Figs02 2nd Edition
description
Transcript of Figs02 2nd Edition
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R. Ludwig and G. BogdanovRF Circuit Design: Theory and Applications
2nd edition
Figures for Chapter 2
Figure 2-1 Voltage distribution as a function of time (z = 0) and as a function of space (t = 0).
20
10
0
10
200 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
0 20 40 60 80 100 120 140 160 180 200
V(z,
t)
20
10
0
10
20
V(z,
t)
z = 0
t = 0
t, s
z, m
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Figure 2-2 Amplitude measurements of 10 GHz voltage signal at the beginning (lo-cation A) and somewhere along a wire connecting load to source.
Channel 1 Channel 2
A B
l
V
zz = l
VA
VB
VG
RG
R L
VA
0
V
0 lz
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Figure 2-3 Partitioning an electric line into small elements over which Kirchhoffs laws of constant voltage and current can be applied.
z z + z
z + z
R1 L1
R2 L2G C
z
I(z) I(z + z)
V(z + z)V(z)+
+
z
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Figure 2-4 Geometry and field distribution in two-wire parallel conductor transmission line.
2aD
Electric Field (solid lines)
Magnetic Field (dashed lines)
r
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Figure 2-5 Coaxial cable transmission line.
2a
2b2c
r
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Figure 2-6 Microstrip transmission line representation.
t
h w
(a) Printed circuit board section (b) Microstrip liner
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Figure 2-7 Electric flux density field leakage as a function of dielectric constants.
(a) Teflon epoxy ( = 2.55) (b) Alumina ( = 10.0)r r
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Figure 2-8 Triple-layer transmission line configuration.
(a) Sandwich structure (b) Cross-sectional field distribution
r r
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Figure 2-9 Parallel-plate transmission line.
z
x
0(b) Field distribution(a) Geometric representation
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Figure 2-10 Segmentation of two-wire transmission line into z-long sections suit-able for lumped parameter analysis.
G C
z
z
z + z
z + z
I(z) I(z + z)
V(z + z)V(z)+
+
G C
R1 L1
R2 L2
R1 L1
R2 L2
R1 L1
R2 L2G C
z
1
2
1
2
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Figure 2-11 Segmentation of a coaxial cable into z length elements suitable for lumped parameter analysis.
+
+
z z + z
z z + z
I(z) I(z + z)
G C G CV(z + z)V(z)C
R1 R1 R1L1 L1 L1
R2 R2 R2L2 L2 L2G
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Figure 2-12 Generic electric equivalent circuit representation.
+
_
+
_
z z + z
I(z) I(z + z)
V(z + z)V(z) C
R L
G
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Figure 1-1 Ampres law linking the current flow to the magnetic field.
I
I
Line path lH(r)
H(r)
I H dl=
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Figure 2-13 Magnetic field distribution inside and outside of an infinitely long wire of radius a = 5 mm carrying a current of 5 A.
0 5 10 15 20 25 30 35 40 45 500
20
40
60
80
100
120
140
160
r, mm
H, A
/m
r a=
=HIr
2pia2
=HI
2pir
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Figure 2-14 The time rate of change of the magnetic flux density induces a voltage.
BE
Path l+
_
V
B
S
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Figure 2-15 Parallel-plate transmission line geometry. The plate width w is large compared with the separation d.
x
yzd
dp
w
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Table 2-1 Transmission line parameters for three line types
Parameter Two-Wire Line Coaxial Line Parallel-Plate Line
R/m
1piacond-----------------------
1piacond-----------------------
12picond-----------------------
1a---
1b---+
2
wcond--------------------
LH/m
pi---
cosh 1 D2a------
2pi------
ba---
ln d
w----
GS/m
pidiel
cosh 1 D 2a( )( )------------------------------------------
2pidielb a( )ln-------------------- diel
w
d----
CF/m
pi
cosh 1 D 2a( )( )------------------------------------------
2pib a( )ln--------------------
w
d----
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Figure 2-16 Segment of a transmission line with voltage loop and current node.
R L
G C
z z + z
I(z) I(z + z)
V(z) V(z + z)+
_
+
_
a
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Figure 2-17 Integration surface element for Faradays law application.
x
yz
J
Hy
I
z
Iw
d
z + z
ith cell plate 2
plate 1
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Figure 2-18 Surface element used to apply Ampres law.
x
yz
I
z
Iw
d
z + z
ith cell plate 2
plate 1
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Figure 2-19 Microstrip characteristic impedance as a function of w/h.
1
10
100
1k
Char
acte
ristic
impe
danc
e Z 0
,
0.1 100.3Line width to dielectric thickness ratio, w/h
= 1
= 12
= 4.6= 7= 10
= 2= 3
31
r
r
r
rr
r
r
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Figure 2-20 Effective dielectric constant of the microstrip line as a function of w/h for different dielectric constants.
0.1 1 100.3 3Line width to dielectric thickness ratio, w/h
0
2
4
6
8
10
12
Effe
ctiv
e di
elec
tric
cons
tant
, ef
f
= 1
= 12
= 10
= 7
= 4= 3= 2
r
r
r
r
r
r
r
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Figure 2-21 Effect of conductor thickness on the characteristic impedance of a mi-crostrip line placed on a 25 mil thick FR4 printed circuit board.
0.1 1 100.3 3Line width to dielectric thickness ratio, w/h
0
50
100
150
Char
acte
ristic
line
impe
danc
e Z 0
,
t = 0
t = 1.5 mil
h = 25 mil= 4.6
FR4
r
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Figure 2-22 Terminated transmission line at location z = 0.
Zin
Z0 ZL
0z = lz
0
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Figure 2-23 Short-circuited transmission line and new coordinate system d.
Zin
Z0 ZL = 0
0d = l
d
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Figure 2-24 Standing wave pattern for various instances of time.
0 0.5pi1
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1
pi 1.5pi 2pi 2.5pi 3pi 3.5pid
t = 1/4pi + 2pin
t = 2pin
t = 1/2pi + 2pint = 3/8pi + 2pin
t = 1/8pi + 2pinV(
d)/(2j
V+)
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Figure 2-25 SWR as a function of load reflection coefficient
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
2
4
6
8
10
12
14
16
18
20
|0|
SWR
0 .
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Figure 2-26 Voltage, current, and impedance as a function of line length for a short-circuit termination.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 12
1.5
1
0.5
0
0.5
1
1.5
2
Short circuit
Open circuit
Short circuit
Open circuit
Short circuit
Zin(d)jZ0
V(d)2jV+
2V+/Z0I(d)
d/
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Figure 2-27 Magnitude of the input impedance for a 10 cm long, short-circuited transmission line as a function of frequency.
1 1.5 2 2.5 3 3.5 40
50
100
150
200
250
300
350
400
450
500
f, GHz
|Z in|,
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Figure 2-28 Voltage, current, and impedance as a function of line length for an open-circuit termination.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 12
1.5
1
0.5
0
0.5
1
1.5
2
d/
Zin(d)jZ0
V(d)2V +
2jV+/Z0I(d)
Short circuit
Open circuit
Open circuit
Open circuit
Short circuit
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Figure 2-29 Impedance magnitude for a 10 cm long, open-circuited transmission line as a function of frequency.
1 1.5 2 2.5 3 3.5 40
50
100
150
200
250
300
350
400
450
500
f, GHz
|Z in|,
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Figure 2-30 Input impedance matched to a load impedance through a line seg-ment.
/4
ZLZ0 = ZLZin
Zin = desired ZL = given
4
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Figure 2-31 Input impedance of quarter-wave transformer.
ZlineZ0 = 50
l = /4
w
ZLZin
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Figure 2-32 Magnitude of Zin for frequency range of 0 to 2 GHz and fixed length d.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
5
10
15
20
25
30
35
40
45
50
f, GHz
|Z in|,
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Figure 2-33 Generic transmission line circuit involving source and load terminations.
in
Z0 ZL
ZG
VG
S
out
L = 0
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Figure 2-34 Equivalent lumped input network for a transmission line configuration.
VG
ZG
ZinV
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Figure 2-35 Impedance of a coaxial cable terminated by a resistor: (a) network analyzer measurement, (b) theoretical prediction.
200 400 600 800 100020
30
40
50
60
70
80
90
100
f, MHz|Z in
|, (a) (b)
100
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Figure 2-36 Network analyzer with the resistive 100 test load attached.