Dsp -Spectral Analysis

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SPECTRAL ANALYSIS

Introduction

At the most basic level, the spectrum analyzer can be described as a frequency-selective, peak-responding voltmeter calibrated to display the rmsvalue of a sine wave. It is important to understandthat the spectrum analyzer is not a power meter,even though it can be used to display powerdirectly. As long as w know some value of a sinewav ( for example, peak or average) and know theresistance across which w measure this value, we

can calibrate our voltmeter to indicate power. Withthe advent of digital technology, modern spectrumanalyzers have been given many more capabilities.In this note, w shall describe the basic spectrumanalyzer as well as the many additional capabilitiesmade possible using digital technology and digitalsignal processing.

Frequency domain versus time domain Before wget into the details of describing a spectrumanalyzer, w might first ask ourselves: Just what is aspectrum and why would w want to analyze it? Ournormal frame of reference is time. We note whencertain events occur. This includes electrical vents.We can use an oscilloscope to view theinstantaneous value of a particular electrical vent (or some other event converted to volts through anappropriate transducer) as a function of time. Inother words, w use the oscilloscope to view thewav form of a signal in the time domain.

Fourier 1 theory tells us any time-domain electricalphenomenon is made up of one or more sine wavesof appropriate frequency, amplitude, and phase. Inother words, we can transform a time-domainsignal into its frequency- domain equivalent.Measurements in the frequency domain t ll us howmuch energy is present at each particularfrequency. With proper filtering, a wav form suchas in Figure 1-1 can be decomposed into separatesinusoidal waves, or spectral components, which wcan then valuate independently. Each sine wav isharacterized by its amplitude and phase. If thesignal that we wish to analyze is periodic, as in ourcase here, Fourier says that the constituent sine wavs are separated in the frequency domain by 1/ T,where T is the period of the signal 2

Figure 1-1. Complex time-domain signal

1. Jean Baptiste Joseph Fourier, 1768-1830. AFrench mathematician and physicistwho discovered that periodic functions can beexpandedinto a series of sines and cosines.2. If the time signal occurs only once, then T isinfinite, and the frequency representation is acontinuum of sine waves.

y What is Spectrum

Some measurements require that we preservecomplete information about the signal -frequency,amplitude and phase. This type of signal nalysis iscalled vector signal analysis , which is discussed inApplication Note 150-15, Vector Signal AnalysisBasics . Modern spectrum nalyzers are capable of performing a wide variety of vector signal

measurements. However, another large groupof measurements can be ade ithout knowing the phase relationships among the sinusoidalcomponents. This type of signal analysis is calledspectrum analysis . Because pectrum analysis issimpler to understand, yet extremely useful, w willbegin this application note by looking first at howspectrum analyzers perform spectrum analysismeasurements.


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Theoretically, to make the transformation from thetime domain to the frequency domain, the signalmust be valuated over all time, that is, over infinity. How v r, in practice, we always use a finittime period when making a measurement. Fouriertransformations can also be made from thefrequency to the time domain. This case also

theoretically requires the valuation of all spectralcomponents over frequencies to infinity. Inreality, making measurements in a finite bandwidththat captures most of the signal energy producesacceptable results. When performing a Fouriertransformation on frequency domain data, the phase of the individual components isindeed critical. For example, a square wavtransformed to the frequency domain and backagain could turn into a sawtooth wav if phase werenot preserved.

What is a spectrum?

So what is a spectrum in the context of thisdiscussion? A spectrum is a collection of sinewaves that, when combined properly, produce thetime-domain signal under examination. Figure 1-1shows the wav form of a complex signal. Supposethat we w re hoping to see a sine wav .Although the wav form certainly shows us that thesignal is not a pure sinusoid, it does not give us adefinitive indication of the reason why. Figure 1-2shows our complex signal in both the time andfrequency domains. The frequency-domain display plots the amplitude v rsus the frequency of eachsine wav in the spectrum. As shown, the spectrumin this case comprises just two sine waves. We nowknow why our original waveform was not a puresine wav . It contained a second sine wav , thesecond harmonic in this case. Does this mean whave no need to perform time-domainmeasurements? Not at all. The time domain is bett rfor many measurements, and some can bemade only in the time domain. For example, puretime-domain measurements include pulse rise andfall times, overshoot, and ringing.

Time domain measurements Frequency domainmeasurements

Figure 1-2. Relationship between time andfrequency domain

y Types of Measurements

Common spectrum analyzer measurements includefrequency, pow r, modulation, distortion, and noise.Understanding the spectral content of a signal isimportant, especially in systems with limited bandwidth. Transmitted power is another k ymeasurement. Too little power may mean thesignal cannot reach its intended destination. Toomuch pow r may drain batteries rapidly, createdistortion, and cause excessiv ly high operating tmperatures.

Measuring the quality of the modulation isimportant for making sure a system is working properly and that the information is beingcorrectly transmitted by the system. Tests such asmodulation degree, sideband amplitude,modulation quality, and occupied bandwidth areexamples of common analog modulationmeasurements. Digital modulation metrics includeerror vector magnitude ( EVM) , IQ imbalance, phase error v rsus time, and a variety of othermeasurements. For more information onthese measurements, see Application Note 150-15,Vector Signal Analysis Basics .

In communications, measuring distortion is criticalfor both the receiver and transmitter. Excessivharmonic distortion at the output of atransmitter can int rfere with other communication bands. The pre-amplification stages in a receiv rmust be free of intermodulation distortion to prevent signal crosstalk. An example is the intrmodulation of cable TV carriers as th y mov downthe trunk of the distribution system and distortother channels on the same cable. Commondistortion measurements include intrmodulation, harmonics, and spurious emissions.

Noise is often the signal you want to measure. Any

active circuit or device will generate excess noise.Tests such as noise figure and signal-to-noiseratio ( SNR) are important for characterizing the performance of a d vice and its contribution tooverall system performance.

y Spectrum Analyzer Fundamentals


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Fundamentals This chapter will focus on thefundamental theory of how a spectrumanalyzer works. While today s technology makes it possible to replace many analog circuits withmodern digital implementations, it is very useful tounderstand classic spectrum analyzer architecture

as a starting point in our discussion. In laterchapters, we will look at the capabilities andadvantages that digital circuitry brings to spectrumanalysis. Chapter 3 will discuss digital architecturesused in modern spectrum analyzers.

Figure 2-1. Block diagram of a classicsuperheterodyne spectrum analyzer

Figure 2-1 is a simplified block diagram of asuperheterodyne spectrum analyzer. Heterodynemeans to mix; that is, to translate frequency.And super refers to super-audio frequencies, orfrequencies abov the audio range. Referring to the block diagram in Figure 2-1, we see that aninput signal passes through an attenuator, thenthrough a low-pass filter ( later w shall see why thefilter is here) to a mixer, where it mixes with a

signal from the local oscillator ( LO) . Because themixer is a non-linear d vice, its output includes notonly the two original signals, but also theirharmonics and th sums and differences of theoriginal frequencies and their harmonics. If any ofthe mixed signals falls within the passband of theint rmediate-frequency ( IF) filter, it is further processed ( amplified and perhaps compressed ona logarithmic scale) . It is essentially rectified bythe envelope detector, digitized, and displayed. Aramp generator creates the horizontal movementacross th display from left to right. The ramp alsotunes the LO so that its frequency change is in proportion to the ramp voltage.

Information fromSpectrum Analyzer

Since the output of a spectrum analyzer is an X-Ytrace on a display, let's see what information we getfrom it. The display is mapped on a grid (graticule) with ten major horizontal divisions and

generally ten major vertical divisions. Thehorizontal axis is linearly calibrated in frequencythat increases from left to right. Setting thefrequency is a two-step process. First w adjustthe frequency at the centerline of the graticule withthe center frequency control. Then w adjust thefrequency range ( span) across the full ten divisions

with the Frequency Span control. These controlsare independent, so if w change the centerfrequency, w do not alter the frequency span.Alternatively, w can set the start and stopfrequencies instead of setting center frequencyand span. In either case, we can determine theabsolute frequency of any signaldisplayed and the relative frequency difference between any two signals.The vertical axis is calibrated in amplitude. We havthe choice of a linear scale calibrated in volts or alogarithmic scale calibrat d in dB. The log scale isused far more oft n than the linear scale because ithas a much wider usable range. The log scale

allows signals as far apart in amplitude as 70 to 100dB ( voltage ratios of 3200 to 100,000 and powerratios of 10,000,000 to 10,000,000,000) to bedisplayed simultaneously. On the other hand, thelinear scale is usable for signals differing by nomore than 20 to 30 dB ( voltage ratios of 10 to 32) .In either case, we giv the top line of the graticule,the reference lev l, an absolute value throughcalibration techniques 1 and use the scalingper division to assign values to other locations onthe graticule. Therefore, w can measure either theabsolute value of a signal or the relativeamplitude difference between any two signals.

y RF Input AttenuatorThe first part of our analyzer is the RF inputattenuator. Its purpose is to ensure the signal entersthe mixer at the optimum level to preventoverload, gain compression, and distortion.Because attenuation is a protective circuit for theanalyzer, it is usually set automatically, based onthe reference level. However, manual selection ofattenuation is also available in steps of 10, 5, 2, oreven 1 dB. The diagram below is an example of anattenuator circuit with a maximum attenuation of70 dB in increments of 2 dB. The blockingcapacitor is used to prevent the analyzer from being

damaged by a DC signal or a DC offset of thesignal. Unfortunately, it also attenuates lowfrequency signals and increases the minimumuseable start frequency of the analyzer to 100Hz for some analyzers, 9 kHz for others.In some analyzers, an amplitude reference signalcan be connected as shown in Figure 2-3. Itprovides a precise frequency and amplitude signal,used by the analyzer to periodically self-calibrate.


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Figure 2-3. RF input attenuator circuitry

LO Frequencyand IF

We need to pick an LO frequency and an IF thatwill create an analyzer with the desired tuningrange. Let's assume that we want a tuning rangefrom 0 to 3 GHz. We then need to choose the IFfrequency. Let's try a 1 GHz IF. Since thisfrequency is within our desired tuning range, wecould have an input signal at 1 GHz. Since theoutput of a mixer also includes the original inputsignals, an input signal at 1 GHz would give us aconstant output from the mixer at the IF. The 1

GHz signal would thus pass through the systemand give us a constant amplitude response on thedisplay regardless of the tuning of the LO. Theresult would be a hole in the frequency range atwhich wecould not properly examine signals because theamplitude response would be independent of theLO frequency. Therefore, a 1 GHz IF will notwork.

So we shall choose, instead, an IF that is above thehighest frequency to which we wish to tune. InAgilent spectrum analyzers that can tune to 3

GHz, the IF chosen is about 3.9 GHz. Rememberthat we want to tune from 0 Hz to 3 GHz. (Actuallyfrom some low frequency because we cannot viewa 0 Hz signal with this architecture.) If we start theLO at the IF ( LO minus IF = 0 Hz) and tune itupward from there to 3 GHz above the IF, then wecan cover the tuning range with the LO minus IFmixing product. Using this information, we cangenerate a tuning equation:

y Tuning Single band RF SpectrumAnalyzer

Figure 2-4 illustrates analyzer tuning. In this figure,f LO is not quit high enough to cause the f LO f sigmixing product to fall in the IF passband, so thereis no response on the display. If we adjust the rampgenerator to tune the LO higher, however, thismixing product will fall in the IF passband at some point on the ramp ( sweep) , and we shall see aresponse on the display.

Figure 2-4. The LO must be tuned to fIF + fsig to produce on the display

Since the ramp generator controls both thehorizontal position of the trace on the display andthe LO frequency, we can now calibrate thehorizontal axis of the display in terms of the inputsignal frequency.

We are not quit through with the tuning yet. Whathappens if the frequency of the input signal is 8.2GHz? As the LO tunes through its 3.9 to 7.0GHz range, it reaches a frequency (4.3 GHz) atwhich it is the IF away from the 8.2 GHz inputsignal. At this frequency we have a mixing productthat is equal to the IF, creating a response on thedisplay. In other words, the tuning equation could just as easily have been:

This equation says that the architecture of Figure 2-1 could also result in a tuning range from 7.8 to10.9 GHz, but only if we allow signals in that rangeto reach the mixer. The job of the input low-passfilter in Figure 2-1 is to prevent these higherfrequencies from getting to the mixer. We alsowant to keep signals at the intermediate frequencyitself from reaching the mixer, as previouslydescribed, so the low-pass filter must do a good jobof attenuating signals at 3.9 GHz, as well as in therange from 7.8 to 10.9 GHz.

y Additional Mixing StagesTo separate closely spaced signals (see Resolvingsignals later in this chapter), some spectrumanalyzers have IF bandwidths as narrow as 1kHz; others, 10 Hz; still others, 1 Hz. Such narrowfilters are difficult to achieve at a center frequency


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of 3.9 GHz. So we must add additional mixingstages, typically two to four stages, to down-convert from the first to the final IF. Figure 2-5shows a possible IF chain based on the architectureof a typical spectrum analyzer. The full tuningequation for this analyzer is:

Figure 2-5. Most spectrum analyzers use two tofour mixing steps to reach the final IF

So simplifying the tuning equation by using just thefirst IF leads us to the same answers. Although onlypassive filters are shown in the iagram, the actualimplementation includes amplification in thenarrower IF stages. The final IF section containsadditional components, such aslogarithmic amplifiers or analog to digitalconverters, depending on the design of

the particular analyzer.

Most RF spectrum analyzers allow an LOfrequency as low as, and even below, the first IF.Because there is finite isolation between the LOand IF ports of the mixer, the LO appears at themixer output. When the LO equals the IF, the LOsignal itself is processed by the system and appearsas a response on the display, as if it were an inputsignal at 0 Hz. This response, calledLO feedthrough, can mask very low frequencysignals, so not all analyzers allow the display rangeto include 0 Hz.

y IF gain & Resolving SignalsIF gainReferring back to Figure 2-1, we see the nextcomponent of the block diagram is a variable gainamplifier. It is used to adjust the vertical position ofsignals on the display without affecting the signal

level at the input mixer. When the IF gain ischanged, the value of the reference level is changedaccordingly to retain the correct indicated value forthe displayed signals. Generally, w do not want thereference level to change when we change the inputattenuator, so the settings of the input attenuatorand the IF gain are coupled together. A change in

input attenuation will automatically change the IFgain to offset the effect of the change in inputattenuation, thereby keeping the signal at aconstant position on the display.

Resolving signalsAfter the IF gain amplifier, we find the IF sectionwhich consists of the analog and/ or digitalresolution bandwidth ( RBW) filters.

Analog filtersFrequency resolution is the ability of a spectrumanalyzer to separate two input sinusoids into

distinct responses. Fourier tells us that a sinewave signal only has energy at one frequency, sowe shouldn't have any resolution problems. Twosignals, no matter how close in requency, shouldappear as two lines on the display. But a closerlook at our superheterodyne receiver shows whysignal responses have a definite width on thedisplay. The output of a mixer includes the sum anddifference products plus the two original signals(input and LO). A bandpass filter determines theintermediate frequency, and this filter selects thedesired mixing product and rejects all other signals.Because the input signal is fixed and the localoscillator is swept, the products from the mixer arealso swept. If a mixing product happens to sweeppast the IF, the characteristic shape of the bandpassfilter is traced on the display. See Figure 2-6. Thenarrowest filter in the chaindetermines the overall displayed bandwidth, and inthe architecture of

\Figure 2-5, this filter is in the 21.4 MHz IF.

Figure 2-6. As a mixing product sweeps past the IFfilter, the filter shape is traced on the display


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So two signals must be far enough apart, or else thetraces they make will fall on top of each other andlook like only one response. Fortunately,spectrum analyzers have selectable resolution (IF)filters, so it is usually possible to select one narrowenough to resolve closely spaced signals.

y Agilent DataSheetsAgilent data sheets describe the ability to resolvesignals by listing the 3 dB bandwidths of theavailable IF filters. This number tells us how closetogether equal-amplitude sinusoids can be and stillbe resolved. In this case, there will be about a 3 dBdip between the two peaks traced out by thesesignals. See Figure 2-7. The signals can be closertogether before their traces merge completely, butthe 3 dB bandwidth is a good rule of thumb forresolution of equal-amplitude signals3.

Figure 2-7. Two equal-amplitude sinusoids

separated by the 3 dB BW of the selected IF filtercan be resolved

y BandwidthSelectivityAnother specification is listed for the resolutionfilters: bandwidth selectivity (or selectivity orshape factor). Bandwidth selectivity helpsdetermine the resolving power for unequalsinusoids. For Agilent analyzers, bandwidth selectivity is generally specified as theratio of the 60 dB bandwidth to the 3 dB bandwidth, as shown in Figure 2-9. The analogfilters in Agilent analyzers are a four-pole,synchronously-tuned design, with a nearlyGaussian shape 4 . This type of filter exhibits a bandwidth selectivity of about 12.7: 1.

Figure 2-9. Bandwidth selectivity, ratio of 60 dB to3 dB bandwidths

Some older spectrum analyzer models used five-pole filters for the narrowest resolution bandwidthsto provide improved selectivity of about 10:1.

Modern designs achieve even better bandwidthselectivity using digital IF filters.

y Digital Filters & Residual FMDigital filtersSome spectrum analyzers use digital techniques torealize their resolution bandwidth filters. Digitalfilters can provide important benefits, such asdramatically improved bandwidth selectivity. TheAgilent PSA Series spectrum analyzers implementall resolution bandwidths digitally. Other analyzers,such as the Agilent ESA-E Series, take a hybrid

approach, using analog filters for the wider bandwidths and digital filters for bandwidthsof 300 Hz and below. Refer to Chapter 3 for moreinformation on digital filters.

Residual FMFilter bandwidth is not the only factor that affectsthe resolution of a spectrum analyzer. The stabilityof the LOs in the analyzer, particularly the first LO,also affects resolution. The first LO is typically aYIG-tuned oscillator ( tuning somewhere in the 3 to7 GHz range) . In early spectrum analyzer designs,these oscillators had residual FM of 1 kHz or more.This instability was transferred to any mixing products resulting from the LO andincoming signals, and it was not possible todetermine whether the input signal or the LO wasthe source of this instability.

The minimum resolution bandwidth is determined,at least in part, by the stability of the first LO.Analyzers where no steps are taken to improveupon the inherent residual FM of the YIG


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oscillators typically have a minimum bandwidth of1 kHz. However, modern analyzers havedramatically improved residual FM. For example,Agilent PSA Series analyzers have residual FMof 1 to 4 Hz and ESA Series analyzers have 2 to 8Hz residual FM. This allows bandwidths as low as1 Hz. So any instability we see on a spectrum

analyzer today is due to the incoming signal.

y Phase NoisePhase noiseEven though w may not be able to see the actualfrequency jitter of a spectrum analyzer LO system,there is still a manifestation of the LOfrequency or phase instability that can be observed.This is known as phase noise ( sometimes calledsideband noise) . No oscillator is perfectlystable. All are frequency or phase modulated byrandom noise to some extent. As previously noted,any instability in the LO is transferred to any

mixing products resulting from the LO and inputsignals. So the LO phase-noise modulationsidebands appear around any spectral componenton the display that is far enough above thebroadband noise floor of the system ( Figure 2-11). The amplitude difference between a displayedspectral component and the phase noise is afunction of the stability of the LO. The more stablethe LO, the farther down the phase noise. Theamplitude difference is also a function of theresolution bandwidth. If w reduce the resolution bandwidth by afactor of ten, the level of the displayed phase noisedecreases by 10 dB 5 .

Figure 2-11. Phase noise is displayed only when asignal is displayed far enough above the systemnoise floor

y PSA SeriesSpectrum AnalyzerSome modern spectrum analyzers allow the user toselect different LO stabilization modes to optimize

the phase noise for differentmeasurement conditions. For example, the PSASeries spectrum analyzers offer three differentmodes:

Optimize phase noise for frequency offsets < 50kHz from the carrier In this mode, the LO phasenoise is optimized for the area close in to the carrierat the expense of phase noise beyond 50 kHzoffset. Optimize phase noise for frequency offsets >50 kHz from the carrierThis mode optimizes phase noise for offsets above50 kHz away from the carrier, especially thosefrom 70 kHz to 300 kHz. Closer offsets

are compromised and the throughput ofmeasurements is reduced. Optimize LO for fasttuning When this mode is selected, LO behaviorcompromises phase noise at all offsets from thecarrier below approximately 2 MHz. Thisminimizes measurement time and allows themaximum measurement throughput when changingthe center frequency or span.

y Sweep timeIn any case, phase noise becomes the ultimatelimitation in an analyzer's ability to resolve signalsof unequal amplitude. As shown in Figure 2-13, wemay have determined that we can resolve twosignals based on the 3 dB bandwidth andselectivity, only to find that the phase noise coversup the smaller signal.

If resolution were the only criterion on which we judged a spectrum analyzer, we might design ouranalyzer with the narrowest possible resolution(IF) filter and let it go at that. But resolution affectssweep time, and we care very much about sweeptime. Sweep time directly affects how long ittakes to complete a measurement.

Resolution comes into play because the IF filtersare band-limited circuits that require finit times tocharge and discharge. If the mixing productsare swept through them too quickly, there will be aloss of displayed amplitude as shown in Figure 2-14. (See Envelope detector, later in this chapter,for another approach to IF response time.) If wethink about how long a mixing product stays in the


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passband of the IF filter, that time is directly proportional to bandwidth and inverselyproportional to the sweep in Hz per unit time, or:

where RBW = resolution bandwidth andST = sweep time.

Figure 2-13. Phase noise can prevent resolution ofunequal signals

Figure 2-14. Sweeping an analyzer too fast causes adrop in displayed amplitude and a shift in indicatedfrequency

y DigitalResolution FiltersOn the other hand, the rise time of a filter isinversely proportional to its bandwidth, and if weinclude a constant of proportionality, k, then:

The value of k is in the 2 to 3 range for the

synchronously-tuned, near-Gaussian filters used inmany Agilent analyzers.

y Envelope Detector

Spectrum analyzers typically convert the IF signalto video7 with an envelope detector. In its simplestform, an envelope detector consists of adiode, resistive load and low-pass filter, as shownin Figure 2-15. The output of the IF chain in thisexample, an amplitude modulated sine wave, isapplied to the detector. The response of the detectorfollows the changes in the envelope of the IFsignal, but not the instantaneous value of the IFsine wave itself.

Figure 2-15. Envelope detector

For most measurements, we choose a resolutionbandwidth narrow enough to resolve the individualspectral components of the input signal. If wefix the frequency of the LO so that our analyzer istuned to one of the spectral components of thesignal, the output of the IF is a steady sine wavewith a constant peak value. The output of theenvelope detector will then be a constant (dc)


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voltage, and there is no variation for the detector tofollow.

However, there are times when we deliberatelychoose a resolution bandwidth wide enough toinclude two or more spectral components. At othertimes, we have no choice. The spectral components

are closer in frequency than our narrowest bandwidth. Assuming only two spectralcomponents within the passband, we hav two sinewaves interacting to create a beat note, and theenvelope of the IF signal varies, as shown in Figure2-16, as the phase between the two sine wavesvaries.

Figure 2-16. Output of the envelope detectorfollows the peaks of the IF signal

6. The envelope detector should not be confusedwith the display detectors. See Detector typeslater in this chapter. Additional information onenvelope detectors can be found in Agilent

Application Note 1303, Spectrum AnalyzerMeasurements and Noise, literature number 5966-4008E. 7. A signal whose frequency range extendsfrom zero (dc) to some upper frequency determined by the circuit elements. Historically, spectrumanalyzers with analog displays used this signal todrive the vertical deflection plates of the CRTdirectly. Henceit was known as the video signal.

y DisplaysThe width of the resolution (IF) filter determinesthe maximum rate at which the envelope of the IF

signal can change. This bandwidth determines howfar apart two input sinusoids can be so that after themixing process they will both be within the filter atthe same time. Let's assume a 21.4 MHz finalIF and a 100 kHz bandwidth. Two input signalsseparated by 100 kHz would produce mixingproducts of 21.35 and 21.45 MHz and would meetthe criterion. See Figure 2-16. The detector must beable to follow the changes in the envelope createdby these two signals but not the 21.4 MHz IF signal

itself.

The envelope detector is what makes the spectrumanalyzer a voltmeter. Let's duplicate the situationabove and have two equal-amplitude signals in thepassband of the IF at the same time. A power meterwould indicate a power level 3 dB above either

signal, that is, the total power of the two. Assumethat the two signals are close enough so that, withthe analyzer tuned half way between them, there isnegligible attenuation due to the roll-off of the filter8. Then the analyzer display will vary between avalue that is twice the voltage of either (6 dBgreater) and zero (minus infinity on the log scale).We must remember that the two signals are sinewaves (vectors) at different frequencies, and sothey continually change in phase with respect toeach other. At some time they add exactly in phase;at another, exactly out of phase.

y Digital IF

Since the 1980's, one of the most profound areas ofchange in spectrum analysis has been theapplication of digital technology to replaceortions of the instrument that had previously beenimplemented as analog circuits. With theavailability of high-performance analog-to-igitalonverters, the latest spectrum analyzers digitizeincoming signals much earlier in the signal pathcompared to spectrum analyzer designs of ust a few

years ago. The change has been most dramatic inthe IF section of the spectrum analyzer. Digital IFs1 have had a great impact on pectrum analyzer performance, with significant improvements inspeed, accuracy, and the ability tomeasure complex signals through the se f advancedDSP techniques.

Digital filtersA partial implementation of digital IF circuitry isimplemented in the Agilent ESA-E Series spectrumanalyzers. While the 1 kHz and wider BWsare implemented with traditional analog LC andcrystal filters, the narrowest bandwidths (1 Hz to

300 Hz) are realized using digital echniques. Asshown in Figure 3-1, the linear analog signal ismixed down to an 8.5 kHz IF and passed through a bandpass filter only 1 kHz ide. This IF signal isamplified, then sampled at an 11.3 kHz rate anddigitized.


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Figure 3-1. Digital implementation of 1, 3, 10, 30,100, and 300 Hz resolution filters in ESA-E Series

Once in digital form, the signal is put through a fastFourier transform algorithm. To transform theappropriate signal, the analyzer must be ixed-tuned(not sweeping). That is, the transform must be doneon a time-domain signal. Thus the ESA-E Seriesanalyzers step in 900 Hz ncrements, instead ofsweeping continuously, when we select one of thedigital resolution bandwidths. This stepped tuningcan be seen on he display, which is updated in 900Hz increments as the digital processing iscompleted.

As we shall see in a moment, other spectrumanalyzers, such as the PSA Series, use an all-digitalIF, implementing all resolution bandwidth filtersdigitally.

A key benefit of the digital processing done inthese analyzers is a bandwidth selectivity of about4: 1. This selectivity is available on the arrowestfilters, the ones we would be choosing to separatethe most closely spaced signals.

y Amplitudeand Frequency Accuracy

Now that we can view our signal on the displayscreen, let's look at amplitude accuracy, or perhaps

better, amplitude uncertainty. Most spectrumanalyzers are specified in terms of both absoluteand relative accuracy. However, relative performance affects both, so let's look at thosefactors affecting relative measurement uncertaintyfirst.

Before we discuss these uncertainties, let's lookagain at the block diagram of an analog swept-tuned spectrum analyzer, shown in Figure 4-1, andsee which components contribute to the

uncertainties. Later in this chapter, we will see howa digital IF and various correction and calibrationtechniques can substantially reduce measurementuncertainty.

Figure 4-1. Spectrum analyzer block diagram

Components which contribute to uncertainty are:Input connector (mismatch)

RF Input attenuatorMixer and input filter (flatness)IF gain/attenuation (reference level )RBW filtersDisplay scale fidelityCalibrator (not shown)

y Sensitivityand Noise

SensitivityOne of the primary uses of a spectrum analyzer is

to search out and measure low-level signals. Thelimitation in these measurements is the noisegenerated within the spectrum analyzer itself. Thisnoise, generated by the random electron motion invarious circuit elements, is mplified by multiplegain stages in the analyzer and appears on thedisplay as a noise signal. On a spectrum analyzer,this noise is commonly eferred to as theDisplayed Average Noise Level, or DANL 1 .While there are techniques to measure signalsslightly below the DANL, this oise powerultimately limits our ability to make measurementsof low-level signals. Let's assume that a 50 ohmtermination is attached to the pectrum

analyzer input to prevent any unwanted signalsfrom entering the analyzer. This passive termination generates a small amount ofoise energy equal to kTB, where:


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y Dynamic Range

Definition

Dynamic range is generally thought of as the abilityof an analyzer to measure harmonically relatedsignals and the interaction of two or more signals;for example, to measure second-or third-harmonicdistortion or third-order intermodulation. In dealingwith such easurements, remember that the inputmixer of a spectrum analyzer is a non -linear device,so it always generates distortion of its own. Themixer is non-linear for a reason. It must benonlinear to translate an input signal to the desiredIF. But the unwanted distortion products generatedin the mixer fall at the same frequencies as thedistortion products we wish to measure on the inputsignal.

y Extending the FrequencyRangeAs more wireless services continue to beintroduced and deployed, the available spectrumbecomes more and more crowded. Therefore, therehas been an ongoing trend toward developing new products and services at higher frequencies. Inaddition, new microwave technologies continue toevolve, driving the need for more measurementcapability in the microwave bands. Spectrumanalyzer designers have responded by developinginstruments capable of directly tuning up to 50GHz using a coaxial input. Even higher frequenciescan be measured using external mixing techniques.This chapter describes the techniques used toenable tuning the spectrum analyzer to such highfrequencies.

y Modern Spectrum Analyzers

In previous chapters of this application note, wehave looked at the fundamental architecture ofspectrum analyzers and basic considerationsfor making frequency-domain measurements. On a practical level, modern spectrum analyzers mustalso handle many other tasks to help youaccomplish your measurement requirements. Thesetasks include:

Providing application-specific measurements, suchas adjacent channel power (ACP) , noise figure, and phase noiseProviding digital modulation analysismeasurements defined by industryor regulatory standards, such as GSM, cdma2000,802.11, or Bluetooth

Performing vector signal analysisSaving dataPrinting dataTransferring data, via an I/ O bus, to a computerOffering remote control and operation over GPIB,LAN, or the InternetAllowing you to update instrument firmware to addnew features andcapabilities, as well as to repair defectsMaking provisions for self-calibration,troubleshooting, diagnostics, andrepair Recognizing and operating with optionalhardware and/or firmware to add new capabilities

Application-specific measurementsIn addition to measuring general signalcharacteristics like frequency and amplitude, youoften need to make specific measurements ofcertain signal parameters. Examples includechannel power measurements and adjacent channel power (ACP) measurements, which werepreviously described in Chapter 6. Many spectrumanalyzers now have these built-infunctions available. You simply specify the channel bandwidth and spacing, then press a button toactivate the automatic measurement.

The complementary cumulative distributionfunction (CCDF) , showing power statistics, isanother measurement capability increasingly foundin modern spectrum analyzers. This is shown inFigure 8-1. CCDF measurements provide statisticalinformation showing the percent of time theinstantaneous power of the signal exceeds theaverage power by a certain number of dB. Thisinformation is important in power amplifier design,for example, where it is important to handleinstantaneous signal peaks withminimum distortion while minimizing cost, weight,and power consumption of the device.

y CCDF MeasurementOther examples of built-in measurement functionsinclude occupied bandwidth, TOI and harmonicdistortion, and spurious emissionsmeasurements. The instrument settings, such ascenter frequency, span, and resolution bandwidth,for these measurements depend on thespecific radio standard to which the device is beingtested. Most modern spectrum analyzers have theseinstrument settings stored in memory so thatyou can select the desired radio standard (GSM/


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EDGE, cdma2000, W-CDMA, 802.11a/ b/g, and soon) to properly make the measurements.

Figure 8-1. CCDF measurement

y Noise Figure & Phase NoiseMeasurement

RF designers are often concerned with the noisefigure of their devices,as this directly affects thesensitivity of receivers and other systems.Some spectrum analyzers, such as the PSA Seriesand ESA-E Series models, have optional noisefigure measurement capabilities available. Thisoption provides control for the noise source neededto drive the input of the device under test (DUT), aswell as firmware to automate the measurementprocess and display the results. Figure 8-2 shows atypical measurement result, showing DUT noisefigure (upper trace) and gain (lower trace) as afunction of frequency. For more information onnoise figure measurements using a spectrumanalyzer, see Agilent Application Note 1439,Measuring Noise Figure with a Spectrum Analyzer, literature number 5988-8571EN.

Figure 8-2. Noise figure measurement

Similarly, phase noise is a common measure ofoscillator performance. In digitally modulatedcommunication systems, phase noise cannegatively impact bit error rates. Phase noise canalso degrade the ability of Doppler radar systems tocapture the return pulses from targets. Many

Agilent spectrum analyzers, including the ESA,PSA, and 8560 Series offer optional phase noisemeasurement capabilities. These options providefirmware to control the measurement and displaythe phase noise as a function of frequency offsetfrom the carrier, as shown in Figure 8-3.

Figure 8-3. Phase Noise measurement

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Dsp -Spectral Analysis