Module 10—Introduction to Wave Propagation, Transmission Lines, and Antennas
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Figure 3-32.—Voltage, current, and impedance on open line.
At all odd quarter-wave points (1/4λ
etc.), the voltage is minimum, the current is maximum, and the impedance is minimum. Thus, at all odd quarter-wave
points, the open-ended transmission line acts as a series-resonant circuit. The impedance is equivalent to a very
low resistance, prevented from being zero only by small circuit losses.
At all even quarter-wave points
, etc.), the
voltages is maximum, the current is minimum, and the impedance is maximum. Comparison of the line with an LC
resonant circuit shows that at an even number of quarter-wavelengths, an open line acts as a parallel-resonant
circuit. The impedance is therefore an extremely high resistance.
In addition, resonant open lines may
also act as nearly pure capacitances or inductances. The illustration shows that an open line less than a
quarter-wavelength long acts as a capacitance. Also, it acts
as an inductance from 1/4 to 1/2 wavelength, as a capacitance from 1/2 to 3/4 wavelength, and as an
inductance from 3/4 to 1 wavelength, etc. A number of open transmission lines, with their equivalent circuits, are
shown in the illustration. Impedance of Various Lengths of Shorted Lines
figure 3-33 as we study the shorted line. At the odd quarter-wavelength points, the voltage is high, the current
is low, and the impedance is high. Since these conditions are similar to those found in a parallel-resonant
circuit, the shorted transmission line acts as a parallel-resonant circuit at these lengths.
Figure 3-33.—Voltage, current, and impedance on shorted line.
At the even quarter-wave points voltage is minimum, current is maximum, and impedance is minimum.
Since these characteristics are similar to those of a series-resonant LC circuit, a shorted transmission line
whose length is an even number of quarter-wavelengths acts as a series-resonant circuit.
lines, like open-end lines, also may act as pure capacitances or inductances. The illustration shows that a
shorted line less than 1/4 wavelength long acts as an inductance. A shorted line with a length of from 1/4 to 1/2
wavelength acts as a capacitance. From 1/2 to 3/4 wavelength, the line acts as an inductance; and from 3/4 to 1
wavelength, it acts as a capacitance, and so on. The equivalent circuits of shorted lines of various lengths are
shown in the illustration. Thus, properly chosen line segments may be used as parallel-resonant, series-resonant,
inductive, or capacitive circuits.
STANDING WAVES ON A TRANSMISSION LINE
There is a large variety of terminations for rf lines. Each type of termination has a characteristic
effect on the standing waves on the line. From the nature of the standing waves, you can determine the type of
termination that produces the waves. TERMINATION IN Z0
Termination in Z0
(characteristic impedance) will cause a constant reading on an ac meter when it is
moved along the length of the line. As illustrated in figure 3-34, view A, the curve, provided there are no losses
in the line, will be a straight line. If there are losses in the line, the amplitude of the voltage and current
will diminish as they move down the line (view B). The losses are due to dc resistance in the line itself.
Figure 3-34.—Effects of various terminations on standing waves.
TERMINATION IN AN OPEN CIRCUIT
In an open-circuited rf line (figure 3-34, view
C), the voltage is maximum at the end, but the current is minimum. The distance between two adjacent zero current
points is 1/2λ
, and the distance between alternate zero current points is 1. The
voltage is zero at a distance of 1/4λ
from the end of the line. This is true at any
frequency. A voltage peak occurs at the end of the line, at 1/2λ
from the end, and at
TERMINATION IN A SHORT CIRCUIT
On the line terminated in a short circuit, shown in
figure 3-34, view D, the voltage is zero at the end and maximum at 1/4λ
from the end.
The current is maximum at the end, zero at 1/4λ
from the end, and alternately maximum
and zero every 1/4λ
thereafter. TERMINATION IN CAPACITANCE
When a line is terminated in capacitance, the capacitor does not absorb energy, but returns all of the energy to
the circuit. This means there is 100 percent reflection. The current and voltage relationships are somewhat more
involved than in previous types of termination. For this explanation, assume that the capacitive reactance is
equal to the Z0
of the line. Current and voltage are in phase when they arrive at the end of the line,
but in flowing through the capacitor and the characteristic impedance (Z0
) connected in series, they
shift in phase relationship. Current and voltage arrive in phase and leave out of phase. This results in the
standing-wave configuration shown in figure 3-34, view E. The standing wave of voltage is minimum at a distance of
exactly 1/8 from the end. If the capacitive reactance is greater than Z0
(smaller capacitance), the
termination looks more like an open circuit; the voltage minimum moves away from the end. If the capacitive
reactance is smaller than Z0
, the minimum moves toward the end. TERMINATION IN
When the line is terminated in an inductance, both the current and voltage shift in
phase as they arrive at the end of the line. When XL
is equal to Z0
, the resulting standing
waves are as shown in figure 3-34, view F. The current minimum is located 1/8λ
the end of the line. When the inductive reactance is increased, the standing waves appear closer to the end. When
the inductive reactance is decreased, the standing waves move away from the end of the line.
TERMINATION IN A RESISTANCE NOT EQUAL TO THE CHARACTERISTIC IMPEDANCE (Z0)
the termination is not equal to Z0
, reflections occur on the line. For example, if the terminating
element contains resistance, it absorbs some energy, but if the resistive element does not equal the Z0
of the line, some of the energy is reflected. The amount of voltage reflected may be found by using the equation:
ER = the reflected voltage
Ei = the incident voltage
RR = the terminating resistance
Z0= the characteristic impedance of the line
If you try different values of RL
in the preceding equation, you will find that the reflected
voltage is equal to the incident voltage only when RL
equals 0 or is infinitely large. When RL
, no reflected voltage occurs. When RL is greater than Z0
positive, but less than Ei
. As RL
approaches an infinite value, ER
increases and approaches Ei
in value. When RL
is smaller than Z0
has a negative value. This means that the reflected voltage is of
opposite polarity to the incident wave at the termination of the line. As RL
approaches zero, ER
in value. The smaller the value of ER
, the smaller is the peak amplitude of
the standing waves and the higher are the minimum values. TERMINATION IN A RESISTANCE GREATER THAN
When RL is greater than Z0, the end of the line is somewhat like
an open circuit; that is, standing waves appear on the line. The voltage maximum appears at the end of the line
and also at half-wave intervals back from the end. The current is minimum (not zero) at the end of the line and
maximum at the odd quarter-wave points. Since part of the power in the incident wave is consumed by the load
resistance, the minimum voltage and current are less than for the standing waves on an open-ended line. Figure
3-34, view G, illustrates the standing waves for this condition. TERMINATION IN A RESISTANCE LESS
is less than Z0
, the termination appears as a
short circuit. The standing waves are shown in figure 3-34, view H. Notice that the line terminates in a current
LOOP (peak) and a voltage NODE (minimum). The values of the maximum and minimum voltage and current approach those
for a shorted line as the value of RL
A line does not have to be any
particular length to produce standing waves; however, it cannot be an infinite line. Voltage and current must be
reflected to produce standing waves. For reflection to occur, a line must not be terminated in its characteristic
impedance. Reflection occurs on lines terminated in opens, shorts, capacitances, and inductances, because no
energy is absorbed by the load. If the line is terminated in a resistance not equal to the characteristic
impedance of the line, some energy will be absorbed and the rest will be reflected.
The voltage and
current relationships for open-ended and shorted lines are opposite to each other, as shown in figure 3-34, views
C and D. The points of maximum and minimum voltage and current are determined from the output end of the line,
because reflection always begins at that end.
Q26. A nonresonant line is a line that has no standing waves of current and voltage on it and is considered to
be flat. Why is this true?
Q27. On an open line, the voltage and impedance are maximum at what points on
the line? STANDING-WAVE RATIO
The measurement of standing waves on a transmission
line yields information about equipment operating conditions. Maximum power is absorbed by the load when ZL
. If a line has no standing waves, the termination for that line is correct and maximum power
transfer takes place.
You have probably noticed that the variation of standing waves shows how near the rf
line is to being terminated in Z0
. A wide variation in voltage along the length means a termination far
from Z0. A small variation means termination near Z0
. Therefore, the ratio of the maximum to the
minimum is a measure of the perfection of the termination of a line. This ratio is called the STANDING-WAVE RATIO
(swr) and is always expressed in whole numbers. For example, a ratio of 1:1 describes a line terminated in its
characteristic impedance (Z0
Voltage Standing-Wave Ratio
The ratio of maximum voltage to minimum voltage
on a line is called the VOLTAGE STANDING- WAVE RATIO (vswr). Therefore:
The vertical lines in the formula indicate that the enclosed quantities are absolute and that the two
values are taken without regard to polarity. Depending on the nature of the standing waves, the numerical value of
vswr ranges from a value of 1 (ZL = Z0, no standing waves) to an infinite value for theoretically complete
reflection. Since there is always a small loss on a line, the minimum voltage is never zero and the vswr is always
some finite value. However, if the vswr is to be a useful quantity, the power losses along the line must be small
in comparison to the transmitted power. Power Standing-Wave Ratio
The square of
the voltage standing-wave ratio is called the POWER STANDING-WAVE RATIO (pswr). Therefore:
This ratio is useful because the instruments used to detect standing waves react to the square of the
voltage. Since power is proportional to the square of the voltage, the ratio of the square of the maximum and
minimum voltages is called the power standing-wave ratio. In a sense, the name is misleading because the power
along a transmission line does not vary. Current Standing-Wave Ratio
The ratio of
maximum to minimum current along a transmission line is called CURRENT STANDING-WAVE RATIO (iswr). Therefore:
This ratio is the same as that for voltages. It can be used where measurements are made with loops that
sample the magnetic field along a line. It gives the same results as vswr measurements.
Q28. At what
point on an open-circuited rf line do voltage peaks occur?
Q29. What is the square of the voltage
standing-wave ratio called?
Q30. What does vswr measure?
This chapter has presented information on the characteristics of transmission lines. The information
that follows summarizes the important points of this chapter. TRANSMISSION LINES
devices for guiding electrical energy from one point to another.
is the ratio of voltage to current at the input end of a transmission
line. OUTPUT IMPEDANCE
is the ratio of voltage to current at the output end of the
line. TWO-WIRE OPEN LINES
are parallel lines and have uses such as power lines, rural
telephone lines, and telegraph lines. This type of line has high radiation losses and is subject to noise pickup.
has parallel lines and is most often used to connect televisions to their
A TWISTED PAIR
consists of two insulated wires twisted together. This line has high
A SHIELDED PAIR
has parallel conductors separated by a solid dielectric and
surrounded by copper braided tubing. The conductors are balanced to ground.
RIGID COAXIAL LINE
contains two concentric conductors insulated from each other by
spacers. Some rigid coaxial lines are pressurized with an inert gas to prevent moisture from entering.
High-frequency losses are less than with other lines.
FLEXIBLE COAXIAL LINES
consist of a flexible inner conductor and a concentric outer
conductor of metal braid. The two are separated by a continuous insulating material.
are hollow metal tubes used to transfer energy from one point to another.
The energy travels slower in a waveguide than in free space.
can result from power (I2
R) loss, in the form of heat, or
skin effect. These losses decrease the conductivity of a line. DIELECTRIC LOSSES
are caused by the heating of the dielectric material between conductors, taking power from the source.
and INDUCTION LOSSES
are caused by part of the electromagnetic fields
of a conductor being dissipated into space or nearby objects.
A transmission line is either
if its physical length is not equal to 1/4λ
for the frequency it is to carry. LUMPED CONSTANTS
are theoretical properties
(inductance, resistance, and capacitance) of a transmission line that are lumped into a single component.
are constants of inductance, capacitance and resistance that are
distributed along the transmission line.
Introduction to Matter, Energy, and Direct Current,
to Alternating Current and Transformers, Introduction to Circuit Protection,
Control, and Measurement
, Introduction to Electrical Conductors, Wiring Techniques,
and Schematic Reading
, Introduction to Generators and Motors
Introduction to Electronic Emission, Tubes, and Power Supplies,
Introduction to Solid-State Devices and Power Supplies
Introduction to Amplifiers, Introduction to
Wave-Generation and Wave-Shaping Circuits
, Introduction to Wave Propagation, Transmission
Lines, and Antennas
, Microwave Principles,
, Introduction to Number Systems and Logic Circuits, Introduction
to Microelectronics, Principles of Synchros, Servos, and Gyros
Introduction to Test Equipment
, Radar Principles,
The Technician's Handbook,
Master Glossary, Test Methods and Practices,
Introduction to Digital Computers,
Magnetic Recording, Introduction to Fiber Optics