LEVEL III EXPERIMENTAL ELECTRICAL ENGINEERING
ANTENNAS EXPERIMENT
1.
Objectives
To provide practice in performing basic measurements with a uhf network
analyser.
To provide practice in the use of scattering parameters in the description of the
properties of high frequency networks.
To provide practice in the evaluation of input impedances for various antennas.
To illustrate, through measurement, the concept of antenna pattern.
To illustrate through use the concepts of
reference planes in high frequency measurements;
available source power;
transmission loss and return loss in network measurements;
mismatch loss between ports;
images in ground planes ;
structural baluns for antenna connection.
To give vivid illustration of the effects of multi-path propagation in radiation
measurements.
2.
What you will do
Perform some antenna impedance calculations.
Measure the input impedance of an antenna.
Compare the results.
Measure the radiation pattern of an antenna.
Make a prediction of the transmission loss between an antenna pair.
Measure the transmission loss between that pair of antennas.
Compare the results.
Experience the effects of multi-path propagation in antenna measurements.
3.
Apparatus list
Uhf network analyser HP 8505A.
Scattering parameter test set HP 8503A.
Connecting cables for the ports of the test set.
Antenna range with fixed small loop antenna, quarter wave electric monopole
antenna above a ground plane and moveable short monopole antenna above a
ground plane. Type N short circuit and type N double female union for checking
the calibration of the network analyser and test set.
2
4.
Consumables
Smith Charts are required and should be obtained from the WWW at:
http://www.eleceng.adelaide.edu.au/INFO_UG/7091/smith0.pdf
5.
Equipment assembly
The equipment should be assembled as shown in Figure 1. The large instrument
with the front panel divided into four equal sections is the HP 8505A network
analyser. That instrument sits atop the HP 8503A S-parameter test set. Two
connection cables to the antenna range come from the test set.
Figure 1. Instrument assembly.
On the table can be seen a type N short circuit and an type N union used in
calibration of the network analyzer, and a short moveable electric monopole above
the ground plane used in field exploration.
In all of the experiments to be conducted, the network analyser will be operated as
a frequency swept signal source. Various frequency sweeps will be used. A
photograph of the frequency control section of the front panel of the analyser
showing the settings to be used in the first part of the experiment is provided in
Figure 2 over leaf.
6.
Precautions
The type N connectors used in the experiment must be handled correctly to avoid
damage.
For clarity in the below description we state that the female connector of the pair
is the one with no moving parts and with a thread on the outside of the body. The
male connector of the pair is the one with an outer ring (threaded on its inside)
which can rotated around the main part of the body.
3
Figure 2. Frequency control section of the network analyser.
When the connectors are mated, it is essential that the main part of the male
connector and the female connector not be rotated relative to one another. To do
so will cause damage to the contacts which form the inner conductor of the
coaxial line. The part which rotates is the outer ring on the male connector, and it
should be screwed on to the female connector without the main part of the male
connector itself rotating relative to the female connector. Put another way, one
does not screw the female connector into the male connector. One holds the
female connector stationary, and screws the outer ring only of the male connector
on to it, while holding the rest of the male connector stationary.
Please do not attempt to remove the cables from the Network Analyser test set.
7.
Reference plane concept
We take the opportunity to remind ourselves of important facts about the concepts
of voltage, current and impedance on transmission lines. These are:
(a)
The voltage concept is restricted in validity to the expression of minus the
line integral of the electric field between two points in a plane
perpendicular to the axis of the transmission line.
(b)
For one plane at one position on the line, the voltage will generally be
different from its value at another plane at a different position along the line.
A similar statement can be made about the current, but its variation with
position will be different from the variation of the voltage. It follows that the
concept of impedance on the line is only meaningful if there is firstly
4
provided a clear definition of the reference plane at which the impedance is
being defined.
(c)
8.
It also follows that as a reference plane is moved the impedance defined in
relation to that reference plane will vary, even when the configuration of the
hardware is not changed.
Return loss and transmission loss concepts
The network analyser and test set will measure amplitude and phase of both the
voltage reflection factor at port one and the voltage transmission factor from port
one to port two, and display them in polar form over a frequency range.
It will also provide an LED readout of these variables at a particular and settable
frequency within the sweep range. That frequency is specified by a further LED
readout in the marker section of the network analyser front panel.
The phase readout is simply in degrees and presets no problem of interpretation.
The amplitude readout is, however, converted to decibel form before being
presented on the LED display. The conversion is done by taking ten times the
logarithm to the base ten of the square the magnitude of the voltage ratio.
If the quantity being measured is the reflection factor at port one, we call the result
(with the sign changed) the return loss. If the result being measured is
transmission factor, we call the result (with the sign changed) the transmission
loss or the insertion loss.
If we want to obtain the reflection factor in its amplitude form from its expression
as a return loss in dB, we divide the return loss in dB by 20, change the sign, and
raise the base 10 to that power.
9.
Preliminary work
9.1
Identify the components of the apparatus listed above.
9.2
Consult where necessary the following references:
9.2.1
Lecture notes for 8528 EEEIII, available on the WWW at
http://www.eleceng.adelaide.edu.au/INFO_UG/8528/download.html
9.2.2
9.2.3
Black-Box and “must-knows” reference material, available on the
WWW at http://www.eleceng.adelaide.edu.au/Personal/peter/peter/eeelec.html,
Fields Lines and Guides lecture material, available on the WWW at
http://www.eleceng.adelaide.edu.au/Personal/peter/peter/flg.html
(Chapter 11 and Appendix C) and
http://www.eleceng.adelaide.edu.au/INFO_UG/third_main.html
9.2.4
Text books referred to in 9.2.1 , 9.2.2 and 9.2.3 above.
5
Assemble from information presented (in the references) formulae or
diagrams for
(a)
The inductance of a single turn circular coil in free space. Such an
equation can be found in most text books on electrodynamics, and also
in equation C.51 of Appendix C of the Fields Lines and Guides notes
at the URL http://www.eleceng.adelaide.edu.au/Personal/peter/peter/flg.html.
(b)
The image antenna formed when a semi-circular antenna in a
horizontal plane and fed by a voltage generator is placed against a
vertical ground plane.
(c)
Making use of concepts illuminated by the above diagram and the
definition of self inductance as flux linked per unit current, the
inductance of a semi-circular coil above a ground plane.
(d)
A formula which will enable the calculation of the self inductance L of
an inductor for which the inductive reactance X is known at frequency
f.
The quarter wave monopole antenna and ground plane are shown in the
figure below.
6
(e)
Describe the image antenna formed when a horizontal electric
monopole antenna fed by a voltage generator is placed against a
vertical ground plane.
(f)
The electromagnetic wavelength in free space at 600 MHz.
(g)
The electromagnetic propagation constant in free space at 600 MHz.
(h)
The size of the radian sphere at 600 MHz.
(i)
An equation for the gain of a small loop antenna.
The geometry for a half loop antenna is shown below.
7
The numerical values of the loop parameters used in laboratories N126/N128
are given in the table below.
Component
loop radius
radius of loop section
gap in loop
wire diameter
Symbol
r1
r2
d
g
“South” Range
20.38mm
1.80mm
1.00mm
3.75mm
“North” Range
20.11mm
1.80mm
0.94mm
3.74mm
(j)
The radiation resistance of a single turn circular coil in free space.
(k)
The radiation resistance of a semi-circular coil above a ground plane.
(l)
The power density per unit area at distance r in the direction of
strongest radiation from an antenna of gain g radiating a power P .
8
(m) The effective area of a receiving antenna in terms of its gain g in its
transmitting role.
10.
(n)
The ratio of received power to transmitted power for a pair of
favorably orientated antennas of gains g1 and g2 separated a distance r
in free space when the receiving antenna is conjugately matched.
(o)
A statement of how that ratio will be affected if the transmitting
antenna becomes a monopole antenna above a ground plane and the
receiving antenna becomes a half loop above a ground plane.
(p)
A statement of how that ratio will be affected if the roles of the
transmitting antenna and the receiving antenna are interchanged.
Network analyser calibration
A principal element of the equipment is the Hewlett Packard Network Analyser
and S Parameter Test Set. With the proper connections, these instruments will
measure the reflection factor at port one of the test set, and the transmission factor
from port one to port two.
The instrument requires an elaborate calibration procedure, mainly to compensate
for the effects of the connection cables.
The calibration procedure will be performed twice during the experiment, once in
Section 15 where you will use a frequency range of 1 to 250 MHz, and once in
Section 16 where you will use a frequency range of 550 to 650 MHz.
9
The calibration procedure is described below in a form suitable for Section 15 of
this experiment. Later sections of the experiment require change of frequency
range, and change of position of the short circuit.
(a)
Ensure that the network analyser signal source is set to a sweep mode to
cover the frequencies in which you are interested.
(b)
The first part of the calibration is to ensure that a short circuit placed at a
selected reference plane appears as a short circuit on the network analyser
display at all frequencies in the sweep range.
(c)
In this case the selected reference plane will be the feed point of the semicircular loop antenna, this feed point being at the centre of the semi-circular
loop antenna.
(d)
Walk behind the antenna range, observe that the feed point of the semicircular loop antenna is at he centre of the semi-circle, and short circuit the
feed point by wrapping it in aluminium foil held in place with a peg.
(e)
A photograph of the signal processing section of the network analyser front
panel with switches set at the positions required for calibration is shown in
Figure 3. The photograph shows that there are two signal processing
channels, of which we will only use channel one.
Figure 3. Signal processing controls.
(f)
Check that the slide switches which selects the display mode of channel 1
are set to A/R and POLAR MAG, so that the display is one of reflection
10
factor on a Smith Chart. Also check that the “MODE” switch is on the “10
deg/scan” position.
(g)
Check that the controls for ELECTRICAL LENGTH are set as shown the
photograph, and adjust the LENGTH buttons and the VERNIER A knob so
as to achieve the smallest size of the illuminated spot the CRT display. On
the channel 1 display, touch the MKR button and then hold down the ZRO
button for three seconds. The illuminated spot should now be very near the
periphery of the display, but at any phase angle.
(h)
What we will have achieved by these operations is to make the impedance at
the reference plane (i.e. the short circuit at the chosen feed point) appear to
have a unit magnitude, and a phase angle which is constant for all
frequencies of the sweep. What we want next to achieved is to retain the unit
magnitude but to make the constant phase angle be equal to 180 degrees, as
is appropriate for a short circuit.
(i)
This is done firstly by switching the MODE switch to POLAR PHASE,
touching the MKR button, and pressing the ZRO button for three seconds.
This will move the illuminated spot to the point +1, not yet the desired
point. We get to the desired point of -1 by two presses of the upper left-most
REF OFFSET control, and two presses of the lower centre REF OFFSET
control.
Figure 4. CRT display for a short circuit.
11
(j)
If these operations are correctly done, the illuminated spot will be at the
point -1 which is correct for a short circuit. We have thus moved our
reference plane to the location of the temporarily installed short circuit.
(k)
The CRT display should then appear as in Figure 4 above.
(l)
Check that you have been able to obtain a display of the correct appearance
and consult the demonstrator if you have not.
(m) This calibration procedure will be performed in Section 16 for a different
frequency range, and with the short circuit defining the reference plane
placed at a different point in the measurement system.
(n)
11.
There are additional calibration procedures for through connections between
port one and port two of the test set, but for simplicity they will be omitted.
The result will be a small error in one of the later measurements, but a
considerable saving in time.
Available source power concept
A sinusoidal signal source of internal voltage represented by the phasor VS and of
internal impedance ZS = RS + jXS will, when terminated in a load of impedance ZL
= RL + jXL, deliver to the load a power P which varies with the value of load
impedance.
RS
VS
JXS
jXL
~
RL
Figure 5 A source connected to a load
It is easy to show that the load impedance which extracts the maximum power
from the source is the complex conjugate of the source impedance. This result is
known as the maximum power transfer theorem of circuit analysis.
That maximum power is called the available source power.
12.
Preliminary questions
(a)
Explain briefly why conventional measuring instruments for voltage and
current are not suitable for use in the measurement of impedance at high
frequencies.
12
(b)
Show that for a source of internal voltage represented by the phasor VS and
internal impedance ZS = RS + jXS as shown in Figure 5 above, the available
source power P is given by
| V S |2
8R S
when the phasors represent peak rather than r.m.s values.
P
(c)
Consider the system shown in Figure 6 below in which a source of internal
voltage represented by the phasor VS and internal impedance of Z0 feeds an
antenna of input impedance R + jX.
jX
Z0o
I
~
VSs
R
Figure 6. A source connected to a transmitting antenna .
Show that the ratio of the transmitted power to the available source power is
given by
Transmitted power
4 RZ0

Available source power | Z0  R  jX |2
(d)
Consider the system shown in Figure 7 below in which a receiving antenna
of internal received voltage represented by the phasor VR, and internal
impedance of R + jX, feeds a load of impedance Z0.
R
VS
jX
~
Z0
Figure 7. A receiving antenna connected to a load.
Show that the ratio of the power received by the load resistance Z0 to the available
power which could have been extracted from the receiver antenna with the
optimum load impedance is given by
13
Received power
4 RZ0

Available antenna power | Z0  R  jX |2
13.
Preliminary observations
Examine the apparatus and identify all the components and relevant dimensions.
These include particularly the sizes of the loop and fixed tuned monopole
antennas.
Observe that the semi-circular loop antenna behind the ground plane has a
structural balun so that its feed point is at the centre of that half loop. This is
shown below.
14.
15.
Calculation of loop impedance
(a)
Using a magnetostatic formula, make a theoretical prediction of the self
inductance of the loop antenna.
(b)
Using Pocklington’s theorem, discuss the shape of expected current
distribution on the loop antenna.
(c)
Making the approximation that the current distribution on the loop antenna
is uniform, make a theoretical prediction of the radiation resistance of the
loop antenna.
(d)
Draw an equivalent circuit of the input impedance of the loop antenna.
Measurement of loop antenna inductance
(a)
Connect the port one cable to the loop antenna. Place a short circuiting peg
across the feed point of the semi-circular loop behind the ground plane, set
the sweep setting of the network analyser source at 1 MHz to 250 MHz, set
the MARKER of the frequency control section to 125 MHz, and perform the
calibration procedure for the network analyser test set port one descried
14
earlier, so that the reference pane of the network analyser test set port one
measurement is at the feed point of the loop antenna.
(b)
Remove the shorting peg from the feed point of the antenna, and observe on
the network analyser CRT display the variation of the voltage reflection
factor of the semi-circular loop antenna, relative to the feed point at which a
reference plane was just established, over the frequency range 1 to 250
MHz.
(c)
Determine the frequency at which the reflection factor of the loop antenna
relative to that reference plane becomes approximately j, i.e. 1 at an angle of
90 degrees.
(d)
Calculate the imaginary component of the antenna impedance, and the
antenna inductance.
(e)
Compare the measured and predicted value, and comment on the
comparison.
Some matters which might be taken account in the comparison are set out
below.
We have made no estimate of the resistive losses in the antenna or in the
connecting cables to the network analyser test set.
We have assumed a uniform current distribution on the antenna.
While slotted line measurements achieve their best accuracy near the edge of
the Smith Chart, network analyser measurements achieve their best
performance towards the centre of the chart, and have errors, not to be
discussed here, for measurements near the periphery.
16.
(f)
We will make no attempt to measure the real component of the antenna
impedance as it is too small to allow an accurate measurement with this
equipment at this frequency.
(g)
The use of a more accurate network analyser and of shorter and higher
quality connecting cables, and implementing automatic computer controlled
network analyser calibration using precision short circuits and throughconnections at each measurement frequency, would allow such a
measurement.
Observation of antenna pattern
(a)
Disconnect port one of the test set from the loop antenna, and place the type
N short circuit at the end of port one cable. This placement will, after
calibration, define a new position for the port one reference plane.
15
17.
18.
(b)
Re-calibrate the analyser, for this new reference plane position, using the
frequency range 550 to 650 MHz, and placing the marker frequency at 600
MHz.
(c)
The calibration just performed will serve the purposes of both Sections 16
and 17 of the experiment.
(d)
Connect the moveable short monopole above a ground plane antenna to the
port two cable of the test set, and by placing it in turn in each of the holes in
the semi-circular array of holes in the antenna range, and use it to explore
the antenna pattern of the loop antenna.
(e)
Compare the results with your theoretical expectation.
Impedance of quarter wave monopole above a ground plane
(a)
Connect the port one cable of the test set to the quarter wave monopole
above a ground plane and determine the reflection factor of the quarter wave
monopole above a ground plane antenna at a frequency of 600 MHz.
(b)
Convert the measurement to impedance terms, so that the input impedance
of the fixed tuned monopole above a ground plane antenna becomes known.
(c)
Draw an equivalent circuit for the input impedance of the quarter wave
monopole above a ground plane antenna.
(d)
Compare the physical length of the of the quarter wave monopole above a
ground plane antenna with a quarter of the electromagnetic wave length at
600 MHz.
(e)
Note that the physical length of a fat wire antenna which produces behaviour
similar to that of a thin wire antenna is somewhat less than the physical
length of the thin wire antenna, so your measured length of the “quarter
wave monopole above ground plane” antenna will be found to be a little less
than a quarter of the electromagnetic wave length at 600 MHz.
Prediction of propagation loss
(a)
In this section we make a theoretical prediction of the transmission loss
between the 50 ohm source provided by port one of the network analyser
test set and the 50 ohm load provided by port two of the network analyser
test set via the electromagnetic wave propagation between the two antennas
behind the ground plane.
(b)
We note that neither port of the network analyser test set is a match to its
corresponding antenna.
(c)
Calculate the three ingredients to a theoretical prediction of this
transmission loss:
16
(i)
the mismatch loss between the source and the transmitting antenna,
defined as the ratio of the transmitted power to the power which the
source would deliver to a 50 ohm load.
(ii)
the propagation loss between a transmitting antenna and an ideal
matched receiving antenna.
(iii) the mismatch loss at the receiving antenna, defined as the ratio of the
power delivered by the receiving antenna to a 50 ohm load to the
available source power at the receiving antenna.
and make a theoretical prediction of the measurement performed above by
forming the product of these three factors, or by summing their expressions
in dB terms.
(d)
19.
20.
In the calculation use the measured inductance of the loop, the theoretically
predicted radiation resistance, and the measured impedance of the short
electric monopole antenna above the ground plane.
Observation of multi-path propagation
(a)
Connect the port one of the test set to the semi-circular loop antenna, and the
port two of the test set to the moveable short monopole antenna above
ground plane, and place that antenna in the ground plane hole giving the
strongest coupling.
(b)
Use the reflecting paddle to observe over the frequency band of 550 MHz to
650 MHz being swept the effect of various paddle positions on the
propagation loss between the transmitting and receiving antennas.
(c)
Comment on the significance of the observations for antenna measurements
in reflective environments.
(d)
Note the relationship between paddle positions for minima and maxima of
coupling.
Propagation loss between antennas
(a)
Determine experimentally the insertion loss between the two fixed antenna
ports of the antenna range. Use the insights developed in the section on
multi-path propagation to strike an average value over the band from 550
MHz to 650 MHz.
(b)
Compare the experimental and theoretically predicted results.
17
21.
A Modest Proposal
Peter Cole (cole@eleceng.adelaide.edu.au) would be grateful to receive from
students, by email, suggestions as to how this practical or the associated notes may
be improved.
22.
Revision History
August 1998 PHC & A2
August 2000 PHC & PC & A2