parameter data and its prime use is to implement the Through Line de embedding algorithm NetA also has a number of utilities that he

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