ECE 451 Automated Microwave Measurements. TRL Calibration
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1 ECE 45 utomted Microwve Mesurements L Clibrtion Jose E. Schutt-ine Electricl & Computer Engineering University of Illinois jschutt@emlb.uiuc.edu ECE 45 Jose Schutt ine
2 Coxil Microstrip rnsition ord with trces Center pin Flnge-mount connector screw L-shped support ECE 45 Jose Schutt ine
3 Coxil Microstrip rnsition In SM C L L C L L C L SM C Out Equivlent Circuit D Plot ECE 45 Jose Schutt ine 3
4 With prsitics No prsitics ECE 45 Jose Schutt ine 4
5 L CLIION SCHEME coxil connector coxil connector DU microstrip microstrip Wnt to mesure DU only nd need to remove the effect of cox-to-microstrip trnsitions. Use L clibrtion ECE 45 Jose Schutt ine 5
6 L Error ox Modeling model for the different error boxes cn be implemented Mesurement W Plnes W Port Error ox Error ox Port Error boxes nd ccount for the trnsition prsitics nd the electricl lengths of the microstrip. Mke three stndrds: hru, Line nd eflect ECE 45 Jose Schutt ine 6
7 Step - HU Clibrtion connect thru t b t b ECE 45 Jose Schutt ine 7
8 Step - LINE Clibrtion connect line (Note: difference in length between thru nd line) LINE d LINE L b ECE 45 Jose Schutt ine 8
9 Step 3 - EFLEC Clibrtion connect reflect EFLEC b ECE 45 Jose Schutt ine 9
10 L Mesurement Comprison Mesured S of Microstrip Unknown eltive to OUCHSONE Models 5 PO EX. dt compred to L=.808 nh model L dt compred to L=.948 nh model eltive Mgnitude, d 0-5 PO EX. clibrtion L clibrtion Frequency, GHz ECE 45 Jose Schutt ine 0
11 L Mesurement Comprison 0 Mesured Dt for Microstrip Unknown Mesured 0/8/94-5 S (d) with L clibrtion with 7 ps port ext. (inc. brrel) Frequency, GHz ECE 45 Jose Schutt ine
12 L Derivtion L Objectives - Obtin network prmeters of error boxes nd - emove their effects in subsequent mesurements ECE 45 Jose Schutt ine
13 Model for eflect S S b S S S S b S S b 0 b 0 Mesurements ECE 45 Jose Schutt ine 3
14 Model for hru S S b S S S S b S S b 0 b 0 b 0 b 0 4 Mesurements ECE 45 Jose Schutt ine 4
15 Model for Line L S e -L S b L S S S S b L S e -L S L b L 0 L b L L 0 L b L L 0 L b L L 0 L 4 Mesurements ECE 45 Jose Schutt ine 5
16 Using prmeters (sme s trnsfer prmeters), we cn show tht if b SS b S S Use (or ) Prmeters b Sb S S S S S S S b S S ECE 45 Jose Schutt ine 6
17 L Derivtion he mesurement mtrix M is just the product of the mtrices of the error boxes nd the unknown DU or M M Let be written s r r b r r r c is similrly written s he inverse of is b r bc c ECE 45 Jose Schutt ine 7
18 nd the inverse of is L Derivtion he mtrix of the DU is then found from b M r c b c Note tht lthough there re eight terms in the error boxes, only seven quntities re needed to find. hey re, b, c,,, nd r From the mesurement of the through nd of the line, seven quntities will be found. hey re b, c/,, r, nd e l In ddition to the seven quntities, if were found, the solution would be complete. Let us first find the bove seven quntities. he idel through hs n mtrix which is the x unit mtrix. he mesured mtrix with the through connected will be denoted by nd is given by Where nd re the mtrices of the error box nd respectively. With the line connected, the mesured mtrix will be denoted by D nd is equl to ECE 45 Jose Schutt ine 8
19 D L where L is the mtrix of the line L Derivtion NOE: quntities shown in ED re known Now so tht D L D L Define D Which when substituted into the bove equtions results in L he mtrix is known from mesurements nd will be written s t t t t L l e 0 0 e l, since the line is non-reflecting ECE 45 Jose Schutt ine 9
20 L Derivtion is unknown nd ws written s r r b r r r c similrly ws written s eclling L nd writing the mtrices results in t t t t l b b e 0 l c c 0 e Next, writing out the four equtions gives: ECE 45 Jose Schutt ine 0
21 L Derivtion t t l t ce l t cce l t bt be l t bt be Dividing the first of the bove eqution by the second results in t t t t c c c t c t c t t which gives qudrtic eqution for /c t t t t 0 c c Dividing the third eqution in the group by the fourth results in ECE 45 Jose Schutt ine
22 L Derivtion t t b t b t b which gives the nlogous qudrtic eqution for b s t b t t bt 0 Dividing the fourth eqution in the group by the second results in L t bt t bt e c t t c t t c Since e L is not equl to, b nd c/ re distinct roots of the qudrtic eqution. he following discussion will enble the choice of the root. Now b=r /r =S nd r S S S c r S ECE 45 Jose Schutt ine
23 L Derivtion For well designed trnsition between cox nd the non-cox S, S << which yields b << nd /c >>. herefore, b c which determines the choice of the root eclling L det det det det L or det det L so tht t t t t which implies tht there re only three independent ij. hen there re only three independent results, e.g. b, /c, nd e L. ECE 45 Jose Schutt ine 3
24 L Derivtion Now let us find four more quntities Now r b d e g c f b b c bc c So tht or r r g bd e bc c f g d bf eb bc f cd ce ECE 45 Jose Schutt ine 4
25 L Derivtion from which we cn extrct r We lso hve ce g bc c e g c b d bf e b ce f cd ce from which we obtin nd c f d c e e b d bf ECE 45 Jose Schutt ine 5
26 nd d bf c e L Derivtion he dditionl four quntities found re,, r nd. o complete the solution, one needs to find. Let the reflection mesurement through error box be w. hen w b c which my be solved for in terms of the known b nd /c s w b c w We need method to determine. Use the mesurement for the reflect from through the error box. Let w denote the mesurement w SS S S S S ECE 45 Jose Schutt ine 6
27 L Derivtion or w w my be found in terms of nd s w w ecll w b c w ECE 45 Jose Schutt ine 7
28 ECE 45 Jose Schutt ine 8 w w b c w w d bf c e w w b d bf c c w w e w w b d bf c c w w e so tht From erlier so tht which determines to within sign. L Derivtion or
29 L Derivtion w b c w So if is known to within then my be determined s well. Clibrtion is complete nd we cn now proceed to the mesurement of the DU. From erlier, the mtrix of the DU is found from b M r c b c in which ll the terms hve now been determined. ECE 45 Jose Schutt ine 9
30 L ppliction ECE 45 Jose Schutt ine 30
31 L ppliction hru eflect Line ECE 45 Jose Schutt ine 3
32 L ppliction ECE 45 Jose Schutt ine 3
33 L ppliction ECE 45 Jose Schutt ine 33
34 L ppliction ECE 45 Jose Schutt ine 34
35 ECE 45 Jose Schutt ine 35
36 eferences Pul W. Klock, he heory of eflectometers, 995 gilent Network nlysis, "pplying the 850 L Clibrtion for Non-Coxil Mesurements", Product Note ECE 45 Jose Schutt ine 36
ECE 451 Automated Microwave Measurements. TRL Calibration
utomted Microwve Mesurements Clibrtion Jose E. Schutt-ine Electricl & Computer Engineering University of Illinois jose@emlb.uiuc.edu Copyright by Jose E. Schutt ine, ll ights eserved Coxil Microstrip rnsition
Chapter 3 MATRIX. In this chapter: 3.1 MATRIX NOTATION AND TERMINOLOGY
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