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AgilentSpectrum Analysis Basics Application Note 150

10Chapter 2Spectrum Analyzer FundamentalsThis chapter will focus on the fundamental theory of how a spectrum analyzerworks. While today’s technology m

100Let’s assume that we have some idea of the characteristics of our signal, but we do not know its exact frequency. How do we determine which is ther

101Note that both signal identification methods are used for identifying correctfrequencies only. You should not attempt to make amplitude measurement

102In previous chapters of this application note, we have looked at the fundamental architecture of spectrum analyzers and basic considerations for ma

103Other examples of built-in measurement functions include occupied bandwidth, TOI and harmonic distortion, and spurious emissions measurements. The

104RF designers are often concerned with the noise figure of their devices, as this directly affects the sensitivity of receivers and other systems. S

105Digital modulation analysisThe common wireless communication systems used throughout the worldtoday all have prescribed measurement techniques defi

106Not all digital communication systems are based on well-defined industry standards. Engineers working on non-standard proprietary systems or theear

107Data transfer and remote instrument control In 1977, Agilent Technologies (part of Hewlett-Packard at that time) introduced the world’s first GPIB-

108Firmware updatesModern spectrum analyzers have much more software inside them than do instruments from just a few years ago. As new features are ad

109The objective of this application note is to provide a broad survey of basicspectrum analyzer concepts. However, you may wish to learn more about m

11Since the output of a spectrum analyzer is an X-Y trace on a display, let’s seewhat information we get from it. The display is mapped on a grid (gra

110Absolute amplitude accuracy: The uncertainty of an amplitude measurement in absolute terms, either volts or power. Includes relative uncertainties

111Delta marker: A mode in which a fixed, reference marker has been established and a second, active marker is available that we can place anywhere on

112Dynamic range: The ratio, in dB, between the largest and smallest signals simultaneously present at the spectrum analyzer input that can be measure

113Frequency stability: A general phrase that covers both short- and long-termLO instability. The sweep ramp that tunes the LO also determines where a

114Image response: A displayed signal that is actually twice the IF away from the frequency indicated by the spectrum analyzer. For each harmonic of t

115LO feedthrough: The response on the display when a spectrum analyzer is tuned to 0 Hz, i.e. when the LO is tuned to the IF. The LO feedthrough can

116Noise sidebands: Modulation sidebands that indicate the short-term instability of the LO (primarily the first LO) system of a spectrum analyzer.The

117Residual responses: Discrete responses seen on a spectrum analyzer displaywith no input signal present.Resolution: See Frequency resolution.Resolut

118Spectrum: An array of sine waves of differing frequencies and amplitudes and properly related with respect to phase that, taken as a whole, constit

119Video: In a spectrum analyzer, a term describing the output of the envelopedetector. The frequency range extends from 0 Hz to a frequency typically

12RF attenuator The first part of our analyzer is the RF input attenuator. Its purpose is toensure the signal enters the mixer at the optimum level to

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13We need to pick an LO frequency and an IF that will create an analyzer withthe desired tuning range. Let’s assume that we want a tuning range from 0

14Figure 2-4 illustrates analyzer tuning. In this figure, fLOis not quite highenough to cause the fLO– fsigmixing product to fall in the IF passband,

15To separate closely spaced signals (see “Resolving signals” later in this chapter), some spectrum analyzers have IF bandwidths as narrow as 1 kHz;ot

16•IF gain Referring back to Figure 2-1, we see the next component of the block diagramis a variable gain amplifier. It is used to adjust the vertical

17Agilent data sheets describe the ability to resolve signals by listing the 3 dBbandwidths of the available IF filters. This number tells us how clos

18Another specification is listed for the resolution filters: bandwidth selectivity(or selectivity or shape factor). Bandwidth selectivity helps deter

19This allows us to calculate the filter rejection:H(4000) = –10(4) log10[(4000/1149.48)2+ 1] = –44.7 dB Thus, the 1 kHz resolution bandwidth filter

2Chapter 1 – Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Frequency dom

20Phase noise Even though we may not be able to see the actual frequency jitter of a spectrum analyzer LO system, there is still a manifestation of th

21Some modern spectrum analyzers allow the user to select different LO stabilization modes to optimize the phase noise for different measurement condi

22In any case, phase noise becomes the ultimate limitation in an analyzer’s ability to resolve signals of unequal amplitude. As shown in Figure 2-13,

23On the other hand, the rise time of a filter is inversely proportional to its bandwidth, and if we include a constant of proportionality, k, then:Ri

24Envelope detector6Spectrum analyzers typically convert the IF signal to video7with an envelopedetector. In its simplest form, an envelope detector c

25The width of the resolution (IF) filter determines the maximum rate at whichthe envelope of the IF signal can change. This bandwidth determines how

26Detector typesWith digital displays, we had to decide what value should be displayed for each display data point. No matter how many data points we

27The “bucket” concept is important, as it will help us differentiate the six detector types:SamplePositive peak (also simply called peak)Negative pea

28While the sample detection mode does a good job of indicating the randomnessof noise, it is not a good mode for analyzing sinusoidal signals. If we

29Peak (positive) detectionOne way to insure that all sinusoids are reported at their true amplitudes is to display the maximum value encountered in e

3Chapter 5 – Sensitivity and Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58Sensitivity . . . .

30What happens when a sinusoidal signal is encountered? We know that as amixing product is swept past the IF filter, an analyzer traces out the shape

31The normal detection algorithm: If the signal rises and falls within a bucket:Even numbered buckets display the minimum (negative peak) value in the

32Average detectionAlthough modern digital modulation schemes have noise-like characteristics,sample detection does not always provide us with the inf

33EMI detectors: average and quasi-peak detectionAn important application of average detection is for characterizing devices for electromagnetic inter

34Video filteringDiscerning signals close to the noise is not just a problem when performingEMC tests. Spectrum analyzers display signals plus their o

35The effect is most noticeable in measuring noise, particularly when a wide resolution bandwidth is used. As we reduce the video bandwidth, the peak-

36If we set the analyzer to positive peak detection mode, we notice two things:First, if VBW > RBW, then changing the resolution bandwidth does not

37Thus, the display gradually converges to an average over a number of sweeps.As with video filtering, we can select the degree of averaging or smooth

38Time gatingTime-gated spectrum analysis allows you to obtain spectral information about signals occupying the same part of the frequency spectrum th

39In some cases, time-gating capability enables you to perform measurementsthat would otherwise be very difficult, if not impossible. For example, con

41. Jean Baptiste Joseph Fourier, 1768-1830. A French mathematician and physicist who discovered that periodic functions can be expanded into a serie

40Time gating can be achieved using three different methods that will be discussed below. However, there are certain basic concepts of time gating tha

4101234567TimeslotsFigure 2-35. A TDMA format signal (in this case, GSM) with eight time slotsFigure 2-36. A zero span (time domain) view of the two t

42There are three common methods used to perform time gating:• Gated FFT• Gated video• Gated sweepGated FFTSome spectrum analyzers, such as the Agilen

43Gated sweepGated sweep, sometimes referred to as gated LO, is the final technique. In gated sweep mode, we control the voltage ramp produced by the

44Since the 1980’s, one of the most profound areas of change in spectrum analysis has been the application of digital technology to replace portionsof

45In Chapter 2, we did a filter skirt selectivity calculation for two signals spaced 4 kHz apart, using a 3 kHz analog filter. Let’s repeat that calcu

46In this case, all 160 resolution bandwidths are digitally implemented.However, there is some analog circuitry prior to the ADC, starting with sever

47Custom signal processing ICTurning back to the block diagram of the digital IF (Figure 3-2), after the ADC gain has been set with analog gain and co

48More advantages of the all-digital IFWe have already discussed a number of features in the PSA Series: power/voltage/log video filtering, high-resol

49Now that we can view our signal on the display screen, let’s look at amplitudeaccuracy, or perhaps better, amplitude uncertainty. Most spectrum anal

5Some measurements require that we preserve complete information about thesignal - frequency, amplitude and phase. This type of signal analysis is cal

50The general expression used to calculate the maximum mismatch error in dB is:Error (dB) = –20 log[1 ± |(ρanalyzer)(ρsource)|]where ρis the reflecti

51Following the input filter are the mixer and the local oscillator, both of which add to the frequency response uncertainty. Figure 4-2 illustrates w

52Relative uncertaintyWhen we make relative measurements on an incoming signal, we use either somepart of the same signal or a different signal as a r

53Improving overall uncertaintyWhen we look at total measurement uncertainty for the first time, we may well be concerned as we add up the uncertainty

54Typical performance describes additional product performance informationthat is not covered by the product warranty. It is performance beyond specif

55ExamplesLet’s look at some amplitude uncertainty examples for various measurements.Suppose we wish to measure a 1 GHz RF signal with an amplitude of

56Frequency accuracySo far, we have focused almost exclusively on amplitude measurements. What about frequency measurements? Again, we can classify tw

57In a factory setting, there is often an in-house frequency standard availablethat is traceable to a national standard. Most analyzers with internal

58SensitivityOne of the primary uses of a spectrum analyzer is to search out and measurelow-level signals. The limitation in these measurements is the

59Because the input attenuator has no effect on the actual noise generated in the system, some early spectrum analyzers simply left the displayed nois

6Why measure spectra?The frequency domain also has its measurement strengths. We have already seen in Figures 1-1 and 1-2 that the frequency domain is

60So if we change the resolution bandwidth by a factor of 10, the displayed noise level changes by 10 dB, as shown in Figure 5-2. For continuous wave(

61Noise figureMany receiver manufacturers specify the performance of their receivers interms of noise figure, rather than sensitivity. As we shall see

62The 24 dB noise figure in our example tells us that a sinusoidal signal must be 24 dB above kTB to be equal to the displayed average noise level on

63Using these expressions, we’ll see how a preamplifier affects our sensitivity.Assume that our spectrum analyzer has a noise figure of 24 dB and the

64Finding a preamplifier that will give us better sensitivity without costing us measurement range dictates that we must meet the second of the abov

65Let’s first test the two previous extreme cases.As NFPRE+ GPRE– NFSAbecomes less than –10 dB, we find that system noisefigure asymptotically approac

66We have already seen that both video filtering and video averaging reduce the peak-to-peak fluctuations of a signal and can give us a steady value.

67This is the 2.5 dB factor that we accounted for in the previous preamplifier discussion, whenever the noise power out of the preamplifier was approx

68Let’s consider the various correction factors to calculate the total correctionfor each averaging mode:Linear (voltage) averaging:Rayleigh distribut

69When we add a preamplifier to our analyzer, the system noise figure and sensitivity improve. However, we have accounted for the 2.5 dB factor in our

7Figure 1-3. Harmonic distortion test of a transmitter Figure 1-4. GSM radio signal and spectral mask showing limits of unwanted emissionsFigure 1- 5.

70DefinitionDynamic range is generally thought of as the ability of an analyzer to measureharmonically related signals and the interaction of two or m

71With a constant LO level, the mixer output is linearly related to the input signal level. For all practical purposes, this is true as long as the in

72These represent intermodulation distortion, the interaction of the two input signals with each other. The lower distortion product, 2ω1– ω2, fallsbe

73We can construct a similar line for third-order distortion. For example, a data sheet might say third-order distortion is –85 dBc for a level of –30

74Sometimes third-order performance is given as TOI (third-order intercept).This is the mixer level at which the internally generated third-order dist

75Figure 6-2 shows the dynamic range for one resolution bandwidth. We certainly can improve dynamic range by narrowing the resolution bandwidth,but th

76The final factor in dynamic range is the phase noise on our spectrum analyzerLO, and this affects only third-order distortion measurements. For exam

77Dynamic range versus measurement uncertaintyIn our previous discussion of amplitude accuracy, we included only thoseitems listed in Table 4-1, plus

78Next, let’s look at uncertainty due to low signal-to-noise ratio. The distortioncomponents we wish to measure are, we hope, low-level signals, and o

79Let’s see what happened to our dynamic range as a result of our concern with measurement error. As Figure 6-6 shows, second-order-distortion dynamic

8Types of measurementsCommon spectrum analyzer measurements include frequency, power, modulation, distortion, and noise. Understanding the spectral co

80Gain compressionIn our discussion of dynamic range, we did not concern ourselves with howaccurately the larger tone is displayed, even on a relative

81The range of the log amplifier can be another limitation for spectrum analyzers with analog IF circuitry. For example, ESA-L Series spectrum analyze

82Adjacent channel power measurementsTOI, SOI, 1 dB gain compression, and DANL are all classic measures of spectrum analyzer performance. However, wit

83As more wireless services continue to be introduced and deployed, the available spectrum becomes more and more crowded. Therefore, there hasbeen an

84In Chapter 2, we used a mathematical approach to conclude that we needed a low-pass filter. As we shall see, things become more complex in the situa

85Next let’s see to what extent harmonic mixing complicates the situation.Harmonic mixing comes about because the LO provides a high-level drive signa

86The situation is considerably different for the high band, low IF case. As before, we shall start by plotting the LO fundamental against the signal-

87In examining Figure 7-5, we find some additional complications. The spectrum analyzer is set up to operate in several tuning bands. Depending on the

88Other situations can create out-of-band multiple responses. For example, suppose we are looking at a 5 GHz signal in band 1 that has a significant t

89Can we conclude from this discussion that a harmonic mixing spectrum analyzer is not practical? Not necessarily. In cases where the signal frequency

9While we have defined spectrum analysis and vector signal analysis as distinct types, digital technology and digital signal processing are blurring t

90The word eliminate may be a little strong. Preselectors do not have infiniterejection. Something in the 70 to 80 dB range is more likely. So if we a

91Amplitude calibrationSo far, we have looked at how a harmonic mixing spectrum analyzer respondsto various input frequencies. What about amplitude?Th

92For example, suppose that the LO fundamental has a peak-to-peak deviation of 10 Hz. The second harmonic then has a 20 Hz peak-to-peak deviation; the

93From the graph, we see that a –10 dBm signal at the mixer produces a second-harmonic distortion component of –45 dBc. Now we tune the analyzerto the

94Looking at these expressions, we see that the amplitude of the lower distortion component (2ω1– ω2) varies as the square of V1and linearly with V2.

95Pluses and minuses of preselectionWe have seen the pluses of preselection: simpler analyzer operation, uncluttered displays, improved dynamic range,

96External harmonic mixingWe have discussed tuning to higher frequencies within the spectrum analyzer.For internal harmonic mixing, the ESA and PSA sp

97Table 7-1 shows the harmonic mixing modes used by the ESA and PSA at various millimeter wave bands. You choose the mixer depending on the frequency

98Signal identificationEven when using an unpreselected mixer in a controlled situation, there are times when we must contend with unknown signals. In

99Figure 7-15. Which ones are the real signals?346+56–6LO frequency (GHz)Input frequency (GHz)78+8–10+10–12+12–14+14–16+16–18+18–253035404550556065707