Standing Up
For
Standing Waves
RF Transmission Line &
Antenna Demonstration
Wireless Communications
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1897: “Digital Wireless” was born when Marconi was
awarded a Patent for “Wireless Telegraph”.
1914: “Voice over Radio” was first demonstrated.
1935: “Frequency Modulation” was first demonstrated.
1946: “Mobile Phones” were first deployed.
1960’s: Bell Labs developed “Pulse Code Modulation”
standards. Eventually to become today’s Extended
Super Frame T1 circuit and the basic building block of
modern Digital WAN communications.
1970’s: Wide spread deployment Integrated Circuits.
1980’s: Wide spread deployment of DDS Oscillators.
The beginning of Microprocessor Controlled
Transceivers.
1990’s: Wide spread deployment of the Cellular
Telephone Network.
Digital Wireless Communications Today:
9 3G Cellular with over 100 million phones in US.
9 IEEE 802.11G
9 GigaBit Carrier Class Microwave Radios using
QAM.
Antennas and Transmission Lines:
9 Principles have not changed in the 1st hundred
years and are not likely to change in the next
hundred years.
9 Rule #1:
“Efficient ones have greater range than inefficient
ones.”
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Equipment Setup
¾ Operates on the 2 Meter Amateur Band (145.585MHz).
¾ 1/2Watt Exciter drives a 40Watt Power Amp.
¾ 10’ of 50Ω RG-188U coaxial cable provides approx. 1 dB of
loss. This provides a buffer for the PA during high SWR
conditions.
¾ 30 Watts is applied to a 4:1 coaxial Balun. Baluns are used
to transition from Balanced transmission line to
Unbalanced transmission line. This type of Balun uses a
180° delay line, which causes the voltages on the balanced
transmission line section to appear 180° out of phase. This
effectively doubles the RF voltage. Since the RF power
level has not changed (no loss), this results in a 4 fold
increase in impedance. Hence the term 4:1 Balun as it
makes an efficient electrical transition possible between a
200Ω balanced transmission line and a 50Ω unbalanced
coaxial cable.
¾ 11.5’ of 200Ω balanced transmission line forms the
backbone of the demonstration. This particular line will be
considered ideally “Lossless” with a Velocity Factor of
100%. Balanced transmission line has been selected for the
demonstration as it allows easier access to the conductors.
All of the objectives presented in this demonstration apply
equally to coaxial cable.
¾ Reflectometer Sleds are used to display relative Forward
and Reflected “RF Energy/Power Waves”.
¾ Voltage Sleds are used to display relative RF Voltage (also
referred to as the static field) along the transmission line.
¾ Current Sleds are used to display relative RF Current (also
referred to as flux or magnetic fields) along the
transmission line.
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Ideal Line Conditions
Standing Wave Ratio = 1:1
¾ The balanced transmission line is terminated with a
resistance equal to that of the line. (200Ω, j0)
¾ Forward Reflectometer indicates full power being
delivered from the transmitter.
¾ Reverse Reflectometer indicates no reflected power.
¾ All of the RF energy is being dissipated in the load.
¾ Voltage Sled indicates the same amount of voltage at all
points along the transmission line.
¾ Current Sled indicates the same amount of current at all
points along the transmission line.
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Standing Wave Ratio
¾ Technically called VSWR. Voltage Standing Wave Ratio
¾ Roots of the term “Standing Waves” can be traced back to
the days before WWII, coaxial cable, power and
Reflectometers when operators would notice that when
touching a light bulb to the line, which was not matched to
the load, it would be brighter in some spots than in other
spots.
¾ Definition: Standing Wave: Unlike an Energy Wave which
travels along the transmission line, a Standing Wave
appears to be “Frozen in Time” or “Standing” on the
transmission line. Standing Waves appear in both the
Voltage and Current fields, but they are shifted 180º from
each other.
¾ A reflected “Energy Wave” colliding (or interfering) with
a forward “Energy Wave” causes Standing Waves. Due to
“Propagation Delay” along the transmission line, some
energy waves collide “in phase” and cause an increase in
voltage. At other points along the transmission line, energy
waves collide “out of phase” and cause a decrease in
voltage.
¾ Definition: Standing Wave Ratio: The ratio of Voltage
Maximum to Voltage Minimum along the 1/2λ section of
transmission line nearest the load. Also the ratio of
CurrentMax to CurrentMin.
¾ Voltage and Current Nodes are 180° out of phase on
transmission lines that have Standing Waves.
¾ The length or period of a Standing Wave (i.e. distance or
time from VMax to VMax ) is a 1/2λ of the fundamental
frequency.
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Measuring Standing Waves
¾ When the load is a pure resistance (j=0), then
RLine RLoad
SWR=
or
RLoad RLine
(which ever results in a number greater than 1)
¾ When measuring Voltage or Current, then
SWR = VMax
VMin
SWR = IIMax
Min
(this method is usually not practical on coaxial cables)
¾ When measuring Forward and Reflected Power, then
SWR
=
1+
1−
Reflected
Forward
Reflected
Forward
Power
Power
Power
Power
Fortunately, there are meters with calibrated scales for
this.
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Transmitting Antenna
¾ Single Dipole Antennas in “Free Space” have a nominal
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feedpoint resistance of 70Ω.
For this demonstration, we need an antenna with a 200Ω
feedpoint impedance to match our 200Ω Transmission
Line. One method to accomplish this, is to shorten the
length of the dipoles from their resonate length. A
“Hairpin” inductor-matching device is then used to
cancel the capacitance effect of shortening the antenna.
This transmitting antenna is orientated “Horizontally”
and the “Free Space” radiation pattern could be
visualized by placing a huge doughnut with its center
around the antenna at the feedpoint.
9 “Circular” in the “H Field” or Current Plane (a plane
perpendicular to the dipole).
9 “Figure 8” in the “E Field” or Static Plane (a plane
along the axis of the dipole).
9 In reality, there will be minor distortions in this ideal
radiation pattern caused by the transmission line and
reflections from other objects in the room such as the
floor, ceiling, and etc.
Gain of this antenna can be considered 0dB/dipole or
+2.14dB/isotropic.
Voltage Nodes (high impedance nodes) will appear at the
ends of the dipoles. If the antenna is long enough,
Voltage Nodes will repeat every 1/2λ along the antenna
toward the feedpoint.
Current Nodes (low impedance nodes) will appear 1/4λ
toward the feedpoint from the voltage nodes. If the
antenna is long enough, Current Nodes will repeat every
1/2λ along the antenna toward the feedpoint.
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Receiving Antenna
¾ Yagi, 3 Element Directional Array.
¾ Incandescent lamp displays relative field strength.
¾ Driven Element is in the middle and near “Resonate”
length.
¾ Reflector Element is spaced nearly 1/4λ behind the
Driven Element and approx. 5% longer than the Driven
Element.
¾ Director Element is spaced nearly 1/4λ in the front of the
Driven Element and approx. 5% shorter that the Driven
Element.
¾ Maximum signal strength is realized when the Receiving
Antenna is in the same plane (polarity) as the
Transmitting Antenna and with the Director Element
nearest the Transmitting Antenna.
¾ Voltage and Current nodes are distributed along the
elements in Receiving Antennas the same as in
Transmitting Antennas, except with less intensity.
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Transmission Line Stubs
¾ 1/4λ Transmission Line sections are considered to be
Impedance Transformers.
¾ 1/4λ Transmission Line Stubs, and odd order multiples,
will present an impedance at the Transmission line Node
that is inverted from the impedance that is present at the
end of the stub.
9 Shorted 1/4λ Transmission Line Stubs will present a
high impedance (open) at the point where it connects to
the Transmission Line.
9 Open 1/4λ Transmission Line Stubs will present a low
impedance (short) at the point where it connects to the
Transmission Line.
¾ 1/2λ Transmission Line sections are considered to be
Impedance Transparent.
¾ 1/2λ Transmission Line Stubs, and multiples, will present
an impedance at the Transmission line Node that is the
same as the impedance that is present at the end of the
stub.
9 Shorted 1/2λ Transmission Line Stubs will present a
low impedance (short) at the point where it connects to
the Transmission Line.
9 Open 1/2λ Transmission Line Stubs will present a high
impedance (open) at the point where it connects to the
Transmission Line.
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Conjugate Match Theorem
¾ On any 1/2λ section of Transmission Line, with
“Standing Waves”, there will be 2 points where the “R”
value equals the characteristic impedance of the
Transmission Line. These 2 points will also have equal
but opposite “j” reactance values. One point being
capacitive (-j) and the other point being inductive (+j).
¾ A Conjugate Match will exist if a reactance “j” of a
value that will cancel the “j” of the Transmission Line,
is inserted at one of the these points where “R” value
equals the characteristic impedance of the Transmission
Line.
9 Lumped Constants of Capacitance and Inductance
of the proper reactance value will provide a
Conjugate Match.
9 Distributed Constants using Transmission Line
stubs as Capacitance in open stubs and Inductance
in shorted stubs of the proper length/reactance will
provide a Conjugate Match.
¾ When a Conjugate Match exists, any Reflected RF
Energy is returned back to the antenna to be radiated,
except for what is lost as heat in the Transmission Line.
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Phase Velocity
¾Phase Velocity is the speed in which an Energy Wave
travels through a medium such as a vacuum, air, or
dielectric.
¾The Phase Velocity through a vacuum is considered the
speed of light (near 300,000,000 Meters/Second). All other
Phase Velocity’s are measured as a percentage of this speed
and sometimes referred to as Velocity Factor.
¾Transmission Lines commonly have Velocity Factors
ranging from 65.9% - 89% depending on their dielectric
material.
¾Phase Velocity is an important consideration when
calculating the electrical length of a Transmission Line.
¾Transmission Lines with a dense dielectric such as Solid
Polyethylene have lower Velocity Factors.
¾Transmission Lines with Air Space or Foam Polyethylene
have much higher Velocity Factors.
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Ferrite Beads
¾ Ferrite Beads are commonly used to “Resist” RF
current flow and are sometimes referred to as
“Shielding Beads” or “Chokes”.
¾ Ferrite Beads are produced from different
combinations of materials to have the maximum effect
at different frequencies. (i.e. type “43” Ferrites are
useful from 30 –500MHz while type “J” Ferrites are
useful from 1-7MHz)
¾ Applications for Ferrite Beads include:
9 Placement around telephone and other audio cables
to “shield” them from RFI.
9 Placement around computer monitor cables to
prevent RFI.
9 Placement around DC and AC cables of “Switched
Mode” power supplies to prevent RFI.
9 Placement around coaxial cables to prevent
unwanted RF current from flowing on the outer
skin of the shield that might occur when Standing
Waves are present. The most efficient form of 1:1
Baluns (sometimes referred to as chokes or
isolators) are made this way.
9 Ferrites are also used widely in “Switched Mode”
power supplies and other RF applications as
transformer and inductor cores.
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1/4λ Transmission Line Transformers
¾ 1/4λ sections of Transmission Line are
“Impedance Transformers”.
¾ 1/2λ sections of Transmission Line are
“Impedance Transparent”.
¾
The formula for determining the input impedance of a
1/4λ section of transmission line is:
ZInput =
(ZLine )
2
ZLoad
Where:
ZInput = Impedance @ the Transmitter end of the 1/4λ Line.
ZLoad = Impedance @ the Load end of the 1/4λ Line.
ZLine = Impedance of the 1/4λ Transmission Line section.
Example #1: 200Ω Load and 200Ω 1/4λ Transmission Line.
2 40,000
(
)
200
ZInput =
=
= 200Ω Transformer Ratio: 1:1
200
200
Example #2: 200Ω Load and 300Ω 1/4λ Transmission Line.
2
90,000
(
)
300
ZInput =
=
= 450Ω Transformer Ratio: 2.25:1
200
200
Example #3: 200Ω Load and 600Ω 1/4λ Transmission Line.
2
360,000
(
)
600
ZInput =
=
= 1,800Ω Transformer Ratio: 9:1
200
200
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Voltage and Current Relationships in
Dipole Antennas
Voltage
Current
1/4 Wavelength Dipole
1/4 Wavelength Dipole
Feedline
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ADDITIONAL POWER LOST IN TRANSMISSION LINES
DUE TO REFLECTIONS AND SWR
ADDITIONAL LOSS IN DB CAUSED BY
STANDING WAVES
10.0
1.0
0.1
0.20
0.25
0.32
0.40
0.50
0.63
0.79
1.00
1.26
1.58
2.00
2.51
3.16
3.98
5.01
6.31
7.94
10.00
NORMAL TRANSMISSION LINE LOSS IN DB WHEN PROPERLY TERMINATED
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TRANSMISSION LINE LOSS CHART
USING "SHORTED" OR "OPEN"
TERMINATION
TRANSMISSION LINE LOSS (dB)
10
1
0.1
1.3
1.6
2.0
2.5
3.2
4.0
5.0
6.3
7.9
10.0
12.6
15.8
20.0
25.1
31.6
39.8
50.1
63.1
80.0
SWR @ TRANSMISSION LINE INPUT
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VELOCITY FACTOR
95
0.97
AIR 99.5%
90
85
VELOCITY FACTOR (%)
0.91
AIR SPACE PE 84-89%
0.85
FOAM PE 75-80%
80
0.79
PTFE 70%
75
70
0.73
POLYETHYLENE 66%
65
0.67
60
0.61
55
0.55
50
0.49
45
0.43
40
0.37
35
30
1.00
PHASE VELOCITY (ft/ns )
100
1.26
1.58
2.00
2.51
3.16
3.98
5.01
DIELECTRIC CONSTANT
Standing Up For Standing Waves Copyright 2003
6.31
7.94
0.31
10.00
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VSWR Chart
VSWR
10.0
4.5
3.0 2.5
100.0
2.0
1.80
REFLECTED POWER (Watts)
1.60
1.50
1.40
1.30
1.25
10.0
1.20
1.16
1.14
1.12
1.10
1.0
0.1
0.1
0.3
0.5
1.0
2.0
4.0
7.9
15.8
31.6
63.1
125.9
251.2
501.2
1000.0
FORWARD POWER (Watts)
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Transmission Line Equations
Power and Ohms Law
E = IR ,
I= E,
R=E
R
I
SWR
Max
IMax
SWR = E
EMin = IMin
SWR = RLoad
ZLine
SWR =
SWR =
or
1+
1−






P = I 2R ,
I=
Reflected
Forward
Reflected
Forward
2
E
P=
,
R
2
E
R=
,
P
Pwr
Pwr
Pwr
Pwr
(R + Z Line )2 + j 2  +  (R - Z Line )2 + j 2 
(R + Z Line )2 + j 2  -  (R - Z Line )2 + j 2 
1+ p
SWR =
1− p
P,
R
SWR = ZLine
RLoad
p = Refl Coef
p = SWR − 1 = ZLoad − ZLine
SWR + 1 ZLoad + ZLine
Additional Transmission Line
Loss caused by SWR
 (10dB /10 )2 −(SWR−1 )2 
Loss(dB) = 10log dB /10  SWR+12   − dB
SWR−1 )  
10 1−(SWR
+1  


dB = Loss in perfectly matched Line
SWR = SWR at the Load
1/4λ Transmission Line
Transformers
2
ZInput = ZLine
ZLoad
ZLine = ZInput x ZLoad
E = P,
I
P = EI ,
R = P2
I
E = PR
I=P
E
EMax = Pwr × ZLine × SWR
EMin = EMax
SWR
IMin = EMin
ZLine
IMax = EMax
ZLine
IMin = IMax
SWR
dB = 10log P1 ,
P2
dB = 20log E1
E2
Coaxial Cable
%
ε
C( pf / ft ) = 7.36
VF
= 100
D
ε


log  
d
L( uH / ft ) = .14 log D
d
ZLine =
L
C
=
( ) (log Dd )
138
ε
x
Delay( ns/ ft ) = 1.016 ε
ε = dielectric constant
d = OD of inner conductor
D = ID of outer conductor
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Basic Demo Equipment Setup
10' RG-188U
50 Ohm Unbalanced Line
30W
11.5' of 200 Ohm Balanced Line
40W
P.A.
RG-174U
4:1
Coaxial
Balun
1/4W Exciter
145.585MHz
180 Degree Delay Line
Various Line Terminations
Demonstrated Here
1 Meter
180°
1 / 2λ
90°
1 / 4λ
360° 1.0λ
2 Meters
1 Wavelength @ 145.585MHz
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Free Space Dipole E & H Field Radiation Patterns
E - Field
H - Field
70° 80° 90° 80° 70°
60°
50°
50°
60°
70° 80° 90° 80° 70°
60°
50°
0d
B
60°
0d
B
50°
30°
30°
20°
20°
20°
20°
10°
10°
10°
10°
0°
0°
0°
10°
10°
20°
20°
30°
30°
30°
30°
40°
40°
40°
40°
20°
50°
60°
70° 80° 90° 80° 70°
60°
aka - Magnetic Field
aka - Current Field
50°
50°
B
30°
Axis
-20d
dB
-20
End View
of Dipole
Dipole
B
-10d
B
-10d
10°
B
0d
B
0d B
0d
30°
40°
+1
40°
+1
40°
40°
0°
10°
20°
60°
70° 80° 90° 80° 70°
60°
50°
aka - Static Field
aka - Voltage Field
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