Electronic Design

Knowing The Signal Classes Greatly Simplifies Spectrum Analysis

Learn how to optimize the spectrum analyzer settings for each of the three basic common-factor signal classes.

Spectrum analysis consists of a wide variety of applications and measurements. Each involves a different set of procedure and measurement sequences. For example, what users must do to determine the occupied spectrum width for a digitally modulated QAM signal differs from the procedure for finding the total harmonic distortion of an oscillator, the percentage modulation for an amplitude modulated signal, the level of EMI emissions for regulatory compliance purposes, and the pulse desensitization factor of a pulsed radar signal. There's literally no end to the list that one can invent.

But, this seemingly endless list of applications and associated measurement needs can be greatly reduced by grouping signals into common-factor classes. There are only three basic classes into which all signals fall. Understanding what these classes are, and how to optimize the spectrum analyzer settings for each signal class, will significantly simplify the measurement process. Before beginning a discussion of signal classes, though, we need to examine the basic spectrum analyzer functions that interact with these signals.

The basic signal-processing elements of a spectrum analyzer include a mixer, bandpass filter, envelope detector, low-pass filter, and peak detectors (Fig. 1). The diagram is condensed to show only the essential aspects of the elements being discussed. Some important elements are omitted, such as preselection and logarithmic amplification.

The system in Figure 1 is a specialized version of the standard superheterodyne RF receiver. Such a receiver is recognized by the mixer whose function is to bring the incoming signal frequency into the passband of an intermediate frequency (IF) amplifier. Signal conditioning and signal processing take place there. Known as the resolution filter, the IF amplifier in the spectrum analyzer has a variable bandwidth that's called the resolution bandwidth (Br).

Next to center frequency, the resolution bandwidth control is possibly the most prominent function of the spectrum analyzer. The chosen setting of the Br has an important, and sometimes essential, impact on measurement results, depending on the signal class involved. This will be discussed in the signal class section of this article.

Additionally, the spectrum analyzer has another variable-bandwidth filter, known as the video filter (Bv). This is a confusing name, but we're stuck with it for historical standardization reasons. A more descriptive name would be post-detection filter. By contrast, the resolution filter would then be a pre-detection filter. Identification of location, as before and after a detector, clarifies the function of these filters and what they do to the signal.

The detector intervening between these filters is termed an envelope detector. Its purpose is to detect the envelope (the outer outline) of the output from the IF amplifier, or resolution bandwidth filter. It's immediately apparent that the resolution circuit acts upon the incoming signal, while the video circuit acts upon the detected envelope of the signal.

This type of post-detection filter is equivalent to an arithmetical averaging function. Furthermore, the averaging isn't of the signal, but the envelope of the spectrum. Any application that needs an average will call for a narrow Bv, while those that shouldn't be averaged require a wide Bv.

The final important factor in this discussion is the choice of detector functions. Many spectrum analyzers have additional detector functions. But we are interested in just two of these, the positive peak envelope detector (Dp) and the negative peak envelope detector (Dn). The default turn-on of the spectrum analyzer has both detectors on. About 70% of the time, the negative detector doesn't provide any useful information. Still, having this detector actuated will only rarely cause any harm. So, having both detectors on is the usual default, although turning the negative detector off also is normally acceptable. Yet it isn't typically acceptable to turn the positive detector off. That's a very rare situation, perhaps occurring 1% or 2% of the time at most. This situation calls for a measurement involving only the negative detector.

A summary of the likelihood of needing these detectors follows. There must be Dp about 98% of the time. Both detectors are required around 30% of the time. A Dn-only situation occurs about 2% of the time. Finally, around 70% of the time, it makes no difference whether the Dn is on or off.

Three signal classes and three spectrum analyzer functions make for a 3-by-3 matrix of relationships. But before we can get to such a matrix, we need to look at the signal classes and understand how these are affected by the previously discussed spectrum analyzer functions.

Categorizing The Signals
Three basic signal classes exist, with all signals falling into one or a combination of them. These classes are: sinusoids, also known as continuous wave (CW) signals, random signals, and pulsed signals. Classification of the signals listed in the introduction of this article would prove that the digitally modulated QAM spectrum is in the random class (actually quasirandom, but random is good enough for this discussion). Harmonic distortion of an oscillator belongs to the sinewave or CW class. The pulsed radar signal falls into the pulses class. Finally, the EMI signal can be a combination of any of the classes.

The spectra of the three signal classes differ from each other in a number of ways. One is an important factor in how the signal will be measured. It's the frequency distribution of the signal.

A sinewave is a single-frequency signal—it occupies zero frequency width. This means that a sinusoidal signal can be intercepted and measured with a receiver set for any bandwidth. Just set, or tune, the receiver to the desired frequency and the signal will be intercepted. How wide or narrow the receiver bandwidth is makes no difference. All of the CW signals will pass through the bandwidth. This receiver bandwidth is the resolution bandwidth, Br, on the spectrum analyzer.

A pure sinusoid is of fixed, unvarying amplitude. Therefore, the choice of bandwidth after the detector has no effect on the result. This refers to the video filter bandwidth, Bv, on the spectrum analyzer.

Finally, the sinewave is a symmetrical shape. Deciding between positive peak detection, Dp (the maximum detector), and negative peak detection, Dn (the minimum detector), won't change anything for this signal. In other words, it doesn't matter how the controls are set for a sinusoid. The measured result won't change as long as a reasonable signal-to-noise ratio is maintained.

The situation isn't the same for a random or pseudorandom signal. The signal is distributed in frequency on the basis of power/bandwidth unit, and measured in units of dBm/Hz. The result won't change with bandwidth when normalized to a 1-Hz bandwidth. As a result, it doesn't matter what the Br setting is, just as for the sinewave. Unlike the sinewave, though, the display level will change as a function of bandwidth, and it's only the computed per hertz result that remains invariant with bandwidth changes. This means that the absolute signal power level changes directly with bandwidth.

On a logarithmic scale, the result follows a 10log(Br change) relationship. The absolute result changes with bandwidth, but the normalized result stays the same. Hence, the measurement can be made at any resolution bandwidth setting. Yet, this isn't the case for the post-detection bandwidth, Bv.

Eliminating The Randomness
Random signals yield random measurement results, which isn't a desirable idea. We have to get rid of the randomness by smoothing out the signal. This is done by passing the signal through a narrowband filter after the detector. Analysis shows that the ratio Br to Bv should be at least 100:1 in order to obtain reasonably reproducible results. This will reduce the displayed signal level by about 10 dB from the full-peak value when Bv isn't narrowed.

Selecting a detector function also has a different effect on the random signal compared to the sinusoid. Dp or Dn doesn't matter for the sinewave. The same applies for the random signal when the random perturbations are smoothed out with a very narrow Bv. A signal that doesn't change isn't affected by the choice of detector. But, there's a big difference without smoothing. The peak-to-trough difference for a random signal will be about 15 dB as the detector is switched from positive to negative.

Finally, we come to pulses. Here, the most severe impact with instrument control changes takes place. Because the spectrum is distributed on a V/Hz basis, the displayed level will change at the rate of 20log(Br change). This is a 20-dB level change for a 10x ratio in Br. The same Br ratio will show only a 10-dB variation for a random signal.

Bv also has a greater impact than for random signals. A narrow post-detector bandwidth will yield the average value of the signal. This is an approximately 10-dB change for random signals, as stated previously. But the impact can be much more for a pulsed signal, depending upon the on/off time ratio, known as the duty factor. A 1µs wide pulse, repeating at a 1-kHz rate, has a 1000:1 duty factor ratio. Such a signal will show a 60-dB level change when Bv is significantly reduced.

Furthermore, the detector function impacts the display more severely for pulsed signals. If the positive peak detector, Dp, is chosen, the largest display sample will be displayed. But selecting the negative detector, Dn, displays the smallest display sample. As the smallest display sample is zero for a signal that's periodically turned off, the Dn function will usually show no signal at all for a pulsed input.

The material that follows will help you summarize and cross reference what was previously discussed. We begin with the content of the three-by-three matrix already mentioned (Table 1). This is followed by an exercise example showing that no single spectrum analyzer is necessarily the best under all circumstances. Knowing the signal class to be measured will help you decide what performance you need from your spectrum analyzer.

The behavior shown in Table 1 is illustrated by the basic measurements discussed below. The display traces were obtained from a Rhode & Schwartz model FSP spectrum analyzer.

The resolution bandwidth (Br) setting has an important impact upon the pulsed signal spectrum (Fig. 2). The detector is set to the positive peak detector (Dp). Having both the positive and negative (Dp and Dn) detectors on, as usual, would provide the same information. But, the display would be difficult to interpret in a multitrace environment. Each trace would be a densely filled-in display from Dp on top to Dn on the bottom. Hence, the upper trace would obscure the appearance of the lower traces.

Varying The Resolution Bandwidth
Observing only Dp shows the upper outline of the trace while the inside is empty, so smaller traces can be easily observed. The resolution bandwidth was sequentially set at 100, 30, and 10 kHz. The video bandwidth was set at three times Br in each case, so that Bv doesn't impact the result. The signal consists of a 1-GHz carrier modulated by a 1µs pulse. The result is displayed at a vertical setting of 5 dB/division. Note that the traces differ from each other by 10 dB, which follows a 20log(Br ratio) relationship.

Look at the upper trace of the pulsed spectra that begins with the upper trace of Figure 2 at a setting of Br = 100 kHz, Bv = 300 kHz, and a Dp detector choice (Fig. 3). The middle trace shows the impact of reducing the video bandwidth. The spectrum display has dropped by over 20 dB, and a lower video bandwidth would result in an even greater display reduction. The point is that a narrow Bv significantly reduces the pulsed signal spectrum level. The third trace of Figure 3 is difficult to note, because it consists of a straight line across the bottom of the graticule. This trace started as the upper trace with Br = 100 kHz, Bv = 300 kHz, and a Dp detector setting. Now, however, the detector has been set to Dn. A negative detector setting shows nothing for a pulsed signal.

Bandwidth, both resolution and video, has an impact on a random type signal (Fig. 4). Shown in the figure is the spectrum for a CDMA digitally modulated carrier. The upper trace shows the spectrum at a 100-kHz resolution setting and moderate video bandwidth smoothing. Slightly below this one, the next trace reveals the result of significant video bandwidth reduction as Bv is set at 3 Hz. The change in Bv has an effect on the display, but not at all to the same extent as on a pulsed signal. The last trace has the resolution bandwidth reduced by a factor of 10 to 10 kHz. The spectrum has dropped by 10 dB, indicative of a 10log(Br ratio) relationship.

Consider the same CDMA signal in a vertically expanded mode with a 1-dB/division setting (Fig. 5). The display illustrates the impact of detector function choice. The upper display uses the Dp, while the lower display is set at Dn. The difference between the displays is about 5 dB. This isn't anywhere near the enormous impact of Dn on pulses. The displays aren't smooth and consistent with the peak detection (either positive or negative) of a noise-like random signal. The middle trace is the result obtained using an rms detector. As one would expect, the display is between the top and bottom of the spectrum perturbations.

Also note that the middle trace looks smooth, and not noise-like. This is because the probability density function of the random signal has a fixed, unique rms value. Notice that not all spectrum analyzers have this detector available. So, it's not discussed in the body of this article, which deals only with functions available in all spectrum analyzers.

For the sake of completeness, we should also have a display showing results for the third signal class involving sinusoids. But that's useless in a static display. Changes in detector or bandwidth settings don't affect the result for such a signal. We would only get a bunch of traces falling on top of one another. For that reason, this display isn't shown.

Doing It Yourself
The following exercise will illustrate the importance of signal class and spectrum analysis performance features. You have a choice between three spectrum analyzers. Except in two areas, the instruments are identical. The range of available resolution filter bandwidths (Br), and noise level, known as the sensitivity, at the narrowest available Br are different (Table 2).

Your job is to select the best instrument for the detection, observation, and measurement of very small signals. The next section explains how this will be accomplished, but you should stop reading at this point. Take a bit of time to consider this issue on your own, and proceed only after you arrive at some conclusions. Then you can compare your result to what follows.

Question: which instrument is best for the detection, observation, and measurement of small signals? Answer: it depends on the signal class that your signal belongs to. There are three signal classes, and there are three spectrum analyzers. Each spectrum analyzer is best for one of the signal classes.

Let's start with the sinewave, a zero-bandwidth signal. The choice of Br won't effect the displayed signal level. The best signal-to-noise ratio will be obtained for the smallest noise level, regardless of bandwidth. This is −130 dBm at a 10-Hz Br setting on instrument A. When measuring sinewaves, instrument A is better than B by 3 dB and better than C by 5 dB.

The signal level result is independent of bandwidth for a sinewave, so we choose a bandwidth that yields the lowest noise level. This isn't the case for random signals. Both the signal and the noise are equally affected by the bandwidth. Changing Br will change the intercepted signal level, and it will equally alter the noise level. Both the random signal and instrument noise will go up and down as the bandwidth is changed, but the signal-to-noise (S/N) ratio won't be affected.

S/N is independent of bandwidth for random signals. Finding the best S/N position requires a comparison of instruments at equal bandwidths. Information for instruments B and C is already at equal, 100-Hz bandwidths. Hence, we must convert the result for A to a 100-Hz bandwidth result. Random noise changes at the rate of 10log(Br change). Going from 10 to 100 Hz will increase the noise by 10 dB, or −130 + 10 = −120 dBm. This shows that instrument B is best at −127 dBm. It's 7 dB better than A and 2 dB better than C for random signals.

The pulsed signal provides the most complicated situation. The impact of bandwidth is directly proportional to signal level on a V/Hz basis. The widest bandwidth will yield the largest signal. This will be for instrument C. With a 10x bandwidth increase, C will show a 20-dB greater signal level than A or B. But a 10x bandwidth change will increase the noise level by 10 dB. Consequently, the S/N will improve by 20 − 10 = 10 dB.

We know from previous analysis, however, that C has 2 dB more noise than B at equal bandwidths. For pulsed signals, therefore, C is 20 − 10 − 2 = 8 dB better than B. We know that B has 7 dB less noise than A, so C is 7 + 8 = 15 dB better than A for pulses.

The bottom line is that there's no one best instrument for small-signal analysis. Each of the three is best for one of the signal classes. A critical factor in selecting a spectrum analyzer is signal class. The control settings for whatever instrument is used must be set in accordance with the signal class to be measured. It's best if the user knows the class of the signal from the outset. When in doubt, one can use the impact of Br, Bv, and D control settings on display results in order to determine the signal class.

Recommended Reading:

Modern Spectrum Analyzer Measurements, JMS Consulting, Portland, OR.

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