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Principles of Electronic
Communication Systems
Third Edition
Louis E. Frenzel, Jr.
© 2008 The McGraw-Hill Companies
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Chapter 13
Transmission Lines
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Topics Covered in Chapter 13
 13-1: Transmission-Line Basics
 13-2: Standing Waves
 13-3: Transmission Lines as Circuit Elements
 13-4: The Smith Chart
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13-1: Transmission-Line Basics
 Transmission lines in communication carry telephone
signals, computer data in LANs, TV signals in cable
TV systems, and signals from a transmitter to an
antenna or from an antenna to a receiver.
 Their electrical characteristics are critical and must be
matched to the equipment for successful
communication to take place.
 Transmission lines are also circuits.
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13-1: Transmission-Line Basics

The two primary requirements of a transmission line
are:
1. The line should introduce minimum attenuation to the
signal.
2. The line should not radiate any of the signal as radio
energy.
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13-1: Transmission-Line Basics
Types of Transmission Lines
 Parallel-wire line is made of two parallel conductors
separated by a space of ½ inch to several inches.
 A variation of parallel line is the 300-Ω twin-lead.
Spacing between the wires is maintained by a
continuous plastic insulator.
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13-1: Transmission-Line Basics
Types of Transmission Lines
 The most widely used type of transmission line is the
coaxial cable. It consists of a solid center conductor
surrounded by a dielectric material, usually a plastic
insulator such as Teflon.
 A second conducting shield made of fine wires
covers the insulator, and an outer plastic sheath
insulates the braid.
 Coaxial cable comes in sizes from ¼ inch to several
inches in diameter.
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13-1: Transmission-Line Basics
Types of Transmission Lines
 Twisted-pair cable uses two insulated solid copper
wires covered with insulation and loosely twisted
together.
 Two types of twisted-pair cable are
 Unshielded twisted-pair (UTP) cable
 Shielded twisted-pair (STP) cable
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13-1: Transmission-Line Basics
Figure 13-1: Common types of transmission lines. (a) Open-wire line. (b) Open-wire
line called twin lead. (c) Coaxial cable (d) Twisted-pair cable.
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13-1: Transmission-Line Basics
Balanced Versus Unbalanced Lines
 Transmission lines can be balanced or unbalanced.
 A balanced line is one in which neither wire is
connected to ground.
 The signal on each wire is referenced to ground.
 In an unbalanced line, one conductor is connected to
ground.
 Open-wire line has a balanced configuration.
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13-1: Transmission-Line Basics
Balanced Versus Unbalanced Lines
 Balanced-line wires offer significant protection from
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noise pickup and cross talk.
Coaxial cables are unbalanced lines.
Coaxial cable and shielded twisted-pair provide
significant but not complete protection from noise or
cross talk.
Unshielded lines may pick up signals and cross talk and
can even radiate energy, resulting in an undesirable
loss of signal.
A device called a balun is used to convert from
balanced to unbalanced lines and vice versa.
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13-1: Transmission-Line Basics
Figure 13-2: (a) Balanced line. (b) Unbalanced line.
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13-1: Transmission-Line Basics
Wavelength of Cables
 The electrical length of conductors is typically short
compared to 1 wavelength of the frequency they carry.
 A pair of current-carrying conductors is not considered
to be a transmission line unless it is at least 0.1 λ long
at the signal frequency.
 The distance represented by a wavelength in a given
cable depends on the type of cable.
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13-1: Transmission-Line Basics
Connectors
 Most transmission lines terminate in some kind of
connector, a device that connects the cable to a piece
of equipment or to another cable.
 Connectors are a common failure point in many
applications.
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13-1: Transmission-Line Basics
Connectors: Coaxial Cable Connectors
 Coaxial cables are designed not only to provide a
convenient way to attach and disconnect equipment
and cables but also to maintain the physical integrity
and electrical properties of the cable.
 The most common types are the PL-259 or UHF, BNC,
F, SMA, and N-type connectors.
 The PL-259, also referred to as a UHF connector, can
be used up to low UHF frequencies (less than 500
MHz.)
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13-1: Transmission-Line Basics
Figure 13-3: UHF connectors. (a) PL-259 male connector. (b) Internal construction and
connections for the PL-259. (c) SO-239 female chassis connector.
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13-1: Transmission-Line Basics
Connectors: Coaxial Cable Connectors
 BNC connectors are widely used on 0.25 inch coaxial
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cables for attaching test equipment.
In BNC connectors the center conductor of the cable is
soldered or crimped to a male pin and the shield braid is
attached the body of the connector.
The least expensive coaxial connector is the F-type,
which is used for TV sets, VCRs, DVD players, and
cable TV.
The RCA phonograph connector is used primarily in
audio equipment.
The best performing coaxial connector is the N-type,
which is used mainly on large coaxial cable at higher
frequencies.
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13-1: Transmission-Line Basics
Figure 13-4: BNC connectors. (a) Male. (b) Female. (c) Barrel connector. (d) T
connector.
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13-1: Transmission-Line Basics
Figure 13-6: The F connector used on TV sets, VCRs, and cable TV boxes.
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13-1: Transmission-Line Basics
Figure 13-7: RCA phonograph connectors are sometimes used for RF connectors up
to VHF.
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13-1: Transmission-Line Basics
Figure 13-8: N-type coaxial connector.
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13-1: Transmission-Line Basics
Characteristic Impedance
 When the length of transmission line is longer than
several wavelengths at the signal frequency, the two
parallel conductors of the transmission line appear as a
complex impedance.
 An RF generator connected to a considerable length of
transmission line sees an impedance that is a function
of the inductance, resistance, and capacitance in the
circuit—the characteristic or surge impedance (Z0).
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13-1: Transmission-Line Basics
Velocity Factor
 The speed of the signal in the transmission line is
slower than the speed of a signal in free space.
 The velocity of propagation of a signal in a cable is less
than the velocity of propagation of light in free space by
a fraction called the velocity factor (VF).
VF = Vp/Vc
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13-1: Transmission-Line Basics
Time Delay
 Because the velocity of propagation of a transmission
line is less than the velocity of propagation in free
space, any line will slow down or delay any signal
applied to it.
 A signal applied at one end of a line appears some time
later at the other end of the line.
 This is called the time delay or transit time.
 A transmission line used specifically for the purpose of
achieving delay is called a delay line.
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13-1: Transmission-Line Basics
Figure 13-11: The effect of the time delay of a transmission line on signals. (a) Sine
wave delay causes a lagging phase shift. (b) Pulse delay.
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13-1: Transmission-Line Basics
Transmission-Line Specifications
 Many coaxial cables are designated by an
alphanumeric code beginning with the letters RG or a
manufacturer’s part number.
 Primary specifications are characteristic impedance and
attenuation.
 Other important specifications are maximum breakdown
voltage rating, capacitance per foot, velocity factor, and
outside diameter in inches.
 The attenuation is the amount of power lost per 100 ft of
cable expressed in decibels at 100 MHz.
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13-1: Transmission-Line Basics
Transmission-Line Specifications
 Attenuation is directly proportional to cable length and
increases with frequency.
 A transmission line is a low-pass filter whose cutoff
frequency depends on distributed inductance and
capacitance along the line and on length.
 It is important to use larger, low-loss cables for longer
runs despite cost and handling inconvenience.
 A gain antenna can be used to offset cable loss.
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13-1: Transmission-Line Basics
Figure 13-14: Attenuation versus length for RG-58A/U coaxial cable. Note that both
scales on the graph are logarithmic.
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13-2: Standing Waves
 When a signal is applied to a transmission line, it
appears at the other end of the line some time later
because of the propagation delay.
 If the load on the line is an antenna, the signal is
converted into electromagnetic energy and radiated
into space.
 If the load at the end of the line is an open or a short
circuit or has an impedance other than the
characteristic impedance of the line, the signal is not
fully absorbed by the load.
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13-2: Standing Waves
 When a line is not terminated properly, some of the
energy is reflected and moves back up the line,
toward the generator.
 This reflected voltage adds to the forward or incident
generator voltage and forms a composite voltage that
is distributed along the line.
 The pattern of voltage and its related current
constitute what is called a standing wave.
 Standing waves are not desirable.
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13-2: Standing Waves
Figure 13-15: How a pulse propagates along a transmission line.
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13-2: Standing Waves
Matched Lines
 A matched transmission line is one terminated in a
load that has a resistive impedance equal to the
characteristic impedance of the line.
 Alternating voltage (or current) at any point on a
matched line is a constant value. A correctly terminated
transmission line is said to be flat.
 The power sent down the line toward the load is called
forward or incident power.
 Power not absorbed by the load is reflected power.
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13-2: Standing Waves
Figure 13-16: A transmission line must be terminated in its characteristic impedance for
proper operation.
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13-2: Standing Waves
Calculating the Standing Wave Ratio
 The magnitude of the standing waves on a transmission
line is determined by the ratio of the maximum current
to the minimum current, or the ratio of the maximum
voltage to the minimum voltage, along the line.
 These ratios are referred to as the standing wave ratio
(SWR).
SWR =
Imax
Imin
=
Vmax
Vmin
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13-3: Transmission Lines
as Circuit Elements
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 The standing wave conditions resulting from open-
and short-circuited loads must usually be avoided
when working with transmission lines.
 With quarter- and half-wavelength transmissions,
these open- and short-circuited loads can be used as
resonant or reactive circuits.
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13-3: Transmission Lines
as Circuit Elements
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Resonant Circuits and Reactive Components
 Shorted and open quarter wavelengths act like LC
tuned or resonant circuits at the reference frequency.
 With a shorted line, if the line length is less than onequarter wavelength at the operating frequency, the
shorted line looks like an inductor to the generator.
 If the shorted line is between one-quarter and one-half
wavelength, it looks like a capacitor to the generator.
 These conditions repeat with multiple one-quarter or
one-half wavelengths of shorted line.
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13-3: Transmission Lines
as Circuit Elements
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Resonant Circuits and Reactive Components
 With an open line, a one-quarter wavelength line looks
like a series resonant circuit to the generator, and a
one-half wavelength line looks like a parallel resonant
circuit, just the opposite of a shorted line.
 If the line is less than one-quarter wavelength, the
generator sees a capacitance.
 If the line is between one-quarter and one-half
wavelength, the generator sees an inductance.
 These characteristics repeat for lines that are some
multiple of one-quarter or one-half wavelengths.
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13-3: Transmission Lines
as Circuit Elements
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Figure 13-25: Summary of impedance and reactance variations of shorted and open
lines for lengths up to one wavelength.
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13-3: Transmission Lines
as Circuit Elements
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Stripline and Microstrip
 Special transmission lines constructed with copper
patterns on a printed circuit board (PCB), called
microstrip or stripline, can be used as tuned circuits,
filters, phase shifters, reactive components, and
impedance-matching circuits at high frequencies.
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13-3: Transmission Lines
as Circuit Elements
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Stripline and Microstrip
 Microstrip is a flat conductor separated by an
insulating dielectric from a large conducting ground
plane.
 The microstrip is usually a quarter or half wavelength
long.
 The ground plane is the circuit common and is
equivalent to an unbalanced line.
 The characteristic impedance of microstrip is dependent
on its physical characteristics.
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13-3: Transmission Lines
as Circuit Elements
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Figure 13-26: Microstrip. (a) Unbalanced. (b) Balanced.
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13-3: Transmission Lines
as Circuit Elements
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Stripline and Microstrip
 Stripline is a flat conductor sandwiched between two
ground planes.
 It is more difficult to make than microstrip; however, it
does not radiate as microstrip does.
 The length is one-quarter or one-half wavelength at the
desired operating frequency.
 Shorted lines are more commonly used than open lines.
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13-3: Transmission Lines
as Circuit Elements
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Figure 13-28: Stripline.
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13-4: The Smith Chart
 The mathematics required to design and analyze
transmission lines is complex, whether the line is a
physical cable connecting a transceiver to an antenna
or is being used as a filter or impedance-matching
network.
 This is because the impedances involved are complex
ones, involving both resistive and reactive elements.
 The impedances are in the familiar rectangular form, R
+ jX.
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13-4: The Smith Chart
 The Smith Chart is a sophisticated graph that permits
visual solutions to transmission line calculations.
 Despite the availability of the computing options today,
this format provides a more or less standardized way
of viewing and solving transmission-line and related
problems.
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13-4: The Smith Chart
 The horizontal axis is the pure resistance or zero-
reactance line.
 The point at the far left end of the line represents zero
resistance, and the point at the far right represents
infinite resistance. The resistance circles are centered
on and pass through this pure resistance line.
 The circles are all tangent to one another at the infinite
resistance point, and the centers of all the circles fall
on the resistance line.
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13-4: The Smith Chart
 Any point on the outer circle represents a resistance of
0 Ω.
 The R = 1 circle passes through the exact center of
the resistance line and is known as the prime center.
 Values of pure resistance and the characteristic
impedance of transmission line are plotted on this line.
 The linear scales printed at the bottom of Smith charts
are used to find the SWR, dB loss, and reflection
coefficient.
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13-4: The Smith Chart
Figure 13-30: The Smith chart.
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