Spectrum Analysis Logo Spectrum Analysis

Applications and Tutorials


The following excerpts and summaries from JMS authored materials on spectrum analysis are provided for your reference.

Index To Spectrum Analysis Applications and Tutorials


What Is A Spectrum Analyzer?

Time and frequency have a dual relationship, one being the reciprocal of the other. These are known as the time domain and frequency domain respectively. The primary time domain test instrument is the oscilloscope and the primary frequency domain test instrument is the spectrum analyzer. Fourier mathematics provides a transition between these domains by means of the Fourier transform equations. The ideal way to obtain frequency spectrum information is to sample the signal in the time domain and compute the frequency domain result using Fourier mathematics. There are a number of instruments on the market that follow this process. These are usually known as Fourier analyzers, digital Fourier analyzers (DFT), fast Fourier analyzers (FFT) and sometimes spectrum analyzers. Unfortunately, current technology is limited in the upper frequency for this procedure into the low MHz range. A different methodology needs to be used at RF and microwave frequencies, though sometimes a downconverter is combined with a DAFT instrument to permit digital spectrum analysis at higher frequencies.

The alternate procedure is based on the convolution, or sliding (sweeping) past each other, of the spectrum to be obtained with a very narrow frequency domain filter (ideally an impulse). It can be shown mathematically that such a procedure will result in the frequency domain characteristics (the spectrum) of the signal. This filter is known as the resolution filter, and it is a critical part of all sweeping spectrum analyzers. This type of spectrum analyzer, in the form of a special purpose calibrated receiver, is what is meant by the designation "spectrum analyzer" on this web site.


The Resolution Circuit Filter and Signal Classes

The bandwidth of the intermediate frequency (IF) circuit, known as the resolution filter, is an important measurement parameter. It is controlled by a front-panel control known as the resolution bandwidth (RB) control. There are three bandwidths associated with this circuit, depending on the type of signal to be measured. These are: The resolution bandwidth (RB) for continuous wave sinusoidal signals, the impulse bandwidth (IB) for pulsed signals, and the random noise bandwidth (RNB) for random signals. The numeric values and relationships between these bandwidths depends on the type of circuit used. The following relationships will be correct for most spectrum analyzers.

B6/B3 = 1.5, B60/B3 = 10, Bi/B6 = 1.09, Bn/B3 = 1.13. Where: B3 = 3 dB bandwidth, B6 = 6 dB bandwidth, B60 = 60 dB bandwidth, Bi = impulse bandwidth, Bn = noise bandwidth. For most applications. B3 should be less than the frequency spacing of sine wave signals, Bi should be more than the pulse repetition rate frequency (PRF), and Bn should be less than the occupied bandwidth of a random signal such as in digital modulation.


Signal Sensitivity And Dynamic Range

Sensitivity refers to the smallest signal to which ,or with which, something useful can be done. As such, it is a moving target which depends on the type of signal involved and what is to be done with that signal. To provide a uniform standard, sensitivity is measured as the spectrum analyzer noise level within a chosen resolution bandwidth. We usually choose the narrowest bandwidth, and this is usually indicative of the smallest sinusoidal signal that can be detected. This sensitivity noise level is equal to N = kTBF, where kTB yields the smallest exchangeable thermal noise of the circuit and equal to -174 dBm per one Hz of bandwidth at a temperature T = 290 degrees absolute. The excess noise of the system is represented by F, the noise figure or noise factor. The best current spectrum analyzers have a noise figure F = 15 dB, and a typical instrument has F = 30 dB. Thus, a typical spectrum analyzer will have a -135 dBm sensitivity noise level at a 10 Hz bandwidth and 29 dB noise figure.

Dynamic range (DR) refers to the dB difference of small and large signals tested together. The small signal limit comes from the sensitivity. The large signal limit is usually determined by the third-order intermodulation (TOI) performance. This is indicated by the third-order intercept point, I3, where the main signal and intermodulation spurious signal intersect. The following relationships connect, DR = dynamic range in dB, N = sensitivity noise level in dBm, S = one of two tones signal level in dBm, I = intercept point in dBm, n = intermodulation order number. I = [DR/n -1] + S; DR(best) = (n -1)(I - N)/n, S(best) = [(n -1)I + N]/n.

Example: @ F =29 dB and a 10 Hz bandwidth, N = -135 dBm. We measure a 90 dB DR for -30 dBm signals, then I3 = 90/2 - 30 =15 dBm. Hence the best dynamic range we can get with this instrument is DR(best) = (3 - 1)(15 + 135)/3 = 100 dB. To achieve this result, it is necessary that the signal level be at S(best) = [(3 - 1)15 - 135]/3 = -35 dBm.

The above works reasonably well for sinusoidal signals, but not for digital modulation which generally looks like random noise. Measures for such signals are basically independent of the measuring bandwidth, hence relationships that depend on N = kTBF will not work. There are a number of dynamic range indicators for such signals. A simple rule of thumb is that DR(best) = 70 + I3 - F dB. The expression I - F is known as the dynamic range factor (DRF). For the example used above, we have 70 + 15 - 29 = 56 dB, compared to 100 dB for sinusoidal signals.


Spectrum Analysis Articles and Papers Of Interest

Here is a partial listing of papers on spectrum analysis authored or co-authored by consultant, Morris Engelson, since 1990:

Correcting for Spectrum Analyzer Noise in Digital Modulation Measurements, RF Design, Sept 1999. (See www.rfdesign.com)

Provides table of correction factors and shows how to compute additional correction factors.

Distortion Measurements Using the Spectrum Analyzer, RF Design, March 1995. (See www.rfdesign.com)

Shows how to measure a variety of signals for distortion characteristics.

Digital Modulation Dynamic Range, Microwaves & RF, September 1998. (See www.penton.com – look for Microwaves & RF)

Traditional ways of treating dynamic range for sine wave signals must be reevaluated in the presence of digitally modulated signals. This papers shows how to do it.

Effective Characterization of CDMA Signals, Microwave Journal, January 1995. (See www.horizonhouse.com – look for Microwave Journal)

Discusses the CDMA signal and how to measure using a spectrum analyzer.

Frequency Spectrum Factors of the Digital Video Signal, Communication Systems Design, August 1997.

Analog signals are rarely perfect, and they degrade gradually. Digital signals are frequently perfect, but when they fail, things pretty much go dead. That is why testing for and controlling impairments on a digitally modulated signal is essential.

Gage the Effect of Noise Figure on Spectrum Analyzers, Microwaves & RF, July 1995. (See www.penton.com – look for Microwaves & RF)

Sensitivity is an indicator of the smallest signal that can be detected, identified, or measured with a receiver such as a spectrum analyzer. The usual numeric measure of sensitivity is provided by the instrument's noise level. A novel figure of merit, termed the dynamic-range figure (DRF), describes the measurement range of spectrum analyzers independent of the measurement bandwidth.

Get Fast Measurement Results On The Spectrum Analyzer, EDN, January 20, 2000. (See www.cahners.com)

This paper discusses the relationship between sweep (measurement) time and accuracy, and the impact of different signal types on the above. The reader is provided with procedures and examples to permit much faster measurements, in most cases without loss of very little loss in measurement accuracy.

Improve Measurement Accuracy with Bandwidth Related Factors in Spectrum Analysis, RF Design, October 1994. (See www.rfdesign.com)

Learn how to correct for bandwidth related factors to improve measurement accuracy.

Learn to Gage Spectrum Analyzer Dynamic Range, Microwaves & RF, January 1990. (See www.penton.com – look for Microwaves & RF)

Spectrum analyzer users could benefit from a single dynamic range specification that compares the overall performance of various instruments. Unfortunately, no single measure of dynamic range can predict spectrum analyzer performance in all applications. But being familiar with various specifications and how they relate to the instrument's operation removes much of the confusion from predicting measurement capabilities.

Measures of EMC, EMC Test & Design, Nov/Dec 1990.

A review of basic EMC measurement techniques and standard practices, including a discussion of: narrowband and broadband signals, peak and quasi-peak detectors, bandwidths, derivation and explanation of the antenna factor.

Measurement Of A Small Signal Near A Large Signal Using A Spectrum Analyzer, Microwave Journal, March 1999. (See www.horizonhouse.com – look for Microwave Journal)

Large signals tend to obscure small signals and introduce measurement problems and errors. This paper explores measurement limitations and discusses proper measurement procedures.

The Pulse Desensitization Factor, Microwave Journal, March 1998. (See www.horizonhouse.com – look for Microwave Journal)

An advanced look at the complexities of the signal level loss due to the phenomenon known as "pulse desensitization".

Reciprocal Spreading Equals Spectrum Analysis Minus Math, EDN, May 27, 1999. (See www.cahners.com)

Shows how to determine pulsed-signal spectra using reciprocal spreading relationships.

Signal Near Noise Measurements Using a Spectrum Analyzer, Microwave Journal, May 1992. (See www.horizonhouse.com – look for Microwave Journal)

A discussion on the sources of error and how to correct for it when measuring various types of small signals with a spectrum analyzer.

Spectrum Analysis in Wireless Transmission Systems Design, Communication Systems Design, June 1995. (See www.mfi.com – look for Communication Systems Design)

A tutorial on the use of the spectrum analyzer in the design of wireless systems.

The 6 dB Bandwidth in EMI Measurements, Compliance Engineering, Jan/Feb 1994.

It is true that impulse bandwidths are usually very similar to 6 dB bandwidths. It is also true that usually does not mean always. This paper discusses the difference and impact on various EMI measurements.

The Measurement Sequence In Spectrum Analysis, RF Design, June 2000. (See www.rfdesign.com)

Learn the three-step hierarchy to get the most out of your spectrum analysis measurements.

Use the Spectrum Analyzer's Zero-Span Setting, Microwaves & RF, March 1996. (See www.penton.com – look for Microwaves & RF)

This setting enhances measurement capability by allowing the analyzer to perform as a fixed-frequency receiver. A number of measurement procedures and applications are illustrated.

Use Wide-Bandwidth Analyzers to Gage Signals Effectively, Microwaves & RF, January 1991. (See www.penton.com – look for Microwaves & RF)

Spectrum analyzers are increasingly being designed with greater resolution bandwidths. These high-bandwidth analyzers offer greater measurement accuracy and convenience in certain applications. A proper understanding of the advantages and disadvantages of high-bandwidth analyzers ensures optimum accuracy and measurement ease.

Using A Spectrum Analyzer's Video Filter Bandwidth, Microwaves & RF, March 1999. (See www.penton.com – look for Microwaves & RF)

Most spectrum analyzer users may have only a vague idea what this function is for, or how to use it. By understanding the proper use of the VFB, most spectrum analyzer measurements can be significantly improved.

Using Spectrum Analysis in Digital Design, Electronic Design, April 17, 1995. (See www.penton.com – look for Electronic Design)

The move to higher clock frequencies is forcing digital circuit designers to confront RF transmission issues involving a broadband spectrum analyzer.



All information on this page copyright © JMS, 1999. This information may be copied in whole or in part as long as all copied material is credited to JMS.

For More Information:

Heavenly Time Machine:
Science and Torah

Pricing Logo Business Strategy


Consulting Services


JMS Home Page



Consulting Services


JMS Home Page



Consulting Services


JMS Home Page