Experiment 13: Electromagnetic waves
ELECTROMAGNETIC WAVES
References: Cheng, Chap. 8, p. 332, Chap. 11 Hayt, Chap. 11
Shadowitz, Chap. 15 Skitek and Marshall, Chap. 11
Pre-Laboratory Reading: Background information
PURPOSE OF THIS EXPERIMENT
In this experiment you will be studying some of the properties of electromagnetic waves. The aims of this experiment are:
(i) to set up an electromagnetic standing wave pattern and measure the wavelength of the radiation and the phase difference between the E and H components of the standing wave, and
(ii) to find the components and directional characteristics of the electromagnetic field radiation from a small dipole in free space (radiation pattern).
BACKGROUND INFORMATION & THEORY
The Characteristics of an Electromagnetic Wave
An electromagnetic wave is characterised by its electric vector E and magnetic vector H. In a homogeneous medium, E and H and the direction of propagation are mutually perpendicular. If the E vector is along the y-direction and the H vector is along the z-direction, then the energy will be transported in the x-direction (E x H direction). Such a wave is plane, linearly-polarised and the plane of polarisation is defined by the (E, b) plane (x, y plane) where b is the propagation vector = 2p/l in a non-conducting medium.
Figure 1
The relative directions of the electric & magnetic fields in a plane wave. The magnetic field oscillates along the z-axis and in phase with the electric field which oscillates along the y-axis.
The wave equations for the field in a non-conducting medium are given by:
Ey = Em ej(wt - bx)
and Hz = Hm ej(wt - bx)
where Em and Hm are the amplitudes of the electric and magnetic components of the wave, and w is the angular frequency.
The characteristic impedance of the medium h is given by the ratio of Ey to Hz:
i.e. 
and in a
non-conducting medium, 
where
m
is the magnetic permeability of the medium, and
e
is the electrical permittivity.
The phase velocity of the wave vp is given by:
In free space, this is equal to the velocity of light c:
i.e. 
The Detection of Electromagnetic Waves
In the two parts of this experiment, the alternating electric and magnetic fields are detected by using a rectifying diode placed in a pick-up loop or probe.
1. Detection of the E Vector - The Diode Probe
Figure 2
Note that E is perpendicular to the junction plane of the diode.
An alternating E field parallel to the diode causes a motion of charges across the diode junction and hence in the loop which gives rise to an alternating current. This is rectified by the diode and its magnitude recorded by the meter or detection system. The output is proportional to E2.
Note: The probe only responds to an E field which is parallel to the length of the diode, ie. perpendicular to the diode junction plane (indicated in Figure 2).
2. Detection of the H Vector - The Magnetic Loop
Figure 3
Note that H is perpendicular to the plane of the loop.The changing magnetic field through the loop induces an alternating current in the loop which is rectified by the diode and detected by the meter or data logger system. The output is proportional to H2
Note: The probe only responds to a H field perpendicular to the plane of the loop.
EXPERIMENTAL PROCEDURE
Standing Waves
References: Cheng, p. 332; Skitek, p. 365; Hayt, p. 364
Wavelength of the Standing Waves
1. A General Radio oscillator is used to provide microwave power to a transmitting dipole in a parabolic mirror. This dipole produces plane-polarised waves with the electric vector vertical. The electromagnetic waves are reflected by a metal sheet (reflector) back towards the dipole. The addition of the incident and reflected waves sets up standing waves in the region in front of the reflector. Check that the plane of the reflector is perpendicular to the direction of propagation of the electromagnetic waves.
2. A "T" piece holds two ‘Universal Probe’ detectors of the type described on p. 13-2 orientated in such a way as to measure the E field (detector 1) and H field (detector 2) components of the standing wave respectively. The detectors are connected to channel 1 and channel 2 respectively of a data logger connected to a computer. The detectors are mounted on a carriage which can be driven between the reflector and transmitter by a stepping motor (see Figure 5).
Figure 5
Experimental configuration for measurement of E & H components of the standing wave.
3. Switch on the computer using the log in and password provided for the particular PC on the apparatus. Double click on the PicoLog icon on the desktop to bring up the data recorder dialog box.
Note: The data recorder &/or PC may be shared/changed between experiments. Check for a note on the notice board giving relevant information and the recommended settings.
4. Switch on the oscillator power supply (POWER ON and HV ON) and set the frequency to approximately 1800 MHz.
5. Check the settings on the stepping motor control:
Speed to the white arrow
CCW drives the detectors from right to left
CW drives the detectors from left to right
Configure the data logger
Open PicoLog by double clicking on the desktop icon. Choose ‘Normal’
operation. This is a data logger which will record the output voltage from E
& H universal probes. Later you will copy the logged data or graph to the
clipboard and then paste it into Excel or Word for subsequent graphing and
analysis.
The PicoLog Recorder should come up on the screen. If all goes well, the ADC is all setup correctly and will sample the inputs every 0.2 seconds. An explanation of the basic controls are shown in figure 6.
Figure 6
The PicoLog recorder controls.
To set-up the recorder click on File, New Settings
Recording, OK
Sampling Rate,
Set the sampling rate to 200 milli-seconds and
Readings per sample to As many as possible, OK
Converter details
just click OK
ADC 200 measurements
You then need to define the input signals, click on Add
Enter a Name ie. “E-field” for channel A
Set voltage range to ± 2V DC, OK
You then need to define the second channel input signal, click on Add
Enter a Name ie. “B-field” for channel B
Set voltage range to ± 2V DC, OK
OK
You now need to define a file for the logger to run,
Click on the ‘New File’ button
Name your file (ie. “Freds EM Fields.plw”) and store it in the default directory C:\Program Files\Pico\filename
OK
You are now ready to acquire data.
Press "Play" 
to start
logging the data at the same time you switch on the stepper motor drive. The
amplifier output voltage VS
is sampled by the computer every ˝ second.
Click on the Pico ‘View Graph’ button to monitor the data logging on screen when it is running.
As the stepper motor controller scans through position the graph should automatically update on the screen showing two traces (E & H field components) with both having a sin2 shape.
Press "Stop" 
to stop
logging data at the same time that you stop the stepper motor power supply.
Click on the yellow ‘Copy to clipboard’ button which then copies the graph of the logged data into the computer clipboard
Now activate Word from the task bar, open a new file. Click on the page where you want to insert the graph, choose Edit, Paste Special.
Then paste it in as a picture.
(Depending on the Word set-up you may need to un-check the float over text box or via Format – Picture - Layout).
Note: Using paste special allows it to be saved as a picture format which uses less memory and the whole graph will scale correctly, including any fonts.
If you want the raw data,
Click on the Pico ‘Spreadsheet’ button (see figure 6) to monitor the data logging on screen
Click the blue box on the spreadsheet which selects all your logged data
Click on the yellow clipboard button which copies the data into the clipboard
Now activate Excel from the task bar
Click in a cell on the excel worksheet and paste the data from the clipboard.
You now have the data in Excel and if you have access to scientific software you can fit the data at your discretion.
Add text to your file and print the graphs on the shared printer if required. You can also save your files to a floppy disc or USB memory stick if you have one.
Ready to acquire data
Now re-activate PicoLog (PLW Recorder) from the task bar. Click the reset button on the picolog recorder ready for a new scan.
Set the stepper motor control switch to drive the detectors to the transmitter end of the rails (CCW). Turn the switch to CW and observe the signals on either the PicoLog Recorder dialog box or the graph as the detectors move between the transmitter and reflector. Several maxima and minima should be seen with an amplitude of approximately 0.4V. If the signal is significantly smaller than this, call your demonstrator.
Note: Stop the stepping motor before the carriage hits an end stop.
6. When the detectors are near the reflector, stop the drive and measure the distance from each side of the detector yoke to the reflector to make sure the Universal probe detectors are equidistant from the reflector.
Check the speed setting of the stepping motor by measuring the time taken for the detectors to be driven back to the transmitter end of the rails. The time taken should be 40 to 50 seconds; if not, adjust the speed control and remeasure.
7. Set the detectors to a convenient marker at the transmitter end; note this position. Set the stepping motor to CW.
8. Start the stepping motor and the data recorder simultaneously and plot the E and H standing waves as the detectors move towards the reflector. Stop the detectors and the PicoLog data recorder simultaneously when the detectors reach the marker at the reflector end of the rails.
9.
Measure the distance moved by the detectors along the rails from start to
stop (Y mm) and the distance from the centre of the detectors at the
stop point to the reflector (Z mm). Record all measurements in your log
book. Once you plot/print the graph you can measure the distance on the
graph between the start and finish points (X mm). Hence, scale the graph to
the real distance moved by the detectors.
Real detector distance = 
x
(graph distance).
10. Determine the average wavelength of the standing waves (E and H) over a distance of five to six minima. (Note: Standing wave minima are l/2 apart). Find the average of the E and H wavelengths and hence, calculate the wave frequency.
11. Scale the value of Z measured in 9. above to mm on the graph and mark the position of the reflector on the graph. Extrapolate the graphs from the stop point to the reflector position on the graph and determine whether the E and H waves are at a maximum or minimum (node or antinode) at the reflector.
Phase Difference between the E and H Waves
1. Mark the positions of all the E and H minima on the graph. Measure the distance between all the adjacent E and H minima and find an average value.
2. Use the average shift to find the phase difference (degrees) between the E and H standing waves. Note: On the graph, distance between minima = l/2 = 180.
SUPPLIMENTAL INFORMATION / DATA
Pico ADC 200 is a product of Pico Technologies. Specifications for the various Pico devices used in the laboratory can be found at the company web site http://www.picotech.com/ .
REPORT WRITING
Analysis of the Data
See the EXPERIMENTAL PROCEDURE section.
Questions
The following questions should be addressed in your report
1. Compare the calculated frequency in part A.10 with the value set on the oscillator.
2. Can aluminium (material used as the reflector) be considered a good conductor at the frequency used? (See Formulae and Constants in the notes at the front of the practical manual &/or your EM lecture notes and text book).
3. Calculate the skin depth for aluminium at this frequency. (Assume the resistivity, r = 2.5 10-8 Wm, m = m0, and e = e0).