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Localisation de charge sur abaque de Smith
0.2+j0.5
1+j1
2-j2
4+j0 0.2+j0
0.3-j0.4
0.2+j0.5 1+j1 2-j2 0.3-j0.4 0.2+j0 4+j0
SWR et dmin sur abaque de Smith
1+j1
0.2+j0
0.3-j0.4
0.3-j0.4 1+j1 0.2+j0
dmin = 0.338!
dmin = 0.065!
Admittance sur abaque de Smith
1+j1
0.2+j0
0.3-j0.4
0.3-j0.4 1+j1 0.2+j0
yb=1.2+j1.6
yc=5+j0
ya=0.5-j0.5
Déplacement sur abaque de Smith
zc(0.8)=0.3+j0.43
zc(0.1)=0.5-j0.94
zc=3.26-j1.49
Exemple 9.7
!c (0.8") = 0.6!130°zc (0.8") = ?zc = ?zc (0.1") = ?
0.3
0.1
Charge compliquée sur abaque de Smith
zc=0.24-j0.55
yc=y1(0.21)+y2=2.344-j0.914
y1(0.21)= 0.344-j0.914
Exemple 9.9
0.21
zc = z1(0.71!) ! z2
z1 = 0.24 " j0.55; z2 = 0.5#c = ?
zc=0.37+j0.144
y1=0.666+j1.53
Mesure de charge sur abaque de Smith
rmin
Exemple 9.10 0.355
Zc(dmin)
zc=0.75+j0.97
SWR = 3dmin = 21.3cm; ! = 60cmzc = ?
Adaptation transformateur l/4
rmax=2.618
Exemple 9.12
dmax=0.037
zc0=2+j1
Zc = 100 + j50!Z0 = 50!Zoq = ?; dq = ?
Zc (dq ) = Rmax = SWR !Z0 = 2.618(50) = 130.9"
zcq (dq ) =Zc (dq )
Z0q
=130.980.9
= 1.618
zcq (dq +#q
4) =
11.618
= 0.618
Zc (dq +#q
4) = 0.618 !Zoq = 0.618(80.9) = 50"*1.618=nombre d'or
Adaptation à 1 stub
yc
Exemple 9.13
0.125s
zc=2+j1
yc(ds)=1+j1.0
Zc = 100 + j50!Z0 = Z0s = 50!ds = ?; ! s = ?
Ys = !1.0Y0 = ! jY0s cot"s! s
ys = !1.0cot2#$s
! s
%
&'(
)*
0.199
ycc(s)= ystub=0-j1.0
ycc
Adaptation à 1 stub
yc=0.4+j1.2
Exemple 9.14
0.070s
yc(ds)=1+j2.12
0.045
ycc(s)= ystub=0-j2.12
ycc
yc = 0.4 + j1.2a) Z0s = Z0; !s = ! : ds = ?; ! s = ?b) ! s = 0.125!s : ds = ?; Z0s = ?
Ys = !2.12Y0 = ! jY0s cot"s! s
a) 2.12 = cot2#$s
! s
%
&'(
)*+ ! s = arctan(
12.12
)$s
2#
b) Ys = !2.12Y0 = ! jY0s cot2#$s
0.125$s
%
&'(
)*= ! jY0s
+ Y0s = 2.12Y0
Circuit pour antenne-réseau micro-ondes
ligne 70W
coupleur 3dB
diviseur /3
1 transfo l/4 59W 3 transfo l/4 135W
stub CO l/4=CC
antenne microruban
ligne 120W
transfo l/4 85W 120 !120 = 60!
"11 =60#12060+120
= # 13
SWR = 2
Z0q =120SWR
= 85!
120 ! Zin2 = (135)2
Zin2 = 150"
150 150 150 = 50"
50 ! 70 = (Z0q )2
Z0q = 59"
Adaptations d’un ampli sur abaque de Smith
yc
ls b=0.105s
yc(ds)=1-j1.56 0.099
ystub b=0+j0.78
yco
yc = 2.8 + j1.9Z0s = Z0; !s = !ds = ?; ! sa,b = ?
ystub a=0+j1.56
ls a=0.159s
1+j1.56
0.099s
2.8-j1.9=yc*
Adaptations d’un ampli sur abaque de Smith
yc
ls c=0.375s
Yc+2Ys c=(2.8+j0)/50
ystub c=0-j1.0
yco
yc = 2.8+ j1.9! sc = 0.375!s; dsc = 0Z0sc = ?; Z0qc = ?
! j1.9 / (2"50#) = ! jY0sc cot($s! sc ) = ! jY0sc
Z0sc = (1 / Y0sc ) = 52.6#
Z0qc =50
SWR= 50
2.8= 29.9#
A
Transformation conforme sur abaque de Smith lieu r/g=1 déplacé de 0.1l vers la charge
A’
0.1 B’
C’ B
C
D’=D
Lieu r/g=1 déplacé et lieu r=cte
yc=0.4-j0.2
ajout d’une susceptance à yc =0.4-j0.2
0.4+j0.36
0.1
Intersection de -lieu r/g=1 déplacé de 0.1l vers la charge -lieu r=0.4=cte
0.4+j2.4
Adaptation à 2 stubs
yc=0.4+j0.8
Exemple 9.15
0.125s2
yt1=0.4+j0.2
d12=0.125
ystub2=0-j1.0
ycc2
0.164s1
yt1(d12)=1+j1.0
ystub1=0-j0.6
ycc1
ds1 = 0; d12 = 0.125!yc = yc (ds1) = 0.4+ j0.8Z0 = Z0s1 = Z0s2; vp = vps1 = vps2
! s1 = ?; ! s2 = ?
Adaptation à 2 stubs
yc=2-j1
Autre exemple 0.361s2
yt1=0.7+j0.05
d12=0.125
ystub2=j0.85
ycc2
0.193s1
yt1(d12)=1+j0.38
ystub1=-j0.38
ycc1
ds1 = 0.082!; d12 = 0.125!yc = 2 " j1Z0 = Z0s1 = Z0s2; vp = vps1 = vps2
! s1 = ?; ! s2 = ?
yc(ds1)=0.7-j0.8
ds1=0.082
Optimisation du VSWR avec susceptance
yc
yc(dopt)=0.85+j1.05
Exemple 9.17
yc = 0.6 ! j0.8bp = !0.8 ( yp = 0 ! j0.8)
dopt = ?
A
D
B
E C
F G
dopt=0.279
Optimisation du VSWR avec bout de ligne
zc00
zc00(l00opt)
Exemple 9.18
Zc =100+ j50 !Z00 =100 ! (d0 = 0)!00opt
= ?
A D
B E
C F G
zc0
l00opt=0.356
25 50
200 zc0 10
25 50 100 200 500 zc0q(l/4)
Optimisation du VSWR avec transfo l/4
zc0q
Exemple 9.19
Zc =100+ j50 !Z0 = 50 ! Z0qopt
= ? (dq = 0)
Z0qopt=75W
G
25 50 10
100 200 z0q =500
100
Optimisation du VSWR���avec charge Z=50+jX en série à d=0.1λ Exemple nouveau
Zc = 100 + j50 !Z0 = 50 ! xopt = ? (z = 1+ jx à d = 0.1")
zc=2+j1
A
B
C
D
E
F
G
zc(0.1λ)=1.4-j1.1
zopt=1+j1.1
0.1λ
Xopt = 1.1(Z0 ) = 55!