fundamental transmission line theory · fundamental transmission line theory (part 3) dr. josé...
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![Page 1: Fundamental Transmission Line Theory · Fundamental Transmission Line Theory (Part 3) Dr. José Ernesto Rayas-Sánchez February 6, 2020 4 Dr. J. E. Rayas-Sánchez 7 Standing Wave](https://reader031.vdocuments.mx/reader031/viewer/2022011817/5e81cfc1b455f867c11aba3f/html5/thumbnails/1.jpg)
Fundamental Transmission Line Theory (Part 3)Dr. José Ernesto Rayas-Sánchez
February 6, 2020
1
1
Fundamental Transmission Line Theory(Part 3)
Dr. José Ernesto Rayas-Sánchez
2Dr. J. E. Rayas-Sánchez
Outline
Power along the transmission line
Return loss
Standing wave ratio
Summary on reflection parameters
Transmission coefficient
Insertion loss
Summary on transmission parameters
Analogies and illustrations
![Page 2: Fundamental Transmission Line Theory · Fundamental Transmission Line Theory (Part 3) Dr. José Ernesto Rayas-Sánchez February 6, 2020 4 Dr. J. E. Rayas-Sánchez 7 Standing Wave](https://reader031.vdocuments.mx/reader031/viewer/2022011817/5e81cfc1b455f867c11aba3f/html5/thumbnails/2.jpg)
Fundamental Transmission Line Theory (Part 3)Dr. José Ernesto Rayas-Sánchez
February 6, 2020
2
3Dr. J. E. Rayas-Sánchez
Average Power along the Transmission Line
][)( 0zjzj eeVzV
][)(0
0 zjzj eeZV
zI
})()(Re{21 *zIzVPav
}||1Re{||
21 222*
0
20
zjzjav ee
ZV
P
)||1(||
21 2
0
20
ZV
Pav
The average power flow is constant along the line (if V0+ is constant)
The power delivered is the incident power minus the reflected power
If = 0, maximum power is delivered to the load
If || = 1, no power is delivered to the load
Z0,
0
ZL
z
4Dr. J. E. Rayas-Sánchez
Power Transfer Efficiency
RS
RL
Maximum power is transferred when RL = RS
RL / RS
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7 8 9 10
Lo
ad
Po
wer
(no
rmaliz
ed
)
(Hewlett-Packard's RF Design and Measurement Seminar, 2000)
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Fundamental Transmission Line Theory (Part 3)Dr. José Ernesto Rayas-Sánchez
February 6, 2020
3
5Dr. J. E. Rayas-Sánchez
Power Transfer Efficiency (cont)
For complex impedances, maximum power transfer occurs when ZL = ZS* (conjugate match)
Zs = R + jX
ZL = Zs* = R - jX
Zo
Zo
Rs
RL
+jX
-jX
At high frequencies, maximum power transfer occurs when RS = RL = Zo
(Hewlett-Packard's RF Design and Measurement Seminar, 2000)
6Dr. J. E. Rayas-Sánchez
Return Loss, RL
)||1(||
21 2
0
20
ZV
Pav
It is a way to measure the ability of the TL to avoid energy reflection
It is the ratio of the incident power to the reflected power
dB)(||log20 RL
dB)0|(| RL dB0)1|(| RL
dB)(||log10 2RLZ0, ZL
l
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Fundamental Transmission Line Theory (Part 3)Dr. José Ernesto Rayas-Sánchez
February 6, 2020
4
7Dr. J. E. Rayas-Sánchez
Standing Wave Ratio, SWR
It is a way to measure the mismatch of a line
A mismatch implies a “standing wave” along the line
It is the ratio of the maximum to the minimum wave amplitude along the line
][)( 0zjzj eeVzV
]1[)( 20
zjzj eVzVe
|1||||)(| 20
zjeVzV
je|| Since |||1||||)(| )2(
0ljeVlV
|1||||)(| 20
ljeVlV
Z0,
0l
ZL
z
8Dr. J. E. Rayas-Sánchez
Standing Wave Ratio, SWR (cont)
|||1||||)(| )2(0
ljeVlV
1 when maximum is |)(| )2( ljelV
1 when minimum is |)(| )2( ljelV
|)|1(|||)(| 0maxmax VVlV
|)|1(|||)(| 0minmin VVlV
||1||1
min
max
VV
SWR SWR1
The distance between two maxima or two minima is /2 The distance between a maximum and a minimum is /4
Z0,
0l
ZL
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Fundamental Transmission Line Theory (Part 3)Dr. José Ernesto Rayas-Sánchez
February 6, 2020
5
9Dr. J. E. Rayas-Sánchez
Standing Wave Ratio, SWR (cont)
The Slotted Line
(D. M. Pozar, Microwave Engineering, Wiley, 2005)
(X-band waveguide slotted line)
Used to measure:SWRlmin, lmax
ZL
10Dr. J. E. Rayas-Sánchez
Standing Wave Ratio – EM Simulation
Microstrip lineLaminate: Rogers RO3003
H = 5 mil
r = 3
tan() = 0.0013 at 10 GHz
Lossy metals: Cu = 5.8×107 S/m
t = 0.6 mil (half-once copper)
W = 12.5 mil
L = 187.5 mil
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Fundamental Transmission Line Theory (Part 3)Dr. José Ernesto Rayas-Sánchez
February 6, 2020
6
11Dr. J. E. Rayas-Sánchez
Standing Wave Ratio – EM Simulation (cont)
Using Zport1 = Zport2 = 50
f = 0.1 GHz f = 30 GHz
12Dr. J. E. Rayas-Sánchez
Standing Wave Ratio – EM Simulation (cont)
Using Zport1 = 50 , Zport2 = 1 K
f = 0.1 GHz f = 30 GHz
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Fundamental Transmission Line Theory (Part 3)Dr. José Ernesto Rayas-Sánchez
February 6, 2020
7
13Dr. J. E. Rayas-Sánchez
Standing Wave Ratio, SWR (cont)
14Dr. J. E. Rayas-Sánchez
Transmission Line Terminated with Zo
For reflection, a transmission line terminated in Zo behaves like an infinitely long transmission line
Zs = Zo
Zo
Vrefl = 0 (all the incident power is absorbed in the load)
Vinc
Zo = characteristic impedance of transmission line
(Hewlett-Packard's RF Design and Measurement Seminar, 2000)
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Fundamental Transmission Line Theory (Part 3)Dr. José Ernesto Rayas-Sánchez
February 6, 2020
8
15Dr. J. E. Rayas-Sánchez
Transmission Line Terminated with Short, Open
Zs = Zo
Vrefl
V inc
For reflection, a transmission line terminated in a short or open reflects all power back to source
In phase (0°) for openOut of phase (180°) for short
(Hewlett-Packard's RF Design and Measurement Seminar, 2000)
16Dr. J. E. Rayas-Sánchez
Transmission Line Terminated with 25
Zs = Zo
ZL = 25
Vrefl
V inc
Standing wave pattern does not go to zero as with short or open
(Hewlett-Packard's RF Design and Measurement Seminar, 2000)
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Fundamental Transmission Line Theory (Part 3)Dr. José Ernesto Rayas-Sánchez
February 6, 2020
9
17Dr. J. E. Rayas-Sánchez
Reflection Parameters
dB
No reflection(ZL = Z0)
RL
VSWR
0 1
Full reflection(ZL = open, short)
0 dB
1
=Z L - Z 0
ZL + 0Z
ReflectionCoefficient
=Vreflected
Vincident=
= Return loss = -20 log(),
VSWR = Emax
Emin
=1 + 1
Voltage Standing Wave RatioEmax
Emin
(Hewlett-Packard's RF Design and Measurement Seminar, 2000)
18Dr. J. E. Rayas-Sánchez
Reflection Parameters – Summary
Reflection coefficient, l
Return Loss, RL
Standing Wave Ratio, SWR
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Fundamental Transmission Line Theory (Part 3)Dr. José Ernesto Rayas-Sánchez
February 6, 2020
10
19Dr. J. E. Rayas-Sánchez
Transmission Coefficient, T
It is a measure of the capacity of a TL to transmit an incoming wave
0for )()( 0 zeeVzV zjzj 01
01
ZZZZ
infinite) TL2 (assuming 0for )( 0 zTeVzV zj
TL2TL1
00 ]1[)0( TVVV 1T
20Dr. J. E. Rayas-Sánchez
Transmission Coefficient, T (cont)
T is the ratio of the total transmitted voltage to the incident wave at a transition
T can be greater than 1 (no amplification implied)
TL2TL1
00 ]1[)0( TVVV 1TzjeV
zVT
0
)(
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Fundamental Transmission Line Theory (Part 3)Dr. José Ernesto Rayas-Sánchez
February 6, 2020
11
21Dr. J. E. Rayas-Sánchez
Insertion Loss, IL
It is a measure of the reflections caused by an inserted TL
TL2TL1
(dB) ||log20 TIL
dB)0|(| TIL dB0)1|(| TIL
22Dr. J. E. Rayas-Sánchez
Transmission Parameters – Summary
Transmission coefficient, T
Insertion Loss, IL
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Fundamental Transmission Line Theory (Part 3)Dr. José Ernesto Rayas-Sánchez
February 6, 2020
12
23Dr. J. E. Rayas-Sánchez
Lightwave Analogy to RF Energy
RF
Incident
Reflected
Transmitted
Lightwave
(Hewlett-Packard's RF Design and Measurement Seminar, 2000)