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Experiment 1Frequency Spectrum and the Spectrum Analyzer

1.1 Objective

1- To demonstrate the frequency spectrum approach to signal analysis.2- To introduce the spectrum analyzer as a test tool.

1.2 Basic Information

As signals and systems grow in complexity, their time domain representation becomes inadequate. The frequency domain representation forms a simple and straightforward alternative. Signals are decomposed into the sum of a number of sinusoidalsignals. This makes analysis of such signals and systems much easier. The group of

sinusoids representing any signal is called its spectral components.

If the given signal g(t) is periodic with period T o, the Fourier series expansioncan be used to find the spectral components of the signal:

...2sin2cossincos)( 020201010 t bt at bt aat g where

T dt t g

T tdt nt g

T tdt nt g

ooo T aT bT a o

o

ono

on

)(1

,sin)(2

,cos)(2

0

The representation of a periodic signal by its Fourier series expansion isequivalent to the resolution of the signal into its various harmonic components. Themagnitude of the coefficients give the power in each component.

Figure 1.1 Square wave.

For example the Fourier series expansion coefficients of the square wave shown infigure 1.1 is:

...5sin51

3sin31

(sin4

)( 000 t t t V

t g

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The dBm

The most common power measurement unit in communications is the dBm. It is areference measure compared to 1mW power:

001010

. P log dBm O

The Spectrum Analyzer

The traditional way of observing electrical signals in the time domain using anoscilloscope enables the recovery of relative timing and phase information needed tocharacterize circuit behavior. This is not sufficient for full characterization as it doesnot cover the frequency domain. One instrument used to display the frequency domainis the spectrum analyzer. It graphically displays power or voltage as a function of

frequency on a CRT.

The spectrum analyzer can be viewed as a radio receiver which shows the power of the signal it is tuned to. As the tuning is swept across many stations(frequencies) a graph showing power vs. frequency can be obtained. The mostcommon spectrum analyzers sweep the spectrum of a signal through a fixed bandpassfilter. Similar to the principle of superheterodyne receiver.

A block diagram of a spectrum analyzer is shown in figure 1.2. The analyzer is basically a narrowband receiver, which is electronically tuned in frequency byapplying a sawtooth voltage to a voltage-controlled oscillator (VCO). The samesawtooth is applied to the horizontal deflection plates of the CRT. The VCOfrequency is mixed with the input to produce an intermediate frequency (IF).

Figure 1.2 Spectrum Analyzer block diagram.

The frequency component of the input equal to the difference between VCOand the IF is shifted to the IF, filtered and amplified and passed on to the detector.This produces a voltage proportional to the power in that frequency component of theinput, which causes a comparable vertical deflection of the CRT beam at the relativehorizontal position. This gives a plot of power vs. frequency. It is important to note

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that a peak always occurs at the zero frequency of the analyzer due to feedthroughfrom the VCO. This peak is called the zero frequency indicator and appears evenwhen no signal is applied to the analyzer.

The main controls of a spectrum analyzer are:

The center frequency, which slides the display in the horizontal axisthereby changing the display position relative to the full spectrum.

The span, which changes the horizontal scale allowing wider or narrower range of the display. The resolution of a spectrum analyzer is determined

by its IF filter bandwidth. The marker, used to find the exact amplitude and frequency of a certain

point in the trace on the CRT. The bandwidth, which selects one of several IF filters in the analyzer. Each

filter has different width to allow higher resolution of adjacent signals.

However, there is a limit to the narrowness of the filter bandwidth. Thisresults in a pure sine wave to appear as a bell shaped trace instead of asharp vertical line.

The reference level, spectrum analyzer vertical scale starts from the top of the display. The reference level for the analyzers used in the lab is 27dBm. The vertical display is in dB, Where each vertical unit scale belowthe top represents 10dB step.

The video filter is a process that displays the average of the display. This isuseful when the signal is varying, such as noise.

The display of the analyzer shows a spike at 0Hz. This is internallygenerated due to the VCO signal. This spike is useful in determining the0Hz point on the display. Its amplitude is not important.

Noise is a common pheneomena in all electronic systems. It ismanifested by the shape of grass at the bottom of the spectrum analyzer display. The level of this grass is the noise power measured by thespectrum analyzer. It also puts a lower limit on the signals that can bemeasured by the spectrum analyzer.

Figure 1.3. Spectrum analyzer display.

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The spectrum analyzer display in figure 1.3 shows a single tone signal. If the

center frequency is 20MHz and the span is 10MHz, then the tone is at 18MHz.Given the reference level at 27dBm, then the tone power is about 43dBm. Sincethe spectrum analyzer has a 50 termination, the tone is 1.58mV rms.

1.3 Equipment

Spectrum Analyzer Dual-Trace OscilloscopeDigital Multimeter Frequency Counter

1.4 Procedure

Part A- Calibration1. Set the function generator to supply a 3MHz sine wave of 30mV P-P on

the oscilloscope.2. Use a BNC T splitter to connect this signal to the spectrum analyzer and

the oscilloscope.3. Record the amplitude on the oscilloscope after connecting the spectrum

analyzer.

VPk

4. Explain why the amplitude dropped.

5. Set the analyzer to 20dB attenuation.6. Adjust the signal on the oscilloscope to sine wave

28mV Pk-Pk (-27dBm) at 5MHz.

7. Adjust the Y-position so that the peak of the pulse is atthe level of the top of the 3 rd square of the display of the analyzer (as shown in the figure).

Part B- Spectrum of a simple sinusoid.

1. Set the signal to 800kHz sine wave of 20mV Pk-Pk Remove attenuationof the analyzer.

2. Set the center frequency of the spectrum analyzer to zero Hz, the span of

the display to 2Mhz/div. Remove any attenuation. Set the filter BW tothe maximum value, and the video filter to off.

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3. Sketch the analyzers display.

4. Reduce the span to 0.5MHz/div.5. Record the spectrum on the display, use the marker to identify the

different frequencies and amplitudes.

6. Compare your result with theoretical calculations.

Theoretical MeasuredP(dBm)

Part C- Spectrum of a square wave.

1. Set the spectrum analyzer input to 20dB attenuation.2. Change the signal into the analyzer to a square wave 100mV P-P at 3MHz.3. Record the display, identifying the fundamental frequency and the four

following harmonics.

4.

Compare these results with theoretical calculations.

0 1 2 3 4Frequency (MHz)Theortical (dBm)Measured (dBm)

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Part D- External signals.

1. Switch off the function generator and connect the antenna to the analyzer.2. Find an FM station between 88 and 108MHz, and record its power.

FM station frequency Power(dBm)

3. Expand the span and reduce the filter bandwidth to draw the shape of thesignal.

4. Calculate the cu rrent through the analyzers terminating resistor due to thissignal.

Current (mA)

5. What is the approximate bandwidth of this station?

Bandwidth (kHz)

6. Measure the power of the noise level. Use the video filter to get a clear measurement.

Power (dBm)