June 19, 1997

Spectrum analysis:
blazing trails beyond the frequency domain

DAN STRASSBERG, SENIOR TECHNICAL EDITOR

Spectrum analyzers aren't just for spectrum analysis anymore. With the aid of DSP, they also perform a long list of functions that are essential for pinpointing design flaws in mobile-communications systems.

Spectrum analyzer: "a frequency-domain oscilloscope that displays the energy received at its input as a function of frequency." Not long ago, this definition worked quite well. Now, though, it is far from complete. Today, many spectrum analyzers include DSP functions internally or in companion units. Thanks to DSP, spectrum analyzers provide insights into the complex, often digital, modulation schemes that are the mainstay of modern mobile-communications systems. Designers of these systems need the DSP-based capabilities to evaluate and troubleshoot their designs. A 5-year-old spectrum analyzer is unlikely to have the necessary horsepower.

Modern spectrum-analysis systems display constellation, eye, and I-Q diagrams. (I-Q stands for in-phase vs quadrature, though the diagrams' axes are sometimes reversed to display quadrature vs in-phase signals.) (See box, "Spectrum analyzers unearth communications-system-design flaws.") The systems also measure error-vector magnitude and display it as a function of time. Many modern spectrum-analysis systems are similar to software radios (Reference 1). Such analyzers lock onto a carrier and down-convert the modulated signal to a lower intermediate frequency (IF) or to baseband.

These systems can digitize and store complete records of the modulation over tens of milliseconds or longer. Tools within the instrumentation can display the captured data in a multitude of formats. These analyzers' ability to retain data and present it in so many ways is central to their helping you understand the behavior of the unit under test.

The preceding list of spectrum-analysis capabilities does not even mention the traditional one: displaying received energy as a function of frequency over a broad frequency range. (Often, the received energy comes directly from an antenna.) That capability remains important in many applications, though. For example, you would use broadband sweep to search for signals, especially spurious or potentially interfering ones, that a unit under test might generate.

Analyzers that incorporate a swept-frequency local oscillator (LO) and use the classic heterodyne-based architecture can implement broad frequency sweeps with relative ease. Units that use DSP to convert signals from the time to the frequency domain can find broad sweeps more challenging. Because the two architectures excel at different jobs, some instruments let users select either the DSP or the swept-frequency mode. In other cases, systems that comprise multiple instruments offer a similar choice.

EEs are well-aware of the frequency and time domains' duality (Figure 1). Fourier analysis allows you to represent any signal that is continuous in the time domain as the sum of a group of sine waves of different frequencies and amplitudes. The sine-wave amplitudes and frequencies make up the signal's spectrum; displaying them is one of a spectrum analyzer's main functions. Although the phase of the various sine waves is important in reconstructing the original signal, many applications do not use phase. Classic spectrum analyzers are scalar devices. They do not indicate the phase of a signal's component sine waves, whereas DSP-based analyzers generally do provide phase information.

Fourier analysis in its most basic form applies only to signals that start at minus infinity and continue forever. Nevertheless, mathematical tools allow you to use Fourier techniques on signals that do not meet this criterion. One key technique is the use of windowing functions, which shape portions of finite-duration signals near where they begin and end. DSP software tools apply windowing functions when the tools calculate FFTs from finite-length waveform records.

Whether or not a spectrum analyzer uses DSP techniques, using the instrument on signals of finite duration is the rule, not the exception. Increasingly, communication signals are bursts of modulated sine waves whose amplitudes rapidly ramp up and down. The amplitudes of these sine waves remain constant only for brief intervals. Most modern spectrum analyzers include features to speed the analysis of signal bursts.

DSP-based analyzers usually examine a signal's frequency content over a relatively narrow range. A DSP-based analyzer could cover a broad frequency range by performing successive measurements on adjacent narrow bands, but classic, heterodyne-based, swept-frequency analysis is usually faster and less expensive. Also, although classic techniques don't provide information about complex digital modulation, they do reveal amplitude and frequency, the two signal characteristics of greatest interest to those who conduct wideband searches. Engineers often use an analyzer system's broadband sweep to find signals and use the DSP mode to perform more detailed analyses.

Amplitude and frequency are scalar quantities. DSP-based analyzers can compute both scalar and vector quantities. Examples of vector information are the phase of a signal with respect to a carrier and the magnitude of signal components that are in phase and in quadrature with a carrier. (Signals in quadrature are displaced from each other by 90º.)

DSP-based spectrum analyzers

DSP-based analyzers differ markedly from swept-frequency units for several reasons. First, for a mixer or downconverter to produce a signal from which you can extract a valid FFT, the device must receive a constant-frequency signal at its LO input. In other words, the analyzer must remain tuned to a fixed frequency as the analyzer extracts the information it uses to compute the FFT. This requirement precludes calculating FFTs from swept-frequency data.

Second, the performance of modern DSP-based spectrum analyzers depends on the components the analyzers use. A key component of any DSP-based analyzer is the ADC. As good as modern, high-speed ADCs are, they are far from perfect (Reference 2). Like so many EEs who work with analog signals, designers of DSP-based spectrum analyzers dream of inexpensive, perfectly stable and linear, noise-free ADCs that offer infinite resolution and zero conversion time. On the other hand, if such components existed, designing DSP-based spectrum analyzers would become much less challenging.

At today's state of the art, directly digitizing mobile-communications signals without converting them downward in frequency is impractical. One modern DSO contains an ADC that takes 8G samples/sec in real time, and several other DSOs digitize as fast as 4G or 5G samples/sec. In theory, a 5G-sample/sec ADC is fast enough for spectrum analysis of a signal whose highest frequency component is just below 2.5 GHz. None of these ADCs resolves more than 8 bits, however, and in practice the effective resolution is even lower.

A perfect 8-bit ADC has an SNR of 50 dB (SNR_dB=1.76+6.02×the number of bits). Many spectrum analyzers offer SNRs of 130 dB or more, which might seem well beyond the state of the art for fast ADCs. However, spectrum analyzers' digital filtering reduces both signal and noise bandwidths and results in better SNRs than you might expect. In the world of DSP, this SNR enhancement is known as "process gain."

Also, spectrum-analyzer designers enhance the dynamic range of high-resolution ADCs through techniques such as adding dither to the ADCs' analog-input signals. Still, achieving an SNR greater than 100 dB in a practical system requires an ADC that resolves more than 8 bits. Spectrum analyzers often use 12-bit ADCs. These converters just aren't fast enough to directly digitize gigahertz signals.

Surprisingly fast sampling

Even though a spectrum analyzer's ADC converts a signal that heterodyning has shifted downward in frequency, the ADC's required sampling rate is surprisingly high. The reason is the ADC's need to avoid aliasing (the creation, in the sampled data, of low-frequency artifacts that do not exist in the original signal). The sampling theorem states that, to avoid aliasing, you must sample at more than twice the frequency of any component whose amplitude is significant. Engineers almost always incorrectly rephrase this theorem as "more than twice the highest frequency of interest."

Remember: The highest frequency whose amplitude is significant is often far above the highest frequency you think is important! A good rule is that a component is significant if its amplitude exceeds the ADC's least significant bit.

Suppose you want to analyze a signal on one of the 30-kHz-bandwidth, time-division multiple-access (TDMA) channels of the North American Digital Cellular (NADC) system. NADC carrier frequencies range from 824 to 894 MHz. The signals have a 33% duty cycle and a 20-msec repetition rate. Considering the 30-kHz channel bandwidth, you need to acquire more than 60k samples/sec.

One popular instrument that you could use to acquire and analyze those signals is the HP 89441A RF vector signal analyzer ($58,150). It comprises a downconverter and an 89410A baseband vector signal analyzer. Although HP doesn't call the 89441A a spectrum analyzer, the system can function as a 2.65-GHz spectrum analyzer. Moreover, you can use other spectrum analyzers as downconverters with the 89410A to achieve even broader frequency coverage than the 89441A provides.

Although the following examples draw on the architecture and characteristics of the 89441A, products from other vendors offer the same capabilities. One notable product family is the Rohde and Schwarz (Munich, Germany) FSE series. Tektronix now distributes these products worldwide except in Europe and Japan, where the products are available directly from Rohde and Schwarz. Unlike the 89441A, which comprises a separate downconverter and vector signal analyzer, you can order FSE-series units with an internal vector signal analyzer. A 3.5-GHz analyzer with a color display and vector-signal-analysis option costs $61,495. Other members of the family extend the frequency coverage to 26.5 GHz.

Although the implementation of the FSE series digital-signal-detection function differs in detail from that of the HP 89441A, the underlying concepts are similar (Figure 2).

Use DSP to convert to baseband

In the 89410A, the ADC takes 25.6M samples/sec. Although this sampling rate is more than 400 times the theoretical minimum for an NADC signal, the rate is not excessive. First, the downconverter output is not at baseband; it is modulated onto a 6-MHz IF carrier. Second, using DSP for the final conversion to baseband preserves the dynamic range and the phase relationships among the modulating signals better than analog demodulation would. The 6-MHz carrier requires the ADC to take more than 12M samples/sec to avoid aliasing. But even if no carrier existed, a high sampling rate would be necessary because the unfiltered modulation contains components outside the 30-kHz NADC-channel bandwidth.

Unless the ADC samples rapidly, these high-frequency components generate aliases, which you cannot distinguish from real signals. The system architects might have mitigated the fast-ADC requirement by placing sharp-cutoff analog filters ahead of the ADC. Although the 89441A does use analog filters ahead of the ADC, the architects chose to rely mainly on digital filters, which must follow the ADC. Digital filters offer more advantages than analog filters, including much sharper cutoff, software-modifiable characteristics, higher stability and reproducibility, and optimum performance without tweaking.

An important relationship is that the frequency resolution of an FFT in hertz, f_R, equals 1/T, where T is the record length in seconds. If the record length is 20 msec, the frequency resolution is 50 Hz. This resolution corresponds to the spacing between the FFT's frequency "bins" and can differ from the width of the bins at the ­3-dB points. (Although the bin width and spacing are not necessarily equal, they are related.) The ­3-dB bin width is the characteristic most closely related to a classic swept-frequency spectrum analyzer's resolution bandwidth (RBW).

Remember that in DSP-based analyzers, just as in swept-frequency units, the choice of RBW involves trade-offs. In both types of analyzer, a narrow RBW lets you see more spectral detail and reduces the analyzer's effective noise level, thus letting you see smaller signals. However, in both types of analyzer, narrowing the RBW increases the time necessary to examine a frequency band of a given width.

At 25.6M samples/sec, the original 20-msec record of the NADC signal contains 512k samples. Successive digital filtering and decimation operations reduce the effective sampling rate to 100k samples/sec and the record length to 2k samples. Decimation amounts to discarding samples after reducing the data bandwidth through lowpass filtering in the digital domain.

Decimation, not aliasing

Because of the bandwidth reduction, decimation reduces the number of samples without causing undersampling or aliasing. In the 89410A, the DSP hardware operates on the ADC's output in real time, enabling the instrument's memory to store only the decimated data. Thus, the base unit's 64-kbyte memory is more than adequate for the NADC signal; the 2k, 12-bit samples occupy only 4 kbytes.

The 2k samples produce a 1000-point, complex FFT (1000 values that are in phase with the carrier and 1000 values that are in quadrature). The spacing of the frequency bins is 50 Hz. Using a filter with a Gaussian shape, the width of each bin at the ­3-dB points is approximately 110 Hz. Of the 1000 points, HP considers the central 800 to be meaningful. The values at the edges of the FFT's frequency band are distorted by the characteristics of the digital lowpass-filtering function, which the processing algorithm applies to the original samples. Still, the central 800 points cover 40 kHz, a span that exceeds the width of the 30-kHz NADC channel.

The 89410A's dynamic-range specifications are complicated; they separate the effects of noise, distortion, and aliasing. The aliasing spec says that one full-scale, out-of-band tone produces a spurious response smaller than 80 dB below full scale.

Swept-frequency analyzers

Classic swept-frequency spectrum analyzers are complex, sophisticated instruments. Nevertheless, stripped to their bare essentials, these analyzers are conceptually simple (Figure 3). Although real implementations contain many more elements, a swept-frequency analyzer in its simplest form consists of little more than

• A sweep or ramp generator, which drives a CRT's horizontal deflection system and supplies an input to a wideband VCO, also called the LO;

• The VCO;

• A downconverter or mixer, which accepts the input signal and produces an output at a fixed IF that is lower than the input frequency;

• A variable-bandwidth filter centered at the IF;

• A detector, which converts the filter output to proportional dc;

• An amplifier, which drives the CRT's vertical-deflection circuitry; and

• The CRT.

Although insufficient for constructing a useful spectrum analyzer, these items are adequate to indicate how a spectrum analyzer works. A nonlinear process of heterodyning or multiplication takes place in the downconverter or mixer. Heterodyning combines input signals at different frequencies to produce an output signal that contains the sum and difference of these frequencies. The LO is one of the mixer inputs. If you want to convert 800- to 950-MHz signals to a 10-MHz IF, you might sweep the LO from 810 to 960 MHz. The mixer output would contain the desired 10-MHz component and another component that varies from 1610 to 1910 MHz in synchronism with the LO.

As you sweep the LO from 810 to 960 MHz, input signals of 820 to 970 MHz also produce mixer outputs at the desired 10 MHz. When the LO is at 820 MHz, the desired 10-MHz mixer output can result from an input at either 800 or 820 MHz. Thus, the hypothetical spectrum analyzer might tell you that a peak it displays is at 800 MHz, but, in fact, the peak could just as easily be at 820 MHz.

A practical spectrum analyzer eliminates this "image-frequency" problem through multiple frequency conversions. Instead of directly converting the 800- to 950-MHz band to 10 MHz, the analyzer might first convert the band to, say, 200 MHz. The analyzer could accomplish this conversion by sweeping the LO from 1000 to 1150 MHz. Such a sweep range yields image frequencies from 1200 to 1350 MHz. An appropriate lowpass filter (one with a cutoff frequency of, say, 1000 MHz) at the first mixer's input can make the analyzer insensitive to the higher frequency band, however. A second mixer can then down-convert from 200 to 10 MHz. Practical, heterodyne-based, swept-frequency spectrum analyzers often include four frequency converters.

The mixer successively converts slices of the 800- to 950-MHz range to 10 MHz. However, only if the original signal is a pure sine wave of constant amplitude is the mixer output a pure sine wave. Usually, modulation appears on the mixer's output signal. Stated another way, in the frequency domain, sidebands accompany the signal. The characteristics of the variable-bandwidth IF filter at the mixer output determine how closely you can examine the mixer output. And because the mixer output is a replica of the input in which the frequency is translated downward, the IF-filter characteristics determine how closely you can examine the input signal.

Resolution bandwidth

The narrower the IF filter's passband, the more detail you can see. However, as you narrow the filter passband by narrowing the RBW, you slow the filter's response to changes in the mixer-output amplitude. To obtain a correct output, you must lower the sweep speed. If you sweep the LO too rapidly for the bandwidth you choose, the filter does not respond, or it does not respond fully. The analyzer then either misses some components it could detect at lower sweep speeds or indicates that some components' amplitudes are lower than their true values. Microprocessors in some spectrum analyzers determine the optimum sweep speed for a given RBW, but these instruments often let you choose different settings.

A characteristic of spectrum analyzers, especially when you operate them with narrow RBWs, is wide dynamic range. Presenting signals on the display so that you can see dynamic ranges of 10⁶ or more is impractical using a linear scale. Therefore, in most spectrum analyzers, an amplifier either ahead of the detector or between the detector and the display logarithmically compresses the signals.

The simplified spectrum analyzer in this example uses an analog display. Although spectrum analyzers used such displays for decades, nearly all modern spectrum analyzers use digital displays, similar to those in DSOs. In general, spectrum-analyzer sweep times are long enough that analog displays are difficult to observe. Even with long-persistence phosphors, the trace will likely disappear from the left edge of the screen before the sweep is complete.

Through the use of DSO technology, modern spectrum analyzers eliminate such problems with relative ease (Reference 3). But, like deep-memory DSOs, spectrum analyzers use various algorithms to compress the display's large number of samples into a smaller number of on-screen pixel columns. Some algorithms are best for displaying the spectra of random noise; others are better for making low-amplitude spectral peaks stand out from noise. As a result, many spectrum analyzers offer a choice of display algorithms.

Defined personalities

The mobile-communications business has created a large number of standards to which mobile and base-station equipment must conform. These standards define frequency bands, modulation and data formats, and a host of other details. Setting up a spectrum analyzer to make measurements according to the protocols that these standards define is a tedious, time-consuming, and error-prone operation. Users have a right to expect something better; equipment manufacturers are providing it. Modern spectrum analyzers have software-defined personalities. Selecting a personality configures the instrument to make the tests that the appropriate standard defines.

In some cases, you select the standard from a menu and then select a test from a second menu. Many variations on this theme are possible, including loading personality definitions from a floppy disk or plug-in memory card.

The ability of spectrum analyzers to transmogrify themselves from general-purpose instruments to special-purpose units with narrowly defined functions raises an interesting question, however: When is it appropriate to use a spectrum analyzer, which is inherently a general-purpose device, and when is it appropriate to use a specialized test instrument? The answer is not too surprising. Generally, production, field-installation, and depot-repair activities use special-purpose instruments; R&D uses spectrum analyzers. The rule, of course, is not hard and fast. It is true, however, that R&D engineers often need to perform tests that people who deal with well-defined, released products need not worry about.

So, what should you look for in a spectrum analyzer? Support for the standards you will be working with on your next project is the first thing. However, you probably need to look down the road to at least one more project. For many EEs and managers selecting instrumentation, looking ahead means that, even if your next project deals mainly with carrier frequencies below 1 GHz, you probably need equipment you can use with carriers in the 2-GHz region. Many emerging standards, such as personal-communications service (PCS), use carriers at or near 2 GHz.

The rule of thumb in selecting spectrum analyzers has been to choose a unit that covers frequencies at least three times as high as your system's carrier frequency. A more conservative multiplier is five. If you look at the available instruments, choosing a spectrum analyzer for a 2-GHz-system project would narrow your choice to units whose frequency coverage extends to at least 7 GHz.

Indeed, you probably will need 7-GHz units for your 2-GHz project. But not all of your units may need such high bandwidth. Once you track down the gross sources of error that cause your system to produce or respond to out-of-band signals, you may be able to use units with a narrower bandwidth. For analysis of vector modulation, a unit that merely covers your frequency band may be adequate. On the other hand, you may occasionally need to search for interfering signals over a much wider bandwidth. For that purpose, you may need a unit that covers as high as 22 or even 26.5 GHz.

While you are thinking about instruments for your next few projects, give some thought to a related class of products. Although you need units such as spectrum analyzers to explore the modulated signals your products produce, you also need instruments that produce a variety of known-good signals so that you can investigate how your products respond. Thus, in addition to spectrum analyzers, you will need signal generators.

References

1. Brannon, Brad, "Wide-dynamic-range A/D converters pave the way for wideband digital-radio receivers," EDN, Nov 7, 1996, pg 187.

2. Travis, Bill, "Demystifying ADCs," EDN, March 27, 1997, pg 26.

3. Strassberg, Dan, "Digital oscilloscopes: For best results, understand how they work," EDN, July 4, 1996, pg 42.

4. "Using error-vector-magnitude measurements to troubleshoot vector-modulated signals," Product note 89400-14, part no. 5965-2898E, Hewlett-Packard, Palo Alto, CA, 1997.

5. "Eight hints for making better spectrum-analyzer measurements," Application note 1286-1, part no. 5965-7009E, Hewlett-Packard, Palo Alto, CA, 1997.

6. "Spectrum-analyzer basics," Application note 150, part no. 5952-0292, Hewlett-Packard, Palo Alto, CA, 1989.

7. "Spectrum-analyzer fundamentals," Application note, Tektronix Inc, Beaverton, OR, 1993.

8. "Guide to SPA," Guide to spectrum analyzers, Anritsu-Wiltron, Morgan Hill, CA.

9. Pocket glossary of spectrum- and network-analysis terminology, Wandel and Goltermann GmbH, Einingen, Germany, 1990.

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