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EE 495 Communications Systems Laboratory
Experiment 3: Spectrum Analyzer
* No report is required for this laboratory
Introduction and Tutorial Material
Introduction
The purpose of this laboratory course is to give the student an opportunity to do experiments relating to the topics studied in the communication systems and related courses. The student will have the opportunity to observe AM and FM signals in the time and frequency domains and to learn about the generation and detection of modulated waveforms. The student also will be afforded a chance to learn about measurements of distortion and noise as well as get a familiarity with some instruments not previously encountered such as spectrum analyzers, audio analyzers and noise generators.
The work in this laboratory will
stress and agreement between theory and measurement. It is very important that
the student have a clear idea of what to expect from each measurement, in order
to immediately determine if things are working correctly. The student should
be constantly be wondering -is this reasonable, both qualitatively and quantitatively
? If the lab observations are not in reasonable agreement with what was expected,
then further observation or preparatory analysis are in order to determine the
source, of the discrepancy. There is no point in taking data and going home
to write a lab report only to find out that the data is meaningless because
there was on error in the lab set-up or procedure.
It is very important to get in the habit of working
in a logical, scientific manner. The laboratory experience is valuable for showing
us the small discrepancies between theory and practice, but
there must be reasonable agreement between what we observe and what we expect
to observe.
The Spectrum Analyzer
The spectrum analyzer is an important and useful tool for examining signals in the frequency domain. As it is an instrument with which the student may not be familiar, a brief explanation will be given here, and part of the first lab session will be devoted to becoming familiar with this instrument. For a more detailed explanation of this instrument see the manual which is available in the stockroom.
The spectrum analyzer can be thought of as a band pass filter whose center frequency is varied linearly over a range of frequencies. The center frequency of the filter is plotted on the horizontal axis and the output of the filter is plotted on the vertical axis. The filter must be swept over the frequency range slowly enough so we obtain the steady state filter output. The internal circuitry of the analyzer automatically changes the sweep rate as the filters bandwidth is changed to insure this condition is met. There is a default setting for the filter bandwidth, but it can be changed using the front panel controls. A wide bandwidth allows a more rapid sweep, but a narrow bandwidth is necessary to resolve closely spaced signals. Suppose for example that we wanted to observe a signal that consisted of two sine waves, one at 500 kHz and one at 505 kHz. If we had a filter bandwidth of 30 kHz we would not be able to resolve them as two separate signals, they would appear as one. However, if we reduced the bandwidth to 1 KHz we would be able to resolve them into two distinct signals, and be able to measure their frequency separation and their individual amplitudes.
In operating the spectrum analyzer there are three principal parameters that the operator should set. These are, center frequency, span and amplitude. The center frequency setting determines the frequency that corresponds to the middle of the screen. The calibration of this setting is not very accurate on the older analyzers, but this is not a serious problem in using the analyzer as we are usually interested in frequency differences. The span determines the range of frequencies from one side of the screen to the other. For example, if we set the center frequency to 10MHz and the span to 2 MHz, the screen would cover the range 9 MHz to 11 MHz and any signals in that frequency range applied to the input would be seen on the screen. The amplitude can be set to either the log or linear mode. The log mode is useful for looking at .two or more signals that have large differences in amplitude. In this mode the scale is calibrated in dB/division, with a given reference value corresponding to the top line. In the linear mode, which is good for observing small differences in amplitude, the top line can be set to correspond to a given voltage.
Laboratory Work
To get some experience in working with the spectrum analyzer, the first thing to observe is a single sine wave. Connect the signal generator both to the scope and the spectrum analyzer using a T connector. Adjust the generator so the signal frequency is 10 MHz and the peak to peak amplitude is 0.2 volts. Adjust the center frequency of the spectrum analyzer to 10 MHz, the span to 10 MHz and the signal amplitude so the reference level is 0 dBm and the vertical calibration is 10 dB/div. You should see a line approximately in the middle of the screen. Vary the frequency of the generator and check that the line moves 1 box / MHz.
It is worthwhile to note that the spectrum analyzer is calibrated in dBm. The dBm is a unit of power which is defined as,
The input resistance of the spectrum analyzer is 50 W. A signal that has an amplitude of 0.1 volt has an rms value of 0.0707 volts and a peak to peak voltage of 0.2 volts. Its power is calculated from its rms value below
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= .0001 milliwats = 0.1 milliwats |
When this power is referred to 1 milliwatt, we get
If the spectrum analyzer amplitude settings are adjusted so that the reference is 0 dBm and the vertical scale is at 10 dB/div , then the height of the line on the screen should be one box below the top of the screen. If you turn the attenuator knob on the generator, the height of the line on the screen should decrease one box for each additional 10 dB of attenuation. If you change the amplitude mode to linear, then you should be able to measure the rms value of the signal. In this case, the original 0.2 volt peal to peak signal should measure 70.7 millivolts.
Now try to repeat this measurement using a 1 MHz signal. Adjust the center frequency and span to appropriate values. You will probably notice a line on the screen that corresponds to what the analyzer thinks is zero frequency. This is the zero marker .
When measuring low frequency signals you have to be careful not to confuse the zero marker with the signal. This is a very common error . It is very easy to tell the difference. If you make a change in the amplitude or frequency of the signal and the line does not move, then it is the zero marker . Another quick check is to just remove the input cable from the spectrum analyzer and see if the line disappears.
Having mastered the observation of a single sinusoidal signal on the spectrum analyzer we are ready to try the observation of closely spaced sinusoidal signals. An easy way to obtain three closely spaced sinusoidal signals is to use an amplitude modulated signal. Use the Wavetek generator with internal AM modulation to produce an AM signal with a 5 MHz carrier frequency modulated by a 10kHz tone with a modulation index of 0.5. The equation of this signal is
x ( t ) = (1 + 0.5 cos 2p104t ) cos 2p5 x 106t
Before you proceed you should sketch the waveform of x ( t ) to get an idea of how it should appear on an oscilloscope. When displaying this signal, it is helpful to use the modulating signal on the external sync terminal of the oscilloscope to obtain a steady picture.
To see what kind of spectrum the above will produce, we use trigonometric identities in the above expression, to obtain
x ( t ) = cos 2p5 x 106t + 0.25 cos 2p(5 x 106 + 104) t + 0.25 cos 2p(5 x 106 - 104)t
It is now clear that on the spectrum analyzer you should see 3 lines separated by 10KHz, with the outer two lines having an amplitude 1/4 of the amplitude of the center line. On the log scale this corresponds to a 12 dB difference in amplitude.
What are sensible settings for center frequency and span to observe the amplitude modulated wave ?
Try slowly reducing the modulating frequency -noting that the lines come closer together.
What is the closest spacing of the lines that allows you to see them as individual lines ?
Reduce the resolution bandwidth of the spectrum analyzer when trying to resolve closely spaced signals.
There are many other interesting and useful features of the spectrum analyzer that you can investigate. Using the manual that is available in the stock- room is very helpful. One especially useful feature is the system of markers.
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