Shimshon Levy October 2012 - לימודי תואר שני

1 spectrum analyzer and spectrum AnalysisShimshon LevyOctober 2012 CONTENTS1 spectrum analyzer and spectrum Objectives .. Necessary Background: .. Prelab Exercise .. Problem 1 .. Problem-2 .. Problem-3 .. Problem-4 .. References .. Background Theory -Frequency and Time Domain .. spectrum analyzer Block Diagram and Theory of Operation .. Input Section .. LPF or Preselector (Tunable BPF) .. Mixer and Local oscillator.. IF (Intermediate Frequency) Filter and Selectivity .. Envelope detector .. Video Filter .. Sensitivity .. 102 Experiment Required Equipment .. Reading Amplitude and Frequency .. Setting the Reference Level and Center Frequency.. Setting the Frequency Span.. Using Marker to Read Frequency and Amplitude.. Resolving Two Signals of Equal Amplitude .. Simulation of Resolving Two Signals of Equal Amplitude.

2 Measurement of Resolving Two Signals of Equal Amplitude . Notice! .. Shape Factor .. Simulation of Shape Factor- Butterworth Band Pass Filter.. Measurement the Shape Factor of IF BPF .. Measuring Signals using Logarithmic and Linear mode, Absolute andRelative Quantities.. Simulation of a Squarewave in Frequency Domain .. Squarerave Measurement .. Measuring Frequency Response of LPF .. Simulation of LPF .. Measurement of LPF .. Setting the spectrum analyzer .. Measuring Signal To Noise Ratio of Low-Level Signal.. Measuring a Signal Very Close to the Noise Floor .. Final Report .. 22 Chapter 1 spectrum analyzer AND spectrum ObjectivesUpon completion of the experiment the student will: Learn the basic concept of frequency domain measurements. Learn, and understand how to operate the spectrum analyzer . Understand the function of each block of the spectrum analyzer .

3 Simulate and analysis electrical Necessary Background:The student needs to have a basic understanding of Fourier series, and Fourier Prelab Problem series of a real squarewave- Suppose you need to measure a clocksignal of 100 kHz, amplitude 1 volt, with 20ns edge speeds (10% to 90% ris-ing time see Fig. 1). A frequently asked question, is what is the minimumbandwidth of an oscilloscope I need to perform a reliable Exercise4 Amplitude(V)time(sec)Falltime1-1 RisetimeFig. 1 Time domain of 100kHz, amplitude 1 volt, rise time 20nsec. squarewaveA rule of thumb is to consider the fastest transition time of the signal, the risetimeBW=0:5 Trwithin 20% accuracy( )BW=0:65 Trwithin 10% accuracy( )BW=0:95 Trwithin 3% accuracy( )whereTris the rise time of the signal,1. (a) Find an analytic expression, for an ideal squarewave, frequency 100kHz,amplitude 1Vp:(b) According to equation Eq. (3) , nd the required bandwidth of the oscil-loscope.(c) Find the number of odd harmonics, you need to reconstruct the real square-wave within 3% accuracy.

4 (d) Using Matlab, draw a graph of the reconstructed squarewave, based onthe sum of N odd harmonics. nd the rise, and calculate the error in Problem-2 Fourier transform of a squarewave- Using Matlab, draw a graph of repetitive100kHz squarewave (10 periods) in time domain. Use FFT command to draw afrequency domain graph(magnitude only), use FFT shift command, andfurther adaptation to show a graph, similar to an analytic (a) Use the graph to indicate the amplitude (v) and frequency of the rst,third, fth, and seventh Problem-3 Block diagram of a spectrum analyzer -Draw a block diagram of a spectrumanalyzer, and explain brie y each of the following blocks (Attenuator,ampli er,LPF,IF lter, envelope detector, video lter, display, LO, Ramp generator). Problem-4 Shape factor of a Gaussian lter-The voltage of a gaussian shape lter is givenbyV(f) =1 p2 exp (f f0)22 2!( )wheref0is the center frequency of the lter, and is the standard deviation.

5 Inprobability theory is the standard deviation (About 68% of values drawn froma normal distribution are within one standard deviation, ). Electrical engineeringconsider the envelope of the that the the center frequency is 10 MHz, and the -3dB bandwidth of the lteris (a) Use Eq. (4) to nd the standart deviation of the lter (-3dB is related tothe powerV2(f)).(b) Use Eq. (4) to nd the -60dB bandwidth of the lter, and the shape factorof the lterShape factor 60dBBandwidth (MHz)-3dBaAmplitude(V)Figure problem References1. ROBERT A. WITTE " spectrum and Network Measurements" . New Jersy ,Prentice Hall,1991 Background Theory -Frequency and Time Domain62. CYDE F. COOMBS, Jr. "Electronic Instrument Handbook". McGraw-Hill, second edition C. Rauscher: "Fundamental of spectrum analysis" Rhode&Schwarz Agilent Company: " spectrum Analysis Basics". Application Note 150,January Background Theory -Frequency and Time DomainSo what is a spectrum ?

6 Fourier series theory tells us that: " Any physical signal, isa collection of sine waves that, when combined properly, produce the time-domainsignal under examination" Fourier transform add time and frequency domain, is twodi erent representations, of the same (v))12sin(10f )32sin(310f )52sin(510f )72sin(710f ])12(2sin[1210fnn +Time domain oscilloscopefrequencyAmplitude(v)Frequen cy domain spectrumanalyzerFigure 2 Time and frequency domainFigure 2 shows a squarewave signal in both time and frequency domains. Thefrequency domain display plots the amplitude versus the frequency of each sine wavein the spectrum , while the time domain shows, true amplitude versus time. Does thismean we have no need to perform both domain measurements? Not at all. Somemeasurement can be made only in the time domain. For example, pulse rise and falltimes, overshoot, and ringing, while other measurements like harmonics content, canbe made only in frequency spectrum analyzer Block Diagram and Theory of OperationFigure 3 is a simpli ed block diagram of a superheterodyne spectrum analyzer .

7 Het-erodyne means to mix; that is, to translate frequency. And super refers to super-audiofrequencies. Referring to the block diagram in Figure 3, we see that an input signalpasses through an attenuator, then through a low-pass lter to a mixer, where itInput Section7mixes with a signal from the local oscillator (LO). Because the mixer is a non-lineardevice, its output includes not only the two original signals, but also their harmonicsand the sums and di erences of the original frequencies and their harmonics. If anyof the mixed signals falls within the passband of the intermediate-frequency(IF) lter, it is further processed. It is essentially recti ed by the envelope detector,digitized, and displayed. A ramp generator creates the horizontal movement acrossthe display from left to right. The ramp also tunes the LO so that its frequencychange is in proportion to the ramp sectionBPFPre-selectorReferencesoscillat orFigure 3 Simpli ed block diagram of Heterodyne spectrum Input SectionThe input to the spectrum analyzer block diagram has a step attenuator, followed byan ampli er.

8 The purpose of this input section is to control the signal level appliedto the rest of the (v) (v)AttenuatorAs 4 Signal controlling by input sectionIf the signal level is too large, the analyzer circuits will saturate the mixer and distortthe signal, causing distortion products to appear along with the desired signal. If theMixer and Local level is too small, the signal may be masked by noise present in the problem tends to reduce the dynamic range of the LPF or Preselector (Tunable BPF)The low-pass lter blocks high frequency signals from reaching the mixer. This stageprevents out-of-band signals from mixing with the local oscillator and creating un-wanted responses at the IFtimeAmplitude(v)Desired signaltimeAmplitude(v)High frequency Interfere +LPFT unable BPFF igure 5 Interference rejection by LPF or preselectorMicrowave spectrum analyzers replace the low-pass lter with a preselector, which isa tunable lter that rejects allfrequencies except those that we currently wish to Mixer and Local mixer (Fig-3) is a device that converts a signal from one frequency to another.

9 Itis therefore sometimes called a frequency converter deviceVCOM ixerLORampGeneratorIF filter)](12sin[10 Loff )]3(2sin[310 LOff ]5(2sin[510 LOff )]7(2sin[710 LOff )])12[((2sin[1210 LOffnn ReferencesoscillatorFigure 6 Mixing process, assume down main output of the mixer , consists of the two conversion signalsffLOg+ffRFgandffLOg ffRFg. IF lter select the desired conversion (down conversionin our case), and stopped the other unwanted products. Reference oscillator, whichis high quality quartz oscillator, stabilizes the VCO, which is unstable IF (Intermediate Frequency) Filter and SelectivityThe IF lter is a Band Pass Filter (BPF). IF lter could be implemented as analogor digital lter. This lter is used as the window for detecting signals. Its width isEnvelope detector9also called a Resolution Bandwidth (RB, RBW) of the analyzer , and can be changedvia the front panel of the analyzer . By giving you a broad range of variable resolu-tion bandwidth settings, the instrument can be optimized for the sweep and signalconditions, letting you trade-o frequency selectivity (the ability to resolve signals),signal-to-noise ratio (SNR), and measurement signalIFBandwidthDisplayFrequencyAmplotu deOne things to note is that a signal cannot be displayed as an in nitely narrowline.)]

10 It has some width associated with it. This shape is the analyzer s tracing of itsown IF lter shape as it tuned. Thus, if we change the lter bandwidth, we changethe resolution of the Envelope detectorSpectrum analyzers typically convert the IF signal to video with an envelope its simplest form, an envelope detector consists of a diode, resistive load and low-pass lter, as shown in Figure peakdetectorFigure 8 Peak detector, based on diode and RC Video FilterMany modern spectrum analyzers have digital displays, which rst digitize the videosignal with an analog-to digital converter (ADC). This allows for several di erent de-Sensitivity10tector modes that dramatically e ect how the signal is displayed. Ordinary spectrumanalyzer use peak-detection technic. Video FilterThe video lter is a low-pass lter that is located after the envelope detectorand before the ADC. This lter determines the bandwidth of the video ampli er, andis used to average or smooth the trace seen on the screen as shown in gure.