EE 3324 Electromagnetics Laboratory
Experiment #4
Transmission Lines
1. Objective
The objective of Experiment #4 is to investigate the characteristics of signals (waves)
propagating on transmission lines. A two-wire transmission line is used to demonstrate concepts
such as propagation, attenuation, transmission line matching, partial and total reflection, and
standing waves.
2. Introduction
A transmission line is used to guide energy in the form of electromagnetic waves from a
source (generator) to a load. Common applications of transmission lines are found in power
distribution and communications. The transmission line is made up of at least two conductors which
guide the signal [transverse electromagnetic (TEM) wave] from the source to the load. A critical
parameter associated with the transmission line is the characteristic impedance (Zo) given by
(1)
where R is the resistance per unit length of the conductors, L is the inductance per unit length of the
conductors, G is the conductance per unit length of the medium between the conductors, and C is
the capacitance between the conductors. The characteristic impedance of a two-wire line with
dimensions shown in Figure 1 (conductor diameter = d, center-to-center conductor spacing = D ) is
(2)
where 0 is the intrinsic wave impedance of the medium
between the conductors.
The value of the characteristic impedance
relative to the impedance of the source and the load
dictates whether or not the signal will be reflected at the Figure 1. Two-wire transmission line.
source-transmission line connection or/and at the transmission line-load connection. Unless the
source and load impedances are equal to the characteristic impedance of the transmission line
(matched case), some or all of the propagating signal will be reflected in the opposite direction. The
ratio of the reflected signal to the incident signal at the transmission line-load connection is given
by the reflection coefficient ('L):
(3)
where ZL is the load impedance. If the reflection coefficient is non-zero, the incident wave produces
a reflected wave which travels in the opposite direction (back to the source). When a transmission
line contains waves traveling in opposite directions, standing waves are generated. These standing
wave patterns are oscillatory in nature, but the envelope of the standing wave pattern is stationary.
The standing wave ratio (s) is defined as the ratio of the signal maximum to the signal minimum and
is related to the reflection coefficient by
(4)
According to the previous equations, open-circuit and short-circuit terminations reflect all of the
incident energy since neither of these terminations are capable of absorbing the incident energy.
Another critical parameter associated with the transmission line is the propagation factor (()
which is given by
(5)
where the real part of the propagation constant (") is defined as the attenuation constant and the
imaginary part of the propagation constant ($) is defined as the phase constant. The phasor voltage
at any point along a transmission line may be written in terms of the incident (forward traveling) and
reflected (reverse traveling) waves according to
(6)
where z defines the direction of waves moving from the source (z = 0) to the load (z = l). The phasor
coefficients in Equation (6) with the “+” and “!” superscripts denote the voltage amplitudes of the
incident and reflected waves, respectively. The phasor current at any point on the transmission line
is given by
(7)
When the propagation factor of Equation (5) is inserted into the phasor voltage expression of
Equation (6), we see that the attenuation constant accounts for the exponential attenuation of the
waves in either direction while the phase constant defines the phase shift per meter as the respective
waves propagate. A transmission line with " = 0 (R = 0, G = 0) is defined as a lossless line since
waves travel in both directions unattenuated. According to Equation (5), both the attenuation
constant and the phase constant are functions of frequency. Thus, signals of different frequencies
are attenuated at different rates, in general. This effect is known as dispersion. A special case
transmission line where all frequencies are attenuated at the same rate is known as a distortionless
or non-dispersive transmission line.
3. Equipment List
Two wire transmission line (d = 7mm, D = 19mm, length = 88 mm) with mounting hardware
Short circuit termination, 200S termination, 8/4 section with short circuit
termination, 8/2 coupling loop, plastic adapter, lamp socket with lamp
High Frequency Oscilloscope
UHF transmitter (f = 433.92 MHz)
4. Procedure
Assemble the UHF transmitter and two-wire transmission line as shown in Figure 2. Plug
the sections of two-wire transmission line together, slide two holders onto the two-wire line and
insert the holders in the saddles bases. Screw the UHF transmitter mounting rod into the base of the
UHF transmitter and insert the mounting rod into a saddle base. Insert the 4-mm plugs into the
output terminals of the UHF transmitter. Make sure that the mode selector of the UHF transmitter
is in the continuous wave (CW) position. This setting launches simple time-harmonic waves along
the transmission line. Plug the 12VAC adapter into the bench but do not connect the adapter to the
UHF transmitter.
Figure 2. Two-wire transmission line and UHF transmitter.
1.
2.
System parameters. Determine the theoretical wavelength of the transmission line waves
based on the given frequency of the UHF transmitter. Based on this wavelength, determine
the total electrical length of the two-wire line from the transmitter connection to the end of
the line. Compute the theoretical characteristic impedance of the two-wire line using
Equation (2.).
Open circuited transmission line. Leaving the two-wire line open circuited, supply power
to the UHF transmitter by connecting the 12VAC adapter to the transmitter. A lamp can be
used to probe the fields on the transmission line as shown in Figure 3. Making contact with
one of the transmission line conductors, slide the lamp along the transmission line to detect
the location of the voltage maxima and minima along the line as indicated by the lamp
brightness. Record the location of all maxima and minima using the transmitter /
transmission line connection point as the z = 0 reference. When the lamp is placed within
the electric field of the transmission line, an oscillating potential difference is induced across
the lamp. In the regions where the transmission line voltage (and thus the electric field) is
a maximum, the lamp glows while in regions where the potential is minimum, the lamp does
not glow.
Figure 3. Voltage maxima and minima measurements.
3.
Insert the plugs of the high frequency oscilloscope probe into the plastic adapter.
Repeat the process of locating the voltage maxima and minima using the oscilloscope by
sliding the plastic adapter along the transmission line. Record the locations of the voltage
maxima and minima along with the peak voltages measured for each. Assuming the
measured voltages correlate directly to the actual voltages on the transmission line, determine
the standing wave ratio on the open-circuited transmission line based on the voltage maxima
and minima measurements.
The current maxima and minima can be located using the 8/2 coupling loop as shown
in Figure 4. Slide a holder onto the coupling loop and insert the RF detector into the end of
the coupling loop. The coupling loop/RF detector provides a DC voltage output proportional
to the magnetic field through the loop. This DC output voltage of the RF detector is
measured across the capacitor. Insert the holder into a saddle base and adjust the height of
the coupling loop so that it lies just above the transmission line without making electrical
contact. Center the coupling loop over the conductors of the transmission line. Slide the
coupling loop along the transmission line, carefully keeping the loop position constant
relative to the transmission line. The RF detector output will be maximum where the
transmission line current (and magnetic field) are at a maximum. The RF detector output
will be minimum where the current is at a minimum. Record the positions of the current
maxima and minima based on the coupling loop measurements.
Figure 4. Current maxima and minima measurements.
4.
5.
6.
7.
8.
Remove the RF detector from the coupling loop and insert the plugs of the high
frequency oscilloscope probe. Repeat the process of locating the current maxima and
minima using the oscilloscope by sliding the coupling loop along the transmission line.
Record the locations of the current maxima and minima along with the peak voltages
measured for each. Assuming the measured voltages correlate directly to the actual currents
on the transmission line, determine the standing wave ratio on the open-circuited
transmission line based on the current maxima and minima measurements.
Discuss your measured results for the voltage and current maxima and minima and
how they compare to the theoretical values of the ideal open circuited transmission line.
Short circuited transmission line. Insert the shorting plug into the end of the two-wire
transmission line and repeat the measurements of parts 2 and 3 for the voltage and current
maxima and minima. Discuss your measured results for the voltage and current maxima and
minima and how they compare to the theoretical values of the ideal short circuited
transmission line.
Lengthened short circuited transmission line. Remove the shorting plug from the end of
the two-wire transmission line and insert the 8/4 length section of transmission line
terminated by a short circuit. Again, repeat the measurements of parts 2 and 3 for the voltage
and current maxima and minima. Compare your measured results with those found in part
4.
Matched transmission line. Remove the 8/4 length section of transmission line terminated
by a short circuit and insert the 200 S resistor. Note that this is what should be described as
a “matched” condition. However, the simple connection of the 200 S resistor with
connecting wires actually introduces some reflections based on discontinuity in the
impedance introduced by the connecting geometry. Repeat the measurements of parts 2 and
3 for the voltage and current maxima and minima. Compare the standing wave ratios found
for the open circuited line and the short circuited line with that of the “matched” line.
Reactive termination. Remove the 200 S resistor from the end of the two wire line and
insert a 1 nF capacitor as the termination. Repeat the measurements of parts 2 and 3 for the
voltage and current maxima and minima. Compare the results for this termination with that
of the open circuited transmission line and explain any similarities or differences using the
Smith chart.
Antenna termination. Remove the 1 nF capacitor as the termination and replace it with the
folded dipole antenna. Repeat the measurements of parts 2 and 3 for the voltage and current
maxima and minima. Using your measured results and the Smith chart, estimate the
impedance of the folded dipole antenna.
5. Additional Question
1.
Use MATLAB to plot the magnitude of the voltage and current [as given in Equations (6)
and (7)] along a lossless transmission line [ L = 0.25 :H/m, C = 100 pF/m, l = 4 m] operating
at 150 MHz. Assume that the transmission line is terminated at z = l by a 25 S resistor and
Vo+ = 10 V. Identify Vmax, Vmin, Imax and Imin on your plots and determine the standing wave
ratio.