Microwave couplers. Outline

Transcription

1 Microwave coupler Anja Skrivervik Laboratoire d'electromagnétime et d'acoutique Ecole Polytechnique fédérale de Lauanne CH-05 Lauanne Outline Theoretical approach Ideal coupler Real coupler Application : Hybrid ring Hybrid coupler

2 -port cattering matrix General adapted and reciprocal 3 flow chart a b b a 3 a 3 b 33 b 3 a 3

3 adapted and reciprocal and lole -port * * * 3 3 * * * = * * * * * * What doe it mean? + = 0 ( line3xcolumn ) x * * * = 0 ( linexcolumn ) x * * * ( ) * 3 3 = 0 6

4 ( ) * 3 3 = 0 t olution : 3 = 0, 0, 3 0 thu : + = 0 = 0 * * a b a 3 b b a b a 7 ( ) * 3 3 = 0 nd olution : = 3 election of reference plane : = 3 = jβ = ( linexcolumn) + + = ( line3xcolumn3) thu : = 3 = α with adequate ref. plane 8

5 nd olution ( ) ( ) + = 0 = α + ( linexcolumn ) * * * = 0 = β ( line3xcolumn) * * * α = 0, β = = = Ideal coupler * * * * * * = * * * * 3 3 * * = + = 0 + = + = 0 + = 3 + = 0

6 Ideal coupler = = α 3 = = β 3 α + β = 3 3 = αe = αe = β e = β e jϕ jη jψ jθ with ( ϕ+ η) = π+ ( ψ+ θ) + nπ and α> β by convention ymmetric coupler ψ = θ = π 0 α 0 jβ α 0 jβ 0 0 jβ 0 α jβ 0 α 0 a b a 3 b 3 α jβ α b a b a

7 aymmetric coupler ψ = 0, θ = π 0 α 0 β α 0 β 0 0 β 0 α β 0 α 0 a b a 3 b 3 -β β α β -β α b a b a 3 Summary : ideal coupler Coupling : LC = -0log0 β Attenuation : LA = -0log0 α α β input through 3 iolated coupled input through 3 iolated coupled

8 real coupler ο α β Attenuation : LA = -0log 0 α Coupling : LC = -0log 0 β Iolation : LI 3 = -0log 0 3 Iolation : LI = -0log 0 Directivity : LD 3 = LI 3 -LC = -0log 0 3 /β Directivity : LD = LI -LC = -0log 0 /β 5 example : 0 db waveguide coupler 6

9 example : magic T 7 example : magic T combined with 0dB coupler 8

10 Example : E Band 0 db coupler 9 Example LC [db] β α LA[dB]

11 Directivity : meaure of quality Microtrip hybrid coupler : 30 db Multihole waveguide coupler : 0 db Waveguide coupler ued in metrology : db Coupler ued in meaurement

12 with coupler amplitude meaurement with coupler Reflectometry preciion meaurement phae and amplitude meaurement 3 coupler reflectometry a 3 b3?

13 coupler reflectometry b3 3 3 b3c 3 3 a a - b 3 = ii 3 a b 3 b 3c = ii b 3c = 3 a 5 real coupler ii, 3, <<, but non equal to zero we need : coupling LC=-0logβ iolation LI3=-0log 3 LI=-0log The quality of the coupler i given by : directivity LD3=LI3-LC=-0log 3 /β LD=LI-LC=-0log /β 6

14 coupler reflectometry b3 b3c a a b 3 = a ii b3 ii3+ 3 = b + ( ) b 3c = a ( ) 3c coupler reflectometry 3 i non negligible at the numerator if ii << 3 i negligible at the denominator if the couple i of good quality : b3 3 = ii b 3c 3 The phae of the ignal are not known b b + b b ii 3c 3 3c 3 8

15 coupler reflectometry For a weak coupling (LC large) S The error term i directly the directivity of the coupler : b b + b b ii 3c 3 3c 3 LD [db] 3/ coupler reflectometry br b a A A A? b Aii + B = b C + D r 30 ii A= B= C = D= Ue adapter to put B=C=0 b ii3 = b r

16 coupler reflectometry ued for feed back amplitude meaurement br b a A A A? 3 coupler reflectometry ratiometer br b a A A A? 3

17 coupler reflectometry zero detector + A ϕ br b a A A A? 33 coupler reflectometry network analyer A ϕ br b a A A A? 3

18 Network analyer (principle) 35 Network analyer (principle) I f = 0 MHz L f = 300 khz U=Uo ρ co(ω if t+ϕ) U=Uo ρ co(ω Lf t+ϕ) ρ inϕ ρ coϕ Ur=Uoco(ω if t) Ur=Uoco(ω LF t) 36

19 Attenuation meaurement br b a? load Same principle than reflectometry 37 Microwave meaurement 38

20 Network Analyor 39 the quadrature hybrid the 80 hybrid example of utilization Example of coupler in printed technology 0

21 The quadrature hybrid [ S] = 0 0 j 0 j 0 0 j 0 j 0 0 a b a 3 b b a b 3 a input through 3 j iolated coupled The quadrature hybrid

22 quadriport with double ymmetry () = = = = 33 = = = = 3 3 = = = = = = = = 3 3 quadriport with double ymmetry () o.c left-right : ymmetric excitation top-bottom : ymmetric excitation 3 o.c a = a = a = a 3 b = b = b = b 3 b ρ = = a

23 quadriport with double ymmetry (3) c.c left-right : antiymmetric excitation top-bottom : antiymmetric excitation 3 c.c a = a = a = a 3 b = b = b = b ρ 3 b aa aa = = aaa quadriport with double ymmetry () o.c left-right : ymmetric excitation top-bottom : antiymmetric excitation 3 c.c a = a = a = a 3 b = b = b = b 3 b ρa = a a a = + 3 6

24 quadriport with double ymmetry (5) c.c left-right : antiymmetric excitation top-bottom excitation 3 o.c a = a = a = a 3 b = b = b = b 3 b ρa = a a a = quadriport with double ymmetry (6) ρ ρ = ρa 3 ρ aa a ρ ρ a = 3 ρa ρaa 8

25 quadriport with double ymmetry (7) matching : =0 directivity : 3 =0 ρ + ρa + ρa + ρaa = 0 ρ+ ρa ρa ρaa = 0 ( ) arg ( ) ( ) arg ( ) ρ = ρ arg ρ ρ = π a a ρ = ρ arg ρ ρ = π aa a aa a 9 quadriport with double ymmetry (7) Lole cae : ( ρ ρ ) aa = = α ( ρ + ρ ) aa = = β ρ = ij by choice of reference plane Im ρ aa jβ ρ α Re ρ a ρa 50

26 application to printed hybrid 5 The quadrature hybrid ρ = Y c jy tan( β d ) jy tan( β d ) Y c + jy tan( β d )+ jy tan( β d ) ejϕ ρ a = Y Y Y c c + jy cot( β d ) jy tan( β d ) Y c jy cot( β d )+ jy tan( β d ) ejϕ β d β d ρ a = Y Y c jy tan( β d )+ jy cot( β d ) Y c + jy tan( β d ) jy β d ) e jϕ c.c. ρ aa = Y c.o. c + jy cot( β d )+ jy cot( β d ) Y c jy cot( β d ) jy cot( β d ) ejϕ with ρ = ρ a =α+jβ we get : ϕ = π Y Y = Y c ρ aa = ρ a = α+ jβ Y cot( β d )+ Y cot( β d )= 0 c.c. c.o. 5

27 The quadrature hybrid "eay" olution β d =β d = π Y = Y c α Y = Y c β α β take a negative value. Lenght : d = λ 8 d =λ 8 Hybrid coupler (3 db): α = β = Y = Y c Y = Y c 53 The quadrature hybrid "not o eay" olution Y = Y c cot β d Y ( ) = cot( β d ) [ ( )] [ ( )] α= Y c Y tan( β d )+ Y tan β d Y c + Y tan( β d )+ Y tan β d [ ( )] ( ) β= Y c Y tan( β d )+ Y tan β d Y c + Y tan( β d )+ Y tan β d [ ] ( ) Y c cot β d cot( β d ) 5

28 meaured verification 55 Near field meaurement at 3 GHz non corrigé Q-hybride - f=3 GHz - non corrigé corrigé Q-hybride - f=3 GHz - corrigé Y [mm] 0 - Y [mm] X [mm] X [mm] [db] [db] 56

29 The 80 Hybrid [ S] = a b a 3 b 3 b a b a input Σ through 3 j iolated coupled 57 The printed 80 Hybrid rat race Hybrid ring 58