When
and How to Apply
FFT-Based Spectrum Analyzers
by
Mike Beane, Contributing Editor
Spectrum analyzers are designed in two
hardware configurations, so dissimilar that it is difficult to recognize
them as performing the same function. Depending upon the application, each
configuration has its place in the engineer’s arsenal of test tools.
A classic spectrum analyzer is a narrowband
radio receiver tuned rapidly over a band of frequencies. The output signal
of the receiver is plotted or graphed as the vertical component against the
frequency as the horizontal component. This plot usually is done in real
time on an oscilloscope screen. This classical approach is still used for
frequencies above 200 MHz.
Vast improvements in receiver stabilization
and the application of automated controls have resulted in spectrum
analyzers that can be used with far less training, setup, and measurement
know-how than those available a couple of decades ago. "The capability
of an instrument to calculate and make decisions takes the evaluation of the
measured results out of your hands and puts it into the hands of the design
engineer," said Tom Rittenhouse, application engineer at IFR Americas,
formerly Marconi Instruments. "In the past, all phases of the test were
a possible source of error."
Aside from fewer knobs to turn, the
capability of producing a hard-copy graphical spectrum output has been the
single improvement that has kept the classical spectrum analyzer a highly
useful engineering tool.
A more recent spectrum-analyzer design
produces the same output with a much different technique. This approach uses
a digital data acquisition system to capture or sample the waveform of
interest and then performs a digital mathematical operation called a fast
Fourier transform (FFT) upon the stored data. The result of this process is
a set of numbers which, when graphed, is a magnitude vs frequency plot
representing the frequency spectrum of the signal being evaluated.
Sri Welaratna, president and CEO of Data
Physics, described the data acquisition/FFT type of spectrum analyzer
hardware. "Today, the image of a spectrum analyzer is a computer screen
with a graphical user interface and the color signal graphics of infinite
flexibility. The measuring instrument itself is a digital signal processing
(DSP) board with on-board analog-to-digital converters (ADCs) and
digital-to-analog converters (DACs)", he explained.
Both techniques work well within their
limitations. The data acquisition/FFT technique is limited in the maximum
frequency that it can detect, with the ADC that digitizes the input waveform
being the limiting factor.
Currently, these devices have an upper limit
of around 400 MHz for their conversion speed. The FFT process only will
correctly identify frequency information in a sampled waveform if the
sampling process operates at least twice the frequency as the highest
frequency of interest. This limitation is known as the Nyquist criteria.
If a frequency higher than one-half the
sampling rate is encountered with this type of system, an effect called
aliasing occurs. Aliasing causes the frequencies above the Nyquist limit to
be read as the difference between the sampling rate and the input
frequencies. Any spectrum obtained under this condition is totally
erroneous.
Most spectrum analyzers that use the FFT
technique include a low-pass filter that eliminates frequencies above the
Nyquist cutoff limit before applying the signal to the DAC. While this makes
aliasing unlikely, it gives no indication of any frequency above the
low-pass filter cutoff.
There is some good news. The hardware for
the FFT/data acquisition type of spectrum analyzer is much less expensive
than the classic variety, and the setup and operation are less complicated.
There also is no delicate detector diode to be damaged by inadvertent
overloading, and instrument stability is inherently better in the FFT/data
acquisition configuration.
Another benefit was mentioned by Wes
Stamper, technical marketing specialist at IFR Americas. "When using an
FFT analysis to evaluate the frequency spectrum, the receiver system is
completely locked to a reference. As a result, there is no frequency drift
in the system, and the signal being tested will be as accurate as the time
base of the system," he said.
Digitizing the input waveform provides two
advantages over the classical spectrum analyzer. These advantages are
especially important when dealing with sporadic or infrequent signals.
The first benefit is a result of the input
section being a data acquisition system. The data-acquisition configuration
allows data capture to be triggered on an event such as reception of a
trigger pulse.
Also, the spectrum will be a captured
waveform of known length. So if a waveform is changing, or of short
duration, data capture can be easily limited to the known interval. During
that interval, no component will be lost, and unwanted signals will not be
included.
By comparison, the classical spectrum
analyzer will only be sensitive to one frequency at any given instant and
possibly miss data that occurs sporadically. This is not a concern for
steady-state signals such as a radio- frequency carrier, but can cause
incorrect results when analyzing nonrepeating signals such as acoustical
signals from shock stimuli or other pulse-induced waveforms.
The FFT is the digital realization of a
method to determine how large each component frequency must be to reproduce
a waveform. Another advantage of the FFT was pointed out by Pete Watridge,
product manager of the Hewlett-Packard Microwave Instruments Division:
"An FFT analyzer determines the phase and magnitude of the frequency
spectrum. A typical swept-tuned spectrum analyzer only provides magnitude
information."
To use an FFT analyzer effectively, we need
to know what conditions must be met to assure that it works properly. This
leads to some terms that you might encounter on the spectrum-analyzer
controls.
FFT length is the first to consider. This is
how many points of data are to be included in the FFT. Strictly speaking,
FFT lengths must be exact powers of 2.
If the instrument allows you to choose a
number other than an exact power of 2, it is performing a behind-the-scenes
calculation to add enough extra points to make a data sample with an exact
power-of-2 data points before performing the FFT. Since this could introduce
an error and requires additional calculations that increase processing time,
it always is best to use an FFT length that is a power of 2.
The FFT length, combined with the sample
speed, also determines the resolution of the spectrum. For example, if a
signal is sampled at 100 kHz for 1,024 samples, the highest detectable
frequency will be 50 kHz, and the smallest difference will be 50 Hz. If the
number of samples is doubled to 2,048, the resolution will double to 25 Hz.
If we increase the sample rate to 200 kHz while keeping the sample size at
2,048, the highest frequency detectable will be 100 kHz with the resolution
reverting to 50 Hz.
As this example illustrates, the uppermost
detectable frequency is determined by the sampling speed and the frequency
resolution or discrimination by the sample length.
As the sample length increases, so does the
computational time required to perform an FFT. Specifically, the
mathematical operations increase logarithmically with greater length. If
your spectrum-analyzer requirement needs fast, high-resolution,
high-frequency performance, look for specifications that include higher
processing speeds. Better yet, use DSP chips that are hardwired and
optimized to perform only this operation at very high speeds.
Spectral Leakage
Windowing is another option when using an
FFT. In this operation, the input data set is multiplied by a set of numbers
that diminishes the data at both ends of the input data set.
Windowing is an attempt to minimize an
effect called spectral leakage. Spectral leakage is a byproduct of one of
the constraints under which the FFT was derived.
The frequencies that an FFT can use to
reproduce the input waveform must be an integer multiple of the sampling
frequency divided by the record length. If a component frequency does not
meet this requirement, the FFT substitutes frequencies that it can use to
reconstruct the input frequency.
As the input frequency differs from the
allowable component frequency, larger amplitudes of more frequencies are
required to reconstruct it. This appears on the output plot as an increasing
noise floor or wider frequency peaks. Three methods can reduce this apparent
noise caused by spectral leakage.
The first method is the easiest—simply
increase the sample rate and size. With more points of input, there are more
frequencies closer together for the FFT to use and less spectral leakage.
The second method is to change the sampling
frequency slightly to find a frequency that minimizes the variance between
the FFT frequencies and the input waveform frequency components. This can be
done visually, tuning the frequency for a minimum noise floor or narrowest
spectral peaks.
The technique of last resort is windowing.
This operation only is useful if you are looking for harmonics and wish to
exclude or minimize other signals. Using an FFT window increases processing
time and distorts the results.
If your FFT analyzer contains a control to
select different windows, "no window" usually is not indicated as
an option. Instead, a selection labeled "rectangular window" will
be present. A rectangular window is the same as no window.
For best resolution, use the rectangular or
no window. For minimum spectral leakage, use a Blackman/Harris window. If a
window type other than rectangular is used, center the input waveform in the
sample window.
Spectrum Analyzers
New Products
Two-Channel Analyzer Provides
Printer and Computer Interface
The SR785 Signal Analyzer offers two
independent 32-bit channels of 100-kHz real-time bandwidth with a 90-dB
dynamic range in the FFT mode or 145 dB in the swept sine mode. Data may be
saved to a built-in 3.5" disk drive or outputted directly to a printer,
plotter, or a host computer via GPIB or RS-232 formats. The 8-MB memory is
expandable to 32 MB. $10,950. Stanford Research Systems, (408)
744-9040.
Analyzer Targets Cable TV Needs
The 2625 Spectrum Analyzer covers
frequencies from 150 kHz to 1.05 GHz with a dynamic range of 80 dB. It
accepts up to a +20-dBm input signal and has a built-in step attenuator.
Scan widths are switch-selectable from 50 kHz/div to 50 MHz/div. A 4-digit
LED identifies the tuned center frequency. The unit weighs 13 lb. $2,195. B+K
Precision, (714) 237-9220.
Field Frequency Analyzer
Achieves Minimum Size
The SignalCalc® ACE PCMCIA Data Acquisition
Card and Software weigh in at just 2 oz. When installed in a laptop
computer, these components constitute a portable signal analyzer and data
acquisition system that simplifies field collection, storage, and review of
collected vibration data. The Windows-based software includes full FFT
capabilities and has optional add-ons for high resolution,
throughput-to-disk, replay, and ActiveX connectivity. Call company for
price. Data Physics, (408) 371-7100.
Signal Analyzer Targets
Digital TV Broadcast Market
The HP89441V VSB/QAM Signal Analyzer
performs comprehensive testing of the FCC-mandated digital TV transmission
format including vector modulation analysis of Quadrature Amplitude
Modulation (QAM) and Vestigial Sideband (VSB) formats. It operates over a
frequency range from 0 to 2.65 GHz. The full-color screen output includes
eye, constellation, and vector formats. An optional second input channel
allows simultaneous view of baseband I and Q channels. $58,300.
Hewlett-Packard, Microwave Instruments Division, (800) 452-4844, ext.
5522.
Portable Spectrum Analyzer
Has Microwave Capability
The AN1800 Spectrum Analyzers have a 7-in.
color LCD and a built-in frequency counter accurate to 1 Hz. They also offer
DSO and FFT functions. The fundamental frequency ranges from 9 kHz to 2.9
GHz with options to 26.5 GHz. The amplitude measurement range is -135 to +30
dBm. Digital filters enable bandwidth resolution selectable from 3 Hz to 30
MHz with ±300 divisions of pre- and post-trigger range. The memory stores
up to 99 traces. From $15,695. IFR Americas, Inc., (800) 835-2352.
Spectrum Analyzer Offers
Full CDMA Measurements
The FSE Series Spectrum Analyzers feature a
116-dB dynamic measurement range and a 0-dB figure of merit to direct
adjacent channel power measurement for W-CDMA applications. The unit has a
full-color 9.5" LCD, a printer/plotter output, and disk storage.
Specifications include an input frequency range from 20 Hz to 40 GHz,
resolution to 1 Hz, and a full span sweep time of 5 ms. From $29,995. Tektronix,
(888) 835-2001.