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Agilent PN 89400-12
Understanding Time and Frequency Domain
Interactions in the Agilent 89400 Series
Vector Signal Analyzers
Product Note
A key strength of the Agilent Techno-
logies 89400 Series vector signal
analyzers (VSAs) is their ability to
move easily between time and fre-
quency domain measurements. This
flexibility is ideal for analyzing
signals that change with time, whether
they are modulated, burst, pulsed, or
transient.
However, when using both domains
simultaneously, one quickly finds Figure 1. Description of FFT terms
that measurement parameters in one
domain interact with those in the
other. Changing resolution bandwidth T = time record length (sec) while RBW is the analyzer's 3 dB
affects the length of the time display, Nt = number of time samples measurement bandwidth, usually
which may or may not be affected by t = sampling interval spanning more than one frequency
the frequency span selected, and so point.
forth. Each block of Nt samples yields a
block of N frequency points (i.e. a The proportionality constant in equa-
Some of these interactions reflect spectrum) where: tion (1) is simply the ratio of span to
unchanging physical law, while oth- sampling frequency, and is equal to
ers are the result of algorithms or F = spectrum width, or span (Hz) 1/2.56 for baseband spans and 1/1.28
operating modes built into the ana- N = number of frequency points for zoom.
lyzer's firmware for operating con- f = frequency point spacing
venience. Although they can all be Equation (2) may also be written as:
described mathematically, the graphi- The frequency domain data is tied
cal approach developed here will per- to the time domain data by two fun- RBW = ws/T
haps give the user a more intuitive damental relationships that are the
feel for the analyzer's operation. foundation for much of the discussion where ws is the window shape factor.
to follow. These are: The value for ws is dependent on
Fundamental concepts window type, as follows:
Agilent 89400 Series VSAs operate F 1/t (1)
by capturing a waveform in the time RBW l/T (2) Window Type ws
domain and using it to calculate a
spectrum (frequency domain) display. Note that resolution bandwidth Flat Top 3.8
A fast Fourier transform (FFT) algo- (RBW) is not the same as f. Rather, Gaussian 2.2
rithm performs the calculation, begin- as shown in Figure 1, f is the spac- Hanning 1.5
ning with a block of time domain ing of the displayed frequency points, Uniform 1.0
samples where:
Finally, note that this discussion of frequency points, has no effect on
applies only to the analyzer's Vector Tmin). With 10 MHz of span and the
and Analog Demodulation modes, and uniform window, the analyzer's short-
not to the Scalar or Digital Demodula- est possible time record is thus 352
tion modes. nsec, or 333 nsec rounded up to the
next multiple of t where, from equa-
Time vs. Frequency -- tion (1), t = 1/(2.56 x 10 MHz), or
39 nsec.
A Graphical Approach
Any Agilent 89400 Series VSA meas-
urement setup involves a choice of Figure 3. Addition of RBW scales to
measurement span (F) and time the T vs. F axes
record length (T). The values chosen
for these parameters strongly influ- Tmax Lines
ence measurement performance in The first lines plotted on the T vs. F
areas such as resolution, speed, and axes show Tmax, the maximum time
accuracy--in short, they determine record length that the analyzer can
the analyzer's ability to provide the display for a given frequency span and
desired insights into the signal under number of frequency points according
test. Because of this, these two vari- to the relationship
ables are the fundamental axes upon
which the analyzer's operating modes Tmax = (N-1)/F. Figure 5. Tmin as a function of F and
will be portrayed (Figure 2). window type
As will be shown later, T may be
adjusted to be less than Tmax, but Operating Region
can never exceed it. Because N is Using these concepts, an operating
limited to certain discrete values (51, region can now be defined for the
101, 201, 401, 801, 1601, or 3201), a 89400 analyzers (Figure 6), bounded
family of lines shows all possible val- by 1 Hz and 10 MHz on the frequency
ues for Tmax (Figure 4). As shown, a span axis, and by Tmin and Tmax on
frequency span of 2.5 MHz with 401 the time axis. This region is signifi-
points of resolution yields a maximum cant in that it contains all valid com-
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