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 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.

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.

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.

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**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.**