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 ord with trces Center pin Flnge-mount connector screw -shped support Copyright by Jose E. Schutt ine, ll ights eserved
Coxil Microstrip rnsition In SM C C C SM C Out Equivlent Circuit D Plot Copyright by Jose E. Schutt ine, ll ights eserved 3
With prsitics No prsitics Copyright by Jose E. Schutt ine, ll ights eserved 4
CIION 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 clibrtion Copyright by Jose E. Schutt ine, ll ights eserved 5
Error ox Modeling model for the different error boxes cn be implemented Mesurement W Plnes W Port Error ox Γ Γ Error ox Port Error boxes nd ccount for the trnsition prsitics nd the electricl lengths of the microstrip. Mke three stndrds: hru, ine nd eflect Copyright by Jose E. Schutt ine, ll ights eserved 6
Step - HU Clibrtion connect thru t b = t b Copyright by Jose E. Schutt ine, ll ights eserved 7
Step - INE Clibrtion connect line (Note: difference in length between thru nd line) INE d INE b Copyright by Jose E. Schutt ine, ll ights eserved 8
Step 3 - EFEC Clibrtion connect reflect EFEC b Copyright by Jose E. Schutt ine, ll ights eserved 9
Mesurement Comprison Mesured S of Microstrip Unknown eltive to OUCHSONE Models 5 PO EX. dt compred to =.808 nh model dt compred to =.948 nh model eltive Mgnitude, d 0-5 PO EX. clibrtion clibrtion.5.5 3 3.5 4 4.5 5 Frequency, GHz Copyright by Jose E. Schutt ine, ll ights eserved 0
Mesurement Comprison 0 Mesured Dt for Microstrip Unknown Mesured 0/8/94-5 S (d) -0-5 -0 with clibrtion with 7 ps port ext. (inc. brrel).5.5 3 3.5 4 4.5 5 Frequency, GHz Copyright by Jose E. Schutt ine, ll ights eserved
Derivtion Objectives - Obtin network prmeters of error boxes nd - emove their effects in subsequent mesurements Copyright by Jose E. Schutt ine, ll ights eserved
Model for eflect S S b S S Γ Γ S S b S S b = 0 b = 0 Mesurements Copyright by Jose E. Schutt ine, ll ights eserved 3
Model for hru S S b S S S S b S S b = 0 b = 0 b = 0 b = 0 4 Mesurements Copyright by Jose E. Schutt ine, ll ights eserved 4
Model for ine S e -γ S b S S S S b S e -γ S b = 0 b = 0 b = 0 b = 0 4 Mesurements Copyright by Jose E. Schutt ine, ll ights eserved 5
Use (or ) Prmeters Using prmeters (trnsfer prmeters), we cn show tht if b = S+ S b = S + S b Δ S b = S S Δ= S S S S Δ = S S S Copyright by Jose E. Schutt ine, ll ights eserved 6
Derivtion he mesurement mtrix M is just the product of the mtrices of the error boxes nd the unknown DU or = M = M et be written s r r b = r r r = c is similrly written s ρ ρ α β = ρ ρ ρ = γ he inverse of is b = r bc c Copyright by Jose E. Schutt ine, ll ights eserved 7
nd the inverse of is Derivtion β = ρ α βγ γ α he mtrix of the DU is then found from b β = M r c ρ α β b γ c γ α α Note tht lthough there re eight terms in the error boxes, only seven quntities re needed to find. hey re, b, c, α, β, γ, nd r ρ From the mesurement of the through nd of the line, seven quntities will be found. hey re b, c/, β/ α, γ, r ρ, α nd e γl In ddition to the seven quntities, if were found, the solution would be complete. et 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 Copyright by Jose E. Schutt ine, ll ights eserved 8
= D where is the mtrix of the line Derivtion Now = so tht = D D = Define = D Which when substituted into the bove equtions results in = he mtrix is known from mesurements nd will be written s t t = t t γ l e 0 = + γ l 0 e, since the line is non-reflecting Copyright by Jose E. Schutt ine, ll ights eserved 9
Derivtion is unknown nd ws written s r r b = r r r = c similrly ws written s ρ ρ α β = ρ ρ ρ = γ eclling = nd writing the mtrices results in γ l t t b b e 0 t t c = c 0 e + γ l Next, writing out the four equtions gives: Copyright by Jose E. Schutt ine, ll ights eserved 0
Derivtion l t + t c= e γ l t + t c= ce γ l t b+ t = be + γ t b+ t = e +γ l Dividing the first of the bove eqution by the second results in t + t t+ tc = = c t+ t c c t + t c 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 Copyright by Jose E. Schutt ine, ll ights eserved
Derivtion t b+ t t b+ t = b which gives the nlogous qudrtic eqution for b s ( ) t b + t t b t = 0 Dividing the fourth eqution in the group by the second results in γ t b+ t t b+ t e = c = t + tc t + t c Since e γ 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 Copyright by Jose E. Schutt ine, ll ights eserved
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 = ( det )( det ) = ( det )( det ) or ( ) ( ) det = det = so tht tt tt = which implies tht there re only three independent ij. hen there re only three independent results, e.g. b, /c, nd e γ. Copyright by Jose E. Schutt ine, ll ights eserved 3
Derivtion Now let us find four more quntities Now b α β d e rρ g c = = = γ f b b c = bc c So tht or r ρ r α β g b d e γ = bc c f ρ α β g d bf e b γ = bc f cd ce Copyright by Jose E. Schutt ine, ll ights eserved 4
from which we cn extrct We lso hve Derivtion c e ce rρ = g = g bc c b α β d bf e b γ = ce f cd ce from which we obtin nd γ = c f d c e β e b = α d bf Copyright by Jose E. Schutt ine, ll ights eserved 5
nd α = d bf c e Derivtion he dditionl four quntities found re β/α, γ, r ρ nd α. o complete the solution, one needs to find. et the reflection mesurement through error box be w. hen w = Γ + b cγ + which my be solved for in terms of the known b nd /c s = w b c Γ w We need method to determine. Use the mesurement for the reflect from through the error box. et w denote the mesurement w SSΓ S ΔΓ = S + = S Γ S Γ Copyright by Jose E. Schutt ine, ll ights eserved 6
Derivtion or w = w ρ ρ Γ ρ ρ + ρ ρ Γ αγ γ = βγ α my be found in terms of γ nd β/α s α = w + γ β Γ + w α ecll w b = c Γ w Copyright by Jose E. Schutt ine, ll ights eserved 7
so tht = α w w Derivtion β + w b α + γ c w From erlier so tht or α d bf = c e w b d bf = w β + w α + γ c c w e =± w w b d bf β + w α c c + γ w e which determines to within ± sign. Copyright by Jose E. Schutt ine, ll ights eserved 8
Derivtion Γ w b = c w So if Γ 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 β = M r c ρ α β b γ c γ α α in which ll the terms hve now been determined. Copyright by Jose E. Schutt ine, ll ights eserved 9