Curs 2 2018/2019 - rf-opto.etti.tuiasi.ro
Transcript of Curs 2 2018/2019 - rf-opto.etti.tuiasi.ro
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Curs 2 2018/2019
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2C/1L, DCMR (CDM) Minim 7 prezente (curs+laborator) Curs - conf. Radu Damian Vineri 11-13, P7
E – 50% din nota
probleme + (2p prez. curs) + (3 teste) + (bonus activitate) ▪ 3pz=+0.5p
toate materialele permise Laborator – conf. Radu Damian Joi 8-14 impar II.13
L – 25% din nota
P – 25% din nota
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http://rf-opto.etti.tuiasi.ro
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Personalizat
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factorul “andrei” = -2p
2017/8
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COMPETENT: Care este bine
informat într-un anumit domeniu;
care este capabil, care este în
măsură să judece un anumit lucru. [DEX]
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> 2010 < 1950
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0 dBm = 1 mW 3 dBm = 2 mW 5 dBm = 3 mW 10 dBm = 10 mW 20 dBm = 100 mW -3 dBm = 0.5 mW -10 dBm = 100 W -30 dBm = 1 W -60 dBm = 1 nW
0 dB = 1 + 0.1 dB = 1.023 (+2.3%) + 3 dB = 2 + 5 dB = 3 + 10 dB = 10 -3 dB = 0.5 -10 dB = 0.1 -20 dB = 0.01 -30 dB = 0.001
dB = 10 • log10 (P2 / P1) dBm = 10 • log10 (P / 1 mW)
[dBm] + [dB] = [dBm]
[dBm/Hz] + [dB] = [dBm/Hz]
[x] + [dB] = [x]
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Operatii cu numere complexe! z = a + j · b ; j2 = -1
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tipic
f ≈ 1÷3GHz – 300GHz
λ ≈ 1mm – 10cm
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Lungimea electrica a unui circuit l – lungimea fizica
E = β·l – lungimea electrica
Dependenta castigul antenei
imaginea unui obiect pe radar
lllE 2
2
rflc
lE
0
2
V, I variabile ~ inutile
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Comportarea (descrierea) unui circuit depinde de lungimea sa electrica la frecventele de interes E≈0 Kirchhoff
E>0 propagare
lllE 2
2
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Ecuatii constitutive t
BE
Jt
DH
D
0 B
tJ
ED
HB
EJ
• In vid
mH7
0 104
mF12
0 10854,8
smc 8
00
0 1099790,21
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Daca un mediu este metal ideal toate campurile se anuleaza in interior
2 , 2
2 , 2
n S0
S
h
C
l n S
h
1 , 1 1 , 1
a) b)
021 EEn
SJHHn 21
SDDn 21
021 BBn
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Simplificarea ecuatiilor lui Maxwell
122 JjEE
JHH 22
Xjt
XeXX tj
0
dtetfg tj
degtf tj
E
0 H
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cazuri particulare in care exista rezolvare analitica
semnale cu variaţie armonică în timp, transformata Fourier, spectru
Xjt
XeXX tj
0
dtetfg tj
degtf tj
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dtetfg tj
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dtetfF tj
deGtg tj FG
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022 EE
022 HH
j 22
γ – Constanta de propagare
Mediu lipsit de sarcini electrice
Ecuaţiile Helmoltz sau ecuaţiile de propagare
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Camp electric dupa directia Oy, prin alegerea judicioasa propagare dupa directia Oz a sistemului de referinta
zz
y eEeEE
jj2
Exista numai unda progresiva E+=> A
zj
y eAE
Camp armonic
ztjz
y eeAE
Amplitudine
Atenuare
Propagare (variatie in timp si spatiu)
Propagare
Polarizare circulara
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111
ztjzy eeCtzE
2~, EPW
222
ztjzy eeCtzE
12
1
22
22
22
1
2 zz
z
z
eeCt
eCt
P
PA
12210
1
210 log10log10][
zze
P
PdBA
121012 686.8log20][ zzezzdBA
0686.8]/[/ kmdBLA
Atenuarea se exprima de obicei in dB/km de obicei valori pozitive semnul = implicit
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HjE
Mediu fara pierderi, σ = 0
y
x
EjH
j
x
y
H
EImpedanta intrinseca a mediului
ztjz
y eeAE punctele de faza constanta: const zt
Viteza de faza
1
dt
dzv
Viteza de grup
d
d
dt
dzvg in medii dispersive unde β = β(ω)
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Viteza de faza – viteza virtuala cu care circula punctul cu o anumita faza
Viteza de grup – viteza cu care circula informatia (energia)
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In vid
Indice de refractie al mediului
3770
00
smc 8
00
0 1099790,21
0cvv g
rr
cc
0
000
11
rn
Periodicitate in spatiu
f
c00
2
fT
12
Periodicitate in timp
f
c
2
fT
12
rr f
c
00
n
cc 0
In mediu nedispersiv εr
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unda
incidenta
reflectata
unda
directa
inversa
zzy eEeEE
jj2
ztjzy eeEE
ztjzy eeEE
const zt
const zt
punctele de faza constanta:
Camp electric dupa directia Oy, prin alegerea judicioasa propagare dupa directia Oz a sistemului de referinta
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unda
incidenta
reflectata
unda
directa
inversa
ztjzztjzy eeEeeEE
ztjzztjzz eeHeeHH
ztjzztjz eeVeeVzV
ztjzztjz eeIeeIzI
ztjztj eVeVzV
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Câmpuri electromagnetice cu variaţie armonică în timp
simplificarea ecuatiilor lui Maxwell
In medii delimitate solutiile ecuatiilor lui Maxwell trebuie sa verifice conditiile la limita
solutiile trebuie sa respecte anumite conditii suplimentare
Xjt
XeXX tj
0
dtetfg tj
degtf tj
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Campul electric trebuie sa fie perpendicular pe un perete metalic sau nul
Campul magnetic trebuie sa fie tangent la un perete metalic sau nul
2 , 2
2 , 2
n S0
S
h
C
l n S
h
1 , 1 1 , 1
a) b)
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Similar cu transformata Fourier
dtetfg tj
degtf tj
1
, ii ModAEE ii ModEA ,
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cazuri particulare in care exista rezolvare analitica
semnale cu variaţie armonică în timp, transformata Fourier, spectru
Xjt
XeXX tj
0
dtetfg tj
degtf tj
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dtetfg tj
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dtetfF tj
deGtg tj FG
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cazuri particulare in care exista rezolvare analitica
Exista unda in o singura directie
unda
▪ incidenta
▪ reflectata
unda
▪ directa
▪ inversa
zz
IN eEeEE
11
ztjzztjzy eeEeeEE
zz
OUT eEeEE
22
INE
zeE
1
zeE
1
zeE
2
zeE
2
OUTE
EE
EEEE ,
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cazuri particulare in care exista rezolvare analitica
moduri in medii delimitate
1
ii ModAE ii ModEA ,
INEOUTE
N
iiOUT ModBE1
1A
NA
1B
NB
iINi ModEA ,
ii AB
ii AB
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mod TEM, doi conductori I(z,t)
V(z,t)
z
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mod TEM, doi conductori I(z,t)
V(z,t)
Δz
I(z+Δz,t)
V(z+Δz,t)
L·Δz R·Δz
G·Δz C·Δz
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domeniu timp
semnale sinusoidale
t
tziLtziR
z
tzv
,,
,
t
tzvCtzvG
z
tzi
,,
,
zILjR
dz
zdV
zVCjG
dz
zdI
K II
K I
dz
d
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02
2
2
zVdz
zVd
02
2
2
zIdz
zId
CjGLjRj
022 EE
022 HH
j 22
zz
y eEeEE
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Impedanta caracteristica a liniei
zz eVeVzV 00
zz eIeIzI 00
zILjR
dz
zdV
zz eVeVzV 00
zz eVeVLjR
zI
00
CjG
LjRLjRZ
0
CjGLjRj
2 fv f
0
00
0
0
I
VZ
I
V
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R=G=0
CLjCjGLjRj
CL ;0
C
L
CjG
LjRZ
0 Z0 real
zjzj eVeVzV 00
zjzj eZ
Ve
Z
VzI
0
0
0
0LC
2
LCv f
1
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coeficient de reflexie in tensiune
ΓL
Z0 ZL
0
0
0
0
ZZ
ZZ
V
V
L
L
l
0
0
0
I
VZL 0
00
00 ZVV
VVZL
zjzj eVeVzV 00
zjzj eZ
Ve
Z
VzI
0
0
0
0
Z0 real
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coeficientul de reflexie la intrarea liniei
ΓL
Z0 ZL
-l 0
Zin
ΓIN
zjzj eVeVzV 00
ljlj eVeVlV 00
0
00V
VL 000 VVV
zV
zVz
0
0
lj
lj
lj
IN eeV
eVl
2
0
0 0
00 2 ljel
ljel 20
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Puterea medie
zjzj eeVzV 0 zjzj ee
Z
VzI
0
0
Puterea transmisa sarcinii = Puterea incidenta - Puterea “reflectata”
Return Loss [dB]
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impedanta la intrarea liniei
ΓL
Z0 ZL
-l 0
lI
lVZin
lj
lj
ine
eZZ
2
2
01
1
ljlj eVeVlV 00
ljlj eZ
Ve
Z
VlI
0
0
0
0
Zin
lj
Llj
L
ljL
ljL
ineZZeZZ
eZZeZZZZ
00
000
lZjZ
lZjZZZ
L
Lin
tan
tan
0
00
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impedanta la intrarea liniei
lZjZ
lZjZZZ
L
Lin
tan
tan
0
00
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impedanta la intrarea liniei de impedanta caracteristica Z0 , de lungime l , terminata cu impedanta ZL
lZjZ
lZjZZZ
L
Lin
tan
tan
0
00
ΓL
Z0 ZL
-l 0
Zin
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relatia este dependenta de frecventa prin valoarea
lZjZ
lZjZZZ
L
Lin
tan
tan
0
00
ΓL
Z0 ZL
-l 0
Zin
2fv f
l
fv
ll
v
fll
ff
222
dependenta de frecventa este periodica, impusa de functia tangenta
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l = k·λ/2 l = λ/4 + k·λ/2
lZjZ
lZjZZZ
L
Lin
tan
tan
0
00
ΓL
Z0 ZL
-l 0
Zin
kll
20ZZin 0tan l
ltan
L
inZ
ZZ
2
0
Transformatorul in sfert de lungime de unda
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ZL = 0 reactanţa pură
+/- in funcţie de l
lZjZin tan0
lZjZ
lZjZZZ
L
Lin
tan
tan
0
00
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lZjZin cot0
ZL = ∞ → 1 / ZL = 0 reactanţa pură
+/- in funcţie de l
lZjZ
lZjZZZ
L
Lin
tan
tan
0
00
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se defineste factorul de unda stationara (Voltage) Standing Wave Ratio
numar real 1 ≤ VSWR <
o masura a dezadaptarii (SWR = 1 semnifica adaptare)
zjzj eeVzV 0
zjzj eeVzV 20 1
je
zjeVzV 20 1
12 zje amplitudine maxima pentru 10max VV
12 zje 10min VV
1
1
min
max
V
VVSWR
amplitudine minima pentru
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ΓL
Z0 ZL
-l 0
Zin
lj
Lin e 2
lZjZ
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tan
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zz eVeVzV 00
zz eIeIzI 00
ljel 20
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Adaptarea de impedanţa
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Feed line – linie de intrare cu impedanta caracteristica Z0
Sarcina cu impedanta RL
Dorim adaptarea sarcinei la fider cu o linie de lungime λ/4 si impedanta caracteristica Z1
)tan(
)tan(
1
11
ljRZ
ljZRZZ
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Lin
lj
lj
ine
eZZ
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ZR
ZR
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LO
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Pe fider (Z0) avem doar unda progresiva Pe linia in sfert de lungime de unda (Z1) avem
unda stationara
24
2
l
0
0
ZZ
ZZ
in
inin
L
inR
ZZ
2
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0in LRZZ 01 L
Lin
RZZ
RZZ
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Lin
tan
tan
0
00
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Pentru linii non TEM constanta de propagare nu depinde liniar de frecventa, dar in practica influenta este minora in banda ingusta
Sunt neglijate reactantele introduse de discontinuitati (Z0 -> Z1). Compensarea se face printr-o mica modificare a lungimii liniei
Banda depinde de dezadaptarea initiala
cu cat dezadaptarea este mai mica cu atat banda se obtine mai larga
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simulare ADS
GHzf 88.0
51033 GHz
2933.03
88.0
0
f
f
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Transformatorul in sfert de lungime de unda permite adaptarea oricarei impedante reale cu orice impedanta a fiderului (liniei).
Daca banda necesara este mai mare decat cea oferita de transformatorul in sfert de lungime de unda se folosesc transformatoare multisectiune
caracteristica binomiala
tip Cebîşev
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Presupunem ca toate impedantele cresc sau descresc uniform
Toti coeficientii de reflexie vor fi reali si de acelasi semn
Anterior
01
011
ZZ
ZZ
nn
nnn
ZZ
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1
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NL
NLN
ZZ
ZZ
1,1 Nn
je 231
jNN
jj eee 242
210
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Similar Lab. 1
GHzf 169.2
6105.33 GHz
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Similar Lab. 1
GHzf 096.3
51017.43 GHz
09925.0282.2 GHz
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Laboratorul de microunde si optoelectronica http://rf-opto.etti.tuiasi.ro [email protected]