An oscilloscope that has a 1-GHz analog bandwidth and up to a 5-GS/s sample rate will
be used for measurements. These are both important specifications that will tie into
what kinds of measurement applications are possible. The first example measurement
is the capture of a 600-MHz, 632-mV (p-p), 0-dBm, 1-mW sine-wave signal into 50 ?
(orange) and resultant FFT (white) as shown in Figure 1.
[attach]2307[/attach]
Figure 1. Time-domain capture at 1 ns/div and FFT display from a 600- MHz sine-wave input
It’s important to understand how the oscilloscope sampling characteristics play
into the quality of this FFT measurement. The oscilloscope analog bandwidth,
sample rate, memory depth, and related time capture period all can have a
profound effect on the measurement result. This effect is heavily influenced by
the characteristics of the signal under test and how those signal characteristics
are related to the oscilloscope capture performance.
For example, in this simple illustration of measuring a single-tone 600-MHz sine-
wave signal and wanting to see the basic spectral characteristics of that signal,
the oscilloscope has to have enough analog bandwidth to minimally attenuate the
amplitude of the signal. Since this oscilloscope has a maximum 1-GHz analog
bandwidth, there is plenty of oscilloscope bandwidth to measure the 600-MHz
tone.
To avoid aliasing in the digitizing process, sampling must occur at a rate at least
twice the frequency of any appreciable frequencies present in the signal under test.
In this example, a 1.2-GHz sampling rate would be required. Clearly, if the scope is
sampling at its maximum 5-GS/s rate, that is more than sufficient. However, it will
be shown later that for certain scope time-base settings the sample rate (and
bandwidth) will decrease.
So what kind of quality is there in the FFT measurement made on the 600-MHz sine
wave? Referring back to the oscilloscope FFT measurement in Figure 1, notice the
main single frequency spike with a related measurement marker showing around a
600-MHz frequency and 0-dBm power. That matches expectations, but the FFT
response looks very wide for a single frequency input signal.
So what kind of quality is there in the FFT measurement made on the 600-MHz
sine wave? Referring back to the oscilloscope FFT measurement in Figure 1, notice
the main single frequency spike with a related measurement marker showing around
a 600-MHz frequency and 0-dBm power. That matches expectations, but the FFT
response looks very wide for a single frequency input signal.
The spacing between frequency spectrum lines in the FFT, or the width of frequency
buckets that signal energy is apportioned to, is called the frequency resolution. It is
based strictly on the time length of the acquired data and a factor for the FFT windowing
type selected. A rectangular window is used here with a factor of 1, so the frequency
resolution is simply the inverse of the record time. In this example:
Frequency Resolution = 1/(1 ns/div x 10 div) = 100 MHz
So this FFT could distinguish frequency components in the signal spectrum as close as
100 MHz, but any components closer than 100 MHz apart would merge together and
be indistinguishable. That’s actually a really coarse measurement.
How an increased time on screen enhances the FFT responseTo demonstrate the importance of the record time upon FFT results, if the time/division
is panned to 200 ns/div, with a new record time of 2 μs across the screen, the frequency
resolution changes drastically to:
Frequency Resolution = 1/(200 ns/div x 10 div) = 500 kHz
The significant change in the FFT result can be seen in Figure 2 with a much finer display
of the 600-MHz frequency-domain spike. A trade-off is happening here. More time samples
are being processed, the calculated FFT has more spectral lines, and better frequency
resolution results. But the measurement runs slower than before to process more data—
10,000 samples instead of the original 50.
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Figure 2. Time-domain capture at 200 ns/div and resultant FFT calculation with a 600-MHz sine-wave input
An important capability in the FFT calculation and resultant view is to be able to
zoom into an area of interest for analysis. The first example had a wide span from
0 Hz to 2.5 GHz, so it was difficult to see any detail around the 600-MHz carrier.
Suppose there was suspected noise around the 600-MHz carrier frequency and a
desire to inspect that. The FFT controls can set a center frequency at 600 MHz and
a desired span, such as 100 MHz, around the 600-MHz carrier. A start frequency
of 550 MHz and stop frequency of 650 MHz also could have been selected with
the same result. An FFT measurement with these parameters can be seen in
Figure 3.
[attach]2323[/attach]
Figure 3. FFT of 600-MHz sine-wave input when FFT controls set for a 600-MHz center frequency and
100-MHz span
An increasing number of today’s signals have modulation present that can increase
the spectral width to hundreds of megahertz or even multiple gigahertz. If spectral
widths of signals are beyond around 500 MHz, then spectrum analyzers or vector
signal analyzers available today do not have enough analysis bandwidth to make
meaningful measurements. In such cases, an oscilloscope or digitizer is required
that has enough analysis bandwidth for the application.
The carrier frequency of a signal of interest also is important. The carrier frequency
of the signal under test plus half the spectral width of that signal must be less than
or equal to the oscilloscope bandwidth for the oscilloscope to be used on its own for
the measurement. A wideband signal frequency domain measurement will now be
considered.
The signal under test is a 600-MHz RF pulse train, with 4-μs-wide RF pulses repeating
every 20 μs. There is a linear frequency modulation of the signal that chirps the carrier
frequency from 300 MHz at the start of the RF pulse envelope to 900 MHz at the end of
the pulse envelope.
To make a basic FFT measurement of the RF pulse, the first step is to get a clean time-
domain capture of a pulse from the signal on screen. The scope is reset to a known condition
by pressing Default Setup. Then Auto Scale is pressed, and the time/division setting is adjusted
to bring one main RF pulse on screen. The basic default rising-edge trigger is further qualified
with trigger holdoff. This ensures that a trigger doesn’t happen mid-pulse since that would create
instability in the captured trace. The trigger holdoff is set to something slightly longer than the
width of the RF pulse. The RF pulse is 4 μs wide so a trigger holdoff of 5 μs works well.
Markers are placed on the FFT response, and it can be seen that this RF pulse does
have a wide spectral width, from 300 MHz to 900 MHz, or 600 MHz wide. What’s not
yet proven is that the frequency of the carrier shifts from 300 MHz to 900 MHz, linearly,
from the left side of the pulse across to the right side of the pulse.
The gated FFT math functionOne way to quickly see some carrier frequency values across the pulse is to use the gated
FFT function. This is achieved by turning on the normal time-domain trace time gating
function. This function generates a normal trace view at the top half of screen and a
magnified view at the bottom of the screen. The time/division control expands and shrinks
the time-gate window placed on the upper normal trace, and the time delay control moves
the window along the trace. Whatever portion of the waveform is present in this window
shows up in the lower trace, but magnified.
An interesting measurement results from creating a small time-width window at the very
beginning of the pulse. The FFT is calculated from the data contained within the gated time
window as shown in Figure 5.
[attach]2345[/attach]
Figure 5. Time-gated FFT function observing the carrier at the beginning of the RF pulse
The FFT measurement of the peak value amplitude and frequency of the spike
shows that the RF pulse begins with a carrier frequency around 300 MHz. If
the time-gate window is moved to the center of the RF pulse, the frequency
is seen to be around 600 MHz. And it is 900 MHz at the end of the RF pulse.
This appears to be a linear frequency-modulated chirp as desired.
Frequency measurement and measurement trend math functionIn some cases, a measurement trend math function can give a helpful view of
the frequency chirp profile. The oscilloscope is able to display up to 1,000
measurements in a trend format. In a similar signal example, a 600-ns-wide
pulse train, repeating every 20 μs, needs to be verified. The FFT function now is
turned off, and purely time-domain measurements are made.
Clearly, the pulse carrier is shifting in a linear fashion across the pulse, from left
to right, as designed. Notice that the linear ramp display is not going across the
entire width of the RF pulse. This is because the 1,000 measurement limit in the
trend calculation has been reached. It is important that a portion of the pulse FM
function can be seen, and it is linear. For the frequency measurements across the
pulse to have enough precision, it was imperative that the High Resolution
acquisition mode was selected.
SummaryFFTs in oscilloscopes are a valuable tool to give a frequency-domain view of a signal.
This can ultimately be done with very wide bandwidth, enabling measurements not
possible with a narrower band vector signal analyzer. Example FFT measurements
were able to verify that a linear FM chirp signal was shifting the carrier frequency
as it should. There also was a place for other math functions, namely the measurement
trend function. In this example, such a calculation allowed for a very simple verification
of a linear FM chirp.
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