microwave engineering full
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Microwave engineeringTRANSCRIPT
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MICROWAVE ENGINEERINGMICROWAVE ENGINEERING
LECTURE NOTE
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PHPHẠẠM VI CM VI CỦỦA LA LĨĨNH VNH VỰỰC SIÊU C SIÊU CAO TCAO TẦẦN N
TẦN SỐ THÔNG THƯỜNG TỪ 1GHz TRỞ LÊN
BẢNG PHÂN ĐỊNH TẦN SỐ
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ĐƯĐƯỜỜNG DÂY TRUYNG DÂY TRUYỀỀN SN SÓÓNGNG. ĐIỆN ÁP VÀ DÒNG ĐIỆN PHỤ THUỘC CẢKHÔNG GIAN Ở VỊ TRÍ z VÀ THỜI GIAN TẠI
THỜI ĐIỂM t,
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Module 2:Module 2: Transmission LinesTransmission LinesTopic 1: Topic 1: TheoryTheory
OGI EE564Howard Heck
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Where Are We? Where Are We? 1. Introduction2. Transmission Line Basics
1. Transmission Line Theory2. Basic I/O Circuits3. Reflections4. Parasitic Discontinuities5. Modeling, Simulation, & Spice6. Measurement: Basic Equipment7. Measurement: Time Domain Reflectometry
3. Analysis Tools4. Metrics & Methodology5. Advanced Transmission Lines
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ContentsContentsPropagation VelocityCharacteristic ImpedanceVisualizing Transmission Line BehaviorGeneral Circuit ModelFrequency DependenceLossless Transmission LinesHomogeneous and Non-homogeneous LinesImpedance Formulae for Transmission Line StructuresSummaryReferences
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Propagation VelocityPropagation Velocity
Physical example:
Wave propagates in z direction
Circuit: L = [nH/cm]C = [pF/cm]
( )tILdzdz
zV
∂∂
∂∂
−=Total voltage change across Ldz (use ):ΔV L dI
dt= −
Total current change across Cdz (use ):dt
dVCI −=Δ( )
tVCdzdz
zI
∂∂
∂∂
−=
[2.1.1]
[2.1.2]
Simplify [2.1.1] & [2.1.2] to get the Telegraphist’s Equations [2.1.3a]
tIL
zV
∂∂
∂∂
−=
tVC
zI
∂∂
∂∂
−=
[2.1.3b]
I
V
Ldz
Cdz
dz
V+ dzdVdz
I+ dzdIdz
z
xy
V, I
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Propagation Velocity (2)Propagation Velocity (2)
Phase velocity definition: vLC
≡1
[2.1.7]
Equation in terms of current:2
2
22
2
2
2 1tI
tILC
zI
∂∂
=∂∂
=∂∂
ν[2.1.8]
Equate [2.1.4] & [2.1.5]: [2.1.6]2
2
22
2
2
2 1tV
tVLC
zV
∂∂
=∂∂
=∂∂
ν
Differentiate [2.1.3b] by z: [2.1.5]ztIL
zV
∂∂∂
−=∂∂ 2
2
2
Differentiate [2.1.3a] by t: [2.1.4]2
22
tVC
tzI
∂∂
−=∂∂
∂
Equation [2.1.6] is a form of the wave equation. The solution to[2.1.6] contains forward and backward traveling wave components, which travel with a phase velocity.
An alternate treatment of propagation velocity is contained in the appendix.
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Characteristic Impedance Characteristic Impedance (Lossless)(Lossless)
The input impedance (Z1) is the impedance of the first inductor (Ldz) in series with the parallel combination of the impedance of the capacitor (Cdz) and Z2.
Ldz
Cdx
Z1 Z2 Z3
Ldz
Cdz
Ldz
Cdz
dz dz
V1 V3V2 to ∞
a
fed
cb
dz
dz = segment length
C = capacitance per segment
L = inductance per segment
[2.1.9]( )
CdzjZCdzjZLdzjZωωω
/1/1
2
21 +
+=
( ) ( ) ( ) 0/1/1/1 2221 =−+−+ lCjZlCjZlLjlCjZZ ωωωω
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Characteristic Impedance Characteristic Impedance (Lossless)(Lossless)
Assuming a uniform line, the input impedance should be the same when looking into node pairs a-d, b-e, c-f, and so forth. So, Z2 = Z1= Z0.( ) ( ) ( ) 0/1/1/1 0000 =−+−+ CdzjZCdzjZlLdzjCdzjZZ ωωωω [2.1.10]
CdzjLdzjdzLZjZ
CdzjZ
CdzLdzdzLZj
CdzjZZ
ωωω
ωωωω
ω−−==−−−+ 0
20
00
020 0
Allow dz to become very small, causing the frequency dependent term to drop out:
0020 =−−
CLdzLZjZ ω [2.1.11]
020 =−
CLZ [2.1.12]
Solve for Z0:
CLZ =0
[2.1.13]
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Visualizing Transmission Line Visualizing Transmission Line BehaviorBehavior
Water flow– Potential = Wave
height [m]– Flow = Flow rate
[liter/sec]
I
I
V
+++++++
- - - - - - -
Transmission LinePotential = Voltage [V]Flow = Current [A] = [C/sec]
Just as the wave front of the water flows in the pipe, the voltage propagates in the transmission line. The same holds true for current.
Voltage and current propagate as waves in the transmission line.
h
f
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Visualizing Transmission Line Visualizing Transmission Line Behavior #2Behavior #2
Extending the analogy– The diameter of the pipe relates the flow rate
and height of the water. This is analogous to electrical impedance.
– Ohm’s law and the characteristic impedance define the relationship between current and potential in the transmission line.
Effects of impedance discontinuities– What happens when the water encounters a
ledge or a barrier?– What happens to the current and voltage
waves when the impedance of the transmission line changes?
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General Transmission Line General Transmission Line Model (No Coupling)Model (No Coupling)
Transmission line parameters are distributed (e.g. capacitance per unit length).A transmission line can be modeled using a network of resistances, inductances, and capacitances, where the distributed parameters are broken into small discrete elements.
R L
G C
R L
G C
R L
G C
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General Transmission Line General Transmission Line Model #2Model #2
Ω-1•cm -1
GDielectric Conductance
pF•cm-1CTotal CapacitancenH•cm-1LSelf InductanceΩ•cm-1RConductor
Resistance
UnitsSymbol
ParameterParameters
Characteristic Impedance Z R j LG j C0 =++
ωω [2.1.14]
Propagation Constant ( )( ) βαωωγ jCjGLjR +=++= [2.1.15]
α = attenuation constant = rate of exponential attenuationβ = phase constant = amount of phase shift per unit length
βων =pPhase Velocity [2.1.16]
In general, α and β are frequency dependent.
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Frequency DependenceFrequency Dependence
From [2.1.14] and [2.1.15] note that:Z0 and γ depend on the frequency content of the signal.Frequency dependence causes attenuation and edge rate degradation.
Attenuation
Edge rate degradation
Output signal from lossytransmission line
Signal at driven end oftransmission line
Output signal fromlossless transmission line
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Frequency Dependence #2Frequency Dependence #2R and G are sometimes negligible, particularly at low frequencies– Simplifies to the lossless case: no attenuation
& no dispersion In modules 2 and 3, we will concentrate on lossless transmission lines.Modules 5 and 6 will deal with lossy lines.
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Lossless Transmission LinesLossless Transmission Lines
QuasiQuasi--TEM AssumptionTEM AssumptionThe electric and magnetic fields are perpendicular to the propagation velocity in the transverse planes.
x
zy
HE
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Lossless Line ParametersLossless Line Parameters
Lossless line characteristics are frequency independent.As noted before, Z0 defines the relationship between voltage and current for the traveling waves. The units are ohms [Ω].υ defines the propagation velocity of the waves. The units are cm/ns.
S ti th ti d l
CLZ =0
vL C
=1
Characteristic ImpedanceCharacteristic Impedance
Propagation VelocityPropagation Velocity
[2.1.17]
[2.1.18]
Lossless transmission lines are characterized by the following two parameters:
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Lossless Line Equivalent CircuitLossless Line Equivalent Circuit
The transmission line equivalent circuit shown on the left is often represented by the coaxial cable symbol.
L
C
L
C
L
C
Z0, v, lengthZ0, ν, length
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Homogeneous MediaHomogeneous Media
A homogeneous dielectric medium is uniform in all directions.– All field lines are contained within the
dielectric.For a transmission line in a homogeneous medium, the propagation velocity depends only on material properties:
vLC
c cm ns
r r r
= = = =1 1 300
εμ ε μ ε/
[2.1.19]
0εεε r= Dielectric Permittivity
cmFx 14
0 10854.8 −=ε Permittivity of free space
cmHx 8
0 10257.1 −=μ Magnetic Permeability
0μμ ≅ Permeability of free space
εr is the relative permittivity or dielectric constant.
Note: only Note: only εεrris required to is required to calculate calculate νν..
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NonNon--Homogeneous MediaHomogeneous Media
A non-homogenous medium contains multiple materials with different dielectric constants.For a non-homogeneous medium, field lines cut across the boundaries between dielectric materials.In this case the propagation velocity depends on the dielectric constants and the proportions of the materials. Equation [2.1.19] does not hold:
εμ11
≠=LC
v
In practice, an effective dielectric constant, εr,eff is often used, which represents an average dielectric constant.
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Some Typical Transmission Some Typical Transmission Line StructuresLine Structures
And useful formulas for Z0
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rR
εr
TrTrởở khkháángng ccáápp đđồồngng trtrụụcc
2 3 4 5 6 7 8 9 10R/r
20
40
60
80
100
120
140
Z 0[Ω
]
εr = 1
εr= 4rε = 3.5εr = 3εr = 2.5rε = 2
Z0, v, lengthZ0, υ, length
⎟⎠⎞
⎜⎝⎛=
rRZ ln
21
0 εμ
π
[2.1.20]
⎟⎠⎞
⎜⎝⎛
=
rR
Cln
2πε
[2.1.21]
⎟⎠⎞
⎜⎝⎛=
rRL ln
2πμ
[2.1.22]
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Centered Stripline ImpedanceCentered Stripline Impedance( )⎟⎟
⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
+=
wtw
hZ
r 8.067.0
4ln60 2
0πε
w
t
h1
h2
εr
Source: Motorola application note AN1051.
35.02
<− th
wValid for
25.02<h
t
0.003 0.005 0.007 0.009 0.011 0.013 0.015w [in]
10
15
20
25
30
35
40
45
50
55
60Z 0
[Ω] 0.070
0.0600.0500.0400.0300.0250.020
h2
t = 0.0007”εr = 4.0
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Dual Stripline ImpedanceDual Stripline Impedancew
t
h2
h1
εr
w
t
h1
ZYYZZ+
=2
0
( )⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
+=
wtw
hYr 8.067.0
8ln60 1
πε
( )( )⎟⎟
⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
+
+=
wtw
hhZr 8.067.0
8ln60 21
πε
( ) ( )⎥⎦⎤
⎢⎣⎡
++
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛++
−
=twththh
h
Zr 8.0
29.1ln4
180121
1
0 ε
.115.0 hwh ≤≤
Source: Motorola application note AN1051.
OR
0.003 0.005 0.007 0.009 0.011 0.013 0.015w [in]
10
20
30
40
50
60
70
80
90
100
110Z 0
[Ω] 0.020”
0.018”0.015”0.012”0.010”0.008”
0.005”
2h1 + h2 + 2t = 0.062”t = 0.0007”εr = 4.0
h1
[2.1.24]
[2.1.27]
[2.1.25]
[2.1.26]
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Surface Microstrip ImpedanceSurface Microstrip Impedancew
t
h
εr
ε0
[ ]Ω⎟⎠⎞
⎜⎝⎛=
dhZ
eff
4ln21
0 εμ
π
twd 67.0536.0 +=
( ) 067.0475.0 εεε += reff
[ ]Ω⎟⎠⎞
⎜⎝⎛
++=
twhZ
r 8.098.5ln
41.187
0 ε
0.003 0.005 0.007 0.009 0.011 0.013 0.015w [in]
20
40
60
80
100
120
140
160Z 0
[Ω]
0.025”0.020”0.015”0.012”0.009”0.006”0.004”
h
t = 0.0007”
εr = 4.0
[2.1.28]
[2.1.29]
[2.1.30]
[2.1.31]
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Embedded MicrostripEmbedded Microstript
h1
εr
ε0 w
h2
⎟⎠⎞
⎜⎝⎛
++=
twhKZ
r 8.098.5ln
2805.01
0 ε
6560 where ≤≤ K
⎟⎠⎞
⎜⎝⎛
++′=
twhZ
r 8.098.5ln
41.187 1
0 ε
[ ]1255.11 hhrr e−−=′ εε
67.0475.0017.1 += rετ
Or
0.003 0.005 0.007 0.009 0.011 0.013 0.015w [in]
0
20
40
60
80
100
120
140
Z 0[Ω
] 0.015”0.012”0.010”0.008”0.006”0.005”0.003”
h2 - h1 = 0.002“t= 0.0007”εr = 4.0
h1
[2.1.32]
[2.1.33]
[2.1.34]
[2.1.35]
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SummarySummary
System level interconnects can often be treated as lossless transmission lines.Transmission lines circuit elements are distributed. Voltage and current propagate as waves in transmission lines.Propagation velocity and characteristic impedance characterize the behavior of lossless transmission lines.Coaxial cables, stripline and microstrip
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ReferencesReferences
S. Hall, G. Hall, and J. McCall, High Speed Digital System Design, John Wiley & Sons, Inc. (Wiley Interscience), 2000, 1st edition.H. Johnson and M. Graham, High-Speed Signal Propagation: Advanced Black Magic, Prentice Hall, 2003, 1st edition, ISBN 0-13-084408-X.W. Dally and J. Poulton, Digital Systems Engineering, Cambridge University Press, 1998. R.E. Matick, Transmission Lines for Digital and Communication Networks, IEEE Press, 1995.R. Poon, Computer Circuits Electrical Design, Prentice Hall 1st edition 1995
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BBẢẢN CHN CHẤẤT CT CỦỦA QUA QUÁÁ TRÌNH TRÌNH TRUYTRUYỀỀN SN SÓÓNGNG
THỰC CHẤT LÀ ĐƯỜNG DÂY TRUYỀN SÓNG TRUYỀN NĂNG LƯỢNG DƯỚI DẠNG SÓNG CAO TẦNQUÁ TRÌNH TRUYỀN NÀY CÓ VẬN TỐC NHẤT ĐỊNHĐIỆN ÁP VÀ DÒNG ĐIỆN THAY ĐỔI TƯƠNG ỨNG THEO
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( )txv ,
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PHƯƠNG TRÌNH TRUYPHƯƠNG TRÌNH TRUYỀỀN SN SÓÓNG NG TRÊN ĐƯTRÊN ĐƯỜỜNG DÂYNG DÂY
HỆ PHƯƠNG TRÌNH MAXWELL
tBE∂∂
−=r
rrot
tDJH∂∂
+=r
rrrot
ρ=Dr
div
0div =Br
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MÔ HÌNH VMÔ HÌNH VẬẬT LÝT LÝ
+
-
SZ
SV LZ
x xx Δ+ l
( )txv , ( )tzxv ,Δ+
( )txi , ( )tzxi ,Δ+
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MÔ HÌNH VMÔ HÌNH VẬẬT LÝT LÝ
+
-
SZ
SV LZ
x xx Δ+ l
( )txv , ( )tzxv ,Δ+
( )txi , ( )tzxi ,Δ+
x xx Δ+
( )txv , ( )tzxv ,Δ+
( )txi ,
( )tzxi ,Δ+
( )txv , ( )tzxv ,Δ+
( )txi , ( )tzxi ,Δ+
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LZ
l
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RΔ
x xx Δ+
( )txv , ( )tzxv ,Δ+
( )txi , ( )tzxi ,Δ+
xLΔ
xGΔxCΔ
xRΔ LΔ
GΔCΔ
xΔRất nhỏ
xRR ΔΔ =xLL ΔΔ =xGG ΔΔ =xCC ΔΔ =
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x xx Δ+
( )txv , ( )tzxv ,Δ+
( )txi , ( )tzxi ,Δ+
xLΔ
xGΔ xCΔ
xRΔ
( ) ( ) ( ) ( )txxvx
txixLtxixRtxv ,,,, ΔΔΔ ++∂
∂•+•=
( ) ( ) ( ) ( )txxix
txxvxCtxxvxGtxi ,,,, ΔΔ
ΔΔΔ ++∂+∂
•++•=
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ĐĐểể ttíínhnh
ccầầnn xxéétt mmộộtt đođoạạnn nhnhỏỏ
( )txv , ( )txi ,
xΔ
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ĐiĐiỆỆNN ÁÁP VP VÀÀ DÒNG DÒNG ĐiĐiỆỆNN
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TTÍÍNH VI SAINH VI SAI
0→Δz
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MIMIỀỀN TN TẦẦN SN SỐỐ
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HHẰẰNG SNG SỐỐ SSÓÓNGNG
[ ]mradLC /2λπωβ ==
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MÔ HÌNH MMÔ HÌNH MẠẠCH ĐƯCH ĐƯỜỜNG DÂY DNG DÂY DÀÀII
+
-
SZ
SV LZ
z l
( )tzv ,
( )tzi ,
( )zV
( )zI
0
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PHƯƠNG TRÌNH TRUYPHƯƠNG TRÌNH TRUYỀỀN SN SÓÓNG NG TRÊN ĐƯTRÊN ĐƯỜỜNG DÂYNG DÂY
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TRTRỞỞ KHKHÁÁNG ĐNG ĐẶẶC TC TÍÍNH CNH CỦỦA A
ĐƯĐƯỜỜNG DÂY NG DÂY 0Z
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TTẢẢI TRÊN ĐƯI TRÊN ĐƯỜỜNG DÂY NG DÂY TRUYTRUYỀỀN SN SÓÓNGNG
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+
-
HHỆỆ SSỐỐ PHPHẢẢN XN XẠẠ
SZSV LZ
zl
+0V
−0V
d
β,0Z
SP
( ) dji eIzI β−+= 0 ( ) dj
r eIzI β−= 0
( ) dji eVzV β−+= 0
( ) djr eVzV β−= 0
−LV
+|LV
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HHỆỆ SSỐỐ PHPHẢẢN XN XẠẠ TTẠẠI TI TẢẢII
0
0
ZZZZ
VV
L
L
L
LL +
−=≡Γ +
−
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HHỆỆ SSỐỐ PHPHẢẢN XN XẠẠ TTẠẠI MI MỘỘT T ĐiĐiỂỂMM TRÊN ĐƯTRÊN ĐƯỜỜNG DÂYNG DÂY
( ) ( )( )
djL
i
r edVdVd β2−•Γ==Γ
zld −=
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+
-
HHỆỆ SSỐỐ PHPHẢẢN XN XẠẠ CÔNG SUCÔNG SUẤẤTT
SZ
SV LZ
zl
+0V
−0V
d
β,0Z
( )zPi
( )zPr
( )lPi
( )lPr
LP
SP
( )0iP
( )0rP
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HHỆỆ SSỐỐ PHPHẢẢN XN XẠẠ CÔNG SUCÔNG SUẤẤTT
( ) 22 dPP
i
r Γ==Γ
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CCÁÁC TRƯC TRƯỜỜNG HNG HỢỢP ĐP ĐẶẶC BIC BIỆỆTTTTẢẢI NGI NGẮẮN MN MẠẠCHCH
0
0
RZRZ
L
LL +
−=Γ
100
0
0 −=+−
=RR
LΓ
( ) ( )lVlV ri −=
( ) ( ) ( ) 0=+= lVlVlV ri
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+
-
TRTRỞỞ KHKHÁÁNG ĐƯNG ĐƯỜỜNG DÂYNG DÂY
SZ
SVLZ
ld( )dZ
β,0Z
INZ
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TRTRỞỞ KHKHÁÁNG TNG TẠẠI I ĐiĐiỂỂMM CCÁÁCH TCH TẢẢI I MMỘỘT KHOT KHOẢẢNG NG dd
( ) ( )( )Ω+
+=
djZZdjZZZdZ
L
L
ββ
tantan
0
00
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TRTRỞỞ KHKHÁÁNG ĐNG ĐẦẦU ĐƯU ĐƯỜỜNG DÂYNG DÂY
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STANDING WAVESTANDING WAVE
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TTỈỈ SSỐỐ SSÓÓNG ĐNG ĐỨỨNG LNG LỚỚNN
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TTỈỈ SSỐỐ SSÓÓNG ĐNG ĐỨỨNG NHNG NHỎỎ
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SSÓÓNG ĐNG ĐỨỨNG TRÊN ĐƯNG TRÊN ĐƯỜỜNG NG DÂY DÂY
TTỈỈ SSỐỐ SSÓÓNG ĐNG ĐỨỨNGNG
min
max
VVVSWR =
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CCÁÁC TRƯC TRƯỜỜNG HNG HỢỢP ĐP ĐẶẶT BIT BIỆỆTT
ĐƯỜNG DÂY NGẮN MẠCH TẢI
( ) ( )( )djZZ
djZZZdZL
Lin β
βtantan
0
00 +
+=
( ) ( )djZdZin βtan0=0=LZ
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CCÁÁC TRƯC TRƯỜỜNG HNG HỢỢP ĐP ĐẶẶT BIT BIỆỆTT
ĐƯỜNG DÂY HỞMẠCH TẢI
( ) ( )( )djZZ
djZZZdZL
Lin β
βtantan
0
00 +
+=
( ) ( )djZdZin βcotan0−=∞=LZ
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ĐƯĐƯỜỜNG TRUYNG TRUYỀỀN MN MỘỘT PHT PHẦẦN N TƯ BƯTƯ BƯỚỚC SC SÓÓNGNG
( ) ( )( )djZZ
djZZZdZL
Lin β
βtantan
0
00 +
+=
( )L
in ZZZ
204 =λ
λπβ 2
=4λ
=d
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DÂY NGẮN MẠCH:
( ) ∞=4λINZ0=LZ
DÂY HỞ MẠCH:
( ) 04 =λINZ∞=LZ
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DÂY NGẮN MẠCH:
( ) ∞=4λINZ0=LZ
DÂY HỞ MẠCH:
( ) 04 =λINZ∞=LZ
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"Threaded Neill-Concelman" connector, according to Johnson Components, it is actually a threaded BNC connector, to reduce vibration problems. Carl Concelmanwas an engineer at Amphenol.
PTFE 15 GHz TNC
Sub-miniature type A developed in the 1960s, perhaps the most widely-used microwave connector system in the universe.
PTFE 25 GHz SMA
Sub-miniature type C, a threaded subminiature connector, not widely used.
PTFE 10 GHz SMC
Micro-miniature coax connector, popular in the wire industry because its small size and cheap price.
PTFE MMCX
MCX was the original name of the Snap-On"micro-coax" connector species. Available in 50 and 75 ohms.
PTFE 6 GHz OSX, MCX, PCX
A surface mount connector PTFE 6 GHz OSMT
"Sub-miniature type B", a snap-on subminiature connector, available in 50 and 75 ohms.
PTFE 4 GHz SMB
"Bayonet type-N connector", or "Bayonet Neill-Concelman" according to Johnson Components. Developed in the early 1950s at Bell Labs. Could also stand for "baby N connector".
PTFE 4 GHz BNC
Comments and historyDielectric Frequency Limit
Connector type
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The original mass-marketed 2.92 mm connector, made by Wiltron (now Anritsu). Named the "K" connector, meaning it covers all of the K frequency bands.
Air 40 GHz K
Precision connector, developed by Mario Maury in 1974. 2.92 mm will thread to cheaper SMA and 3.5 mm connectors. Often called "2.9 mm".
Air 40 GHz 2.92 mm
Smaller than an SMA.PTFE 38 GHz SSMA
OSP stands for "Omni-Spectra subminiature push-on", a smaller version of OSP connector.
PTFE 28 GHz OSSP
A precision (expensive) connector, it mates to cheaper SMA connectors.
Air 26.5 GHz 3.5 mm
OSP stands for "Omni-Spectra push-on", a blind-mate connector with zero detent. Often used in equipment racks.
PTFE 22 GHz OSP
APC-7 stands for "Amphenol precision connector", 7mm. Developed in the swinging 60s, ironically a truly sexless connector, which provides the lowest VSWR of any connector up to 18 GHz.
PTFE 18 GHz APC-7, 7 mm
Named for Paul Neill of Bell Labs in the 1940s, available in 50 and 75 ohms. Cheap and rugged, it is still widely in use. Originally was usable up to one GHz, but over the years this species has been extended to 18 GHz, including work by Julius Botka at Hewlett Packard.
PTFE 11 GHznormal
18 GHzprecision
N
"Threaded Neill-Concelman" connector, according to Johnson Components, it is actually a threaded BNC connector, to reduce vibration problems. Carl Concelman was an engineer at Amphenol.
PTFE 15 GHz TNC
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The Rolls Royce of connectors. This connector species works up to 110 GHz. It costs a fortune! Developed at Hewlett Packard (now Agilent) by Paul Watson in 1989.
Air110 GHz1 mm
Anritsu's term for 1.85 mm connectors because they span the V frequency band.
Air60 GHzV
Mechanically compatible with 2.4 mm connectors. Air60 GHz1.85 mm
2.4 mm, and 1.85 mm will mate with each other without damage. Developed by Julius Botka and Paul Watson in 1986, along with the 1.85 mm connector.
Air 50 GHz 2.4 mm
Smaller version of OSP blind-mate connector.40 GHz OS-50P
"Gilbert push-on", "Omni-spectra microminiaturepush-on"
PTFE 40 GHz GPO, OSMP, SMP
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RETURN LOSSRETURN LOSS
dBRL Γ−= log20
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TRANSMISSION COEFICIENTTRANSMISSION COEFICIENT
Γ+=1T
00
0 21ZZ
ZZZZZT
L
L
L
L
+=
+−
+=
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INSERTION LOSSINSERTION LOSS
dBTIL log20−=
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SMITH CHARTSMITH CHART
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MMỐỐI QUAN HI QUAN HỆỆ GIGIỮỮA TRA TRỞỞKHKHÁÁNG VNG VÀÀ HHỆỆ SSỐỐ PHPHẢẢN XN XẠẠ
( ) ( )( )xxZxZ
Γ−Γ+
=11
0
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CCÁÁC GIC GIÁÁ TRTRỊỊ CHUCHUẨẨN HN HÓÓAA
( ) ( )0RxZxz =
jxrz +=
TRTRỞỞ KHKHÁÁNG CHUNG CHUẦẦN HN HÓÓAA
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0RZz L
L =
10
00 ==
RRr
( ) ( )0YxYxy =
( ) ( )xZxY 1=
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HHỆỆ SSỐỐ PHPHẢẢN XN XẠẠ
( ) ( )( ) 0
0
RxZRxZx
+−
=Γ
( ) ( )( ) 1
1
0
0
+−
=ΓRxZRxZx
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MMỐỐI QUAN HI QUAN HỆỆ GIGIỮỮA HA HỆỆ SSỐỐPHPHẢẢN XN XẠẠ VVÀÀ TRTRỞỞ KHKHÁÁNG NG
CHUCHUẨẨN HN HÓÓAA
11
+−
=Γxzxzx
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CÓ 1 GIÁ TRỊ THÌ CHỈ CÓ DUY NHẤT 1 GIÁ TRỊ
CÓ 1 GIÁ TRỊ THÌ CHỈ CÓ DUY NHẤT 1 GIÁ TRỊ
( )xΓ ( )xz
( )xz ( )xΓ
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BBẢẢN CHN CHẤẤT VT VÀÀ CCÁÁCH BICH BIỂỂU DIU DIỂỂN N HHỆỆ SSỐỐ PHPHẢẢN XN XẠẠ
060
( )xΓ
( )( )xΓRe
( )( )xΓIm
( )ΓRe
( )ΓIm
1+1−
1+
1−
0
Mặt phẳng phức
( ) 0608.0 ∠=Γ x
8.0
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HHỆỆ SSỐỐ PHPHẢẢN XN XẠẠ
( ) ( ) ( )xjxx ir Γ+Γ=Γ
ir jΓ+Γ=ΓDạng đơn giản
( )( )⎩
⎨⎧
Γ=ΓΓ=Γ
ImRe
i
r
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TRTRỞỞ KHKHÁÁNG ĐƯNG ĐƯỜỜNG DÂYNG DÂY
( ) ( ) ( )xjXxRxZ +=
jXRZ +=
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TRTRỞỞ KHKHÁÁNG CHUNG CHUẨẨN HN HÓÓAA
( ) ( ) jxxrxz +=jxrz +=
0RRr =
0RXx =
Trở kháng đườngdây chuẩn hóa
Điện trở đường dâychuẩn hóa
Điện kháng đườngdây chuẩn hóa
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ir
ir
jjjxrΓ−Γ−Γ+Γ+
=+11
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( ) 22
22
11
ir
irrΓ+Γ−Γ−Γ−
=
( ) 2212
ir
ixΓ+Γ−
Γ=
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PHƯƠNG TRÌNH ĐƯPHƯƠNG TRÌNH ĐƯỜỜNG TRÒNNG TRÒN2
22
11
1⎟⎠⎞
⎜⎝⎛+
=Γ+⎟⎠⎞
⎜⎝⎛
+−Γ
rrr
ir
⎟⎠⎞
⎜⎝⎛+
0,1 r
rtâm
bán kínhr+1
1
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( )ΓRe
( )ΓIm
1+1−
1+
1−
0
Mặt phẳng phức
0=r2.0=r
5.0=r1=r 2=r
iΓ
rΓ
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PHƯƠNG TRÌNH ĐƯPHƯƠNG TRÌNH ĐƯỜỜNG TRÒNNG TRÒN
( )22
2 111 ⎟⎠⎞
⎜⎝⎛=⎟
⎠⎞
⎜⎝⎛ −Γ+−Γ
xxir
⎟⎠⎞
⎜⎝⎛
x1,1tâm
bán kínhx1
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( )ΓRe
( )ΓIm
1+1−
1+
1−
0
Mặt phẳng phức
5.0=x 1=x
iΓ
rΓ
5.0−=x 1−=x
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( )ΓRe
( )ΓIm
1+1−
1+
1−
0
Mặt phẳng phức
5.0=x 1=x
iΓ
rΓ
5.0−=x
1−=x
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( )ΓRe
( )ΓIm
1+1−
1+
1−
0
Mặt phẳng phức
0=r2.0=r
5.0=r1=r 2=r
iΓ
rΓ
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( )ΓRe
( )ΓIm
1+1−
1+
1−
0
Mặt phẳng phức
5.0=x1=x
iΓ
rΓ
5.0−=x
1−=x
2.0=r5.0=r
1=r 2=r
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