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Introduction
In recent correspondence with a beta tester, I was
asked to explain the relationship between resolution bandwidth (RBW), span,
dwell, skip and video averaging, and to help him understand why the display
looked the way it does for various signal types, and in particular SSB voice
signals.
This page expands upon my answers to the beta tester
and will be incorporated into the Z90 Operating Manual's next update.
You may also wish to view the page
Modulation to see examples of different
modulation types displayed on the Z90.
These concepts are commonly used in spectrum analyzers
but are not so often found in day-to-day ham radio activities. I'll try to
keep my explanations simple, but I'm not promising success in that effort.
And, remember, I said "simple" not "short."
Since this is a long page, I've provided book marks to
jump to different sections:
Let's start by defining the key terms:
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Span
Span is sweep width, expressed in KHz. Span is measured from the
left side of the display to the right side. In the illustration, span is
set to 200 KHz, so each of the 10 major divisions corresponds to 20 KHz.
The frequency your receiver is tuned to is at the center of the grid.
To the left side, signals are lower in IF frequency
and to the right side signals are higher in IF frequency. Whether that
means that signals on the right hand side of the screen are actually above
the frequency you are tuned to depends on the design of your receiver and
the band to which you are tuned. Some, indeed many, receivers "invert" the
IF so that IF frequencies that are physically higher in frequency than the
center of the passband actually represent signals that are lower in RF
frequency. And some receivers reverse this relationship on different
bands. You can determine whether your receiver is inverting with a bit of
experimentation, or it may be covered in the instruction manual.
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Resolution Bandwidth (RBW)
works the same way as the bandwidth control does on your receiver. 200 Hz
is narrower than 1 KHz.The two screen
captures show a steady sine wave (think of it as tuning your receiver to a
steady carrier signal) with the RBW set at 200 Hz and at 1000 Hz (1 KHz)
with the span identical at 20 KHz in both illustrations.
You should note a couple of things about these
images.
- Although the input signal is of identical
strength in both images, the indicated level in the 1 KHz RBW example is
about 5 dB stronger. This difference is due to the 200 Hz filter having
greater insertion loss. I could have added extra loss to the 1 KHz
filter to make the amplitudes identical (this is normally done in
commercial spectrum analyzers) but I decided to retain the benefit of
slightly better performance with the wider filter.
- Also note the noise level, at the edges of the
display. The 1 KHz filter shows more noise. This is in part due to the
reduced insertion loss, but in greater part it's because the wider
filter lets more noise in. You've probably seen this with your receiver
-- the wider the bandwidth you use, the more noise you hear.
- The filters are not "brick wall" design, but
rather have a rounded nose and gentle flank slope. This is
characteristic of Gaussian filters of the type used in the Z90. This
filter might be a poor choice for a receiver, but it's near optimum for
a frequency swept device such as the pandapter, as it has excellent
transient response.
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Resolution Bandwidth (continued). Why call it "resolution"
bandwidth? After all, your receiver control is labeled simply "bandwidth" in
most cases.
The answer is that the bandwidth setting determines
how closely spaced multiple signals may be and still be distinguished
("resolved" in scientific terminology). Think of it as how you will
use narrow bandwidth when trying to receive one signal with an interfering
signal nearby--you decrease the bandwidth until the interfering signal is
outside the filter passband.
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Let's look at an AM signal, modulated 100% with a 1 KHz
audio tone. Theory says this signal will have three discrete spectral
frequencies; the carrier, the lower sideband and the upper sideband. The
two sidebands will be equally spaced from the carrier, with the separation
equal to the modulating frequency.
Theory also says that for 100% modulation, each
sideband will be 6 dB below the carrier.
The diagram to the right shows our AM waveform's
theoretcial spectrum display.
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| I've set my Telulex SG-100
Function Generator to create a 100% modulated AM signal, with center
frequency 455 KHz and 1 KHz modulating frequency, an exact match for this
theoretical signal. Here's how it looks on the Z91, with 200 Hz RBW and 1
KHz RBW. |
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Here's the scan image with 200 Hz RBW. Both the upper
and lower sidebands are clearly distinguishable, and can be accurately
measured, both in frequency and amplitude. The frequency difference
between the carrier and each sideband is 1000 Hz, as close as can be
measured from the image, and the difference in amplitude between the
carrier and each sideband also matches the theoretical 6 dB value.
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Here's the same waveform, but with 1 KHz RBW. We can
just resolve the modulating frequency, and can more or less estimate the
difference in amplitude, but clearly our job of measuring is much more
difficult than with 200 Hz RBW.In fact, we
can barely separate or resolve the sidebands with 1000 Hz separation.
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Dwell is a measure of how long the Z90
remains on a frequency before taking an amplitude measurement.
A simplified version of the measurement sequence is:
- Go to the next frequency step
- Wait a pre-determined time (dwell)
- Read the signal amplitude with the
microcontroller's analog-to-digital converter
- Output amplitude via RS-232 and plot on LCD (if
Z90)
- Repeat for the next frequency step
Why should there be any wait -- can't you measure the
signal level immediately after each frequency step?
The answer is that although you can do that, the
results will be in error.
From filter theory, we know that a pulsed signal sent
through a bandpass filter of the type used in the Z90 experiences a rise and
fall and that the rise and fall times are approximately 1/bandwidth. For a
200 Hz filter, therefore, we expect that the waveform will achieve 63% of
its final amplitude after 1/200 = 5 milliseconds. 63% of the amplitude
corresponds to about a 4 dB error in amplitude.
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Let's look at the measured response of a Z91, using the
setup shown at the right.
The idea is that we stop the Z91 from scanning and
send a fast rise burst of RF into it, observing the log detector output.
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Here's the rise and fall (upper image) and an expanded
rise time (lower image) for the 1 KHz filter.
Channel 1 is the applied RF envelope, and channel 2 is
the DC output of U403. the log amplifier buffer. The oscilloscope computes
the rise time (second image) as 1.158 ms (10% to 90%). But that's for the
DC output, which is proportional to the log of the signal input. The
AD8307's output is approximately 250 mV per 10 dB, so channel 2's vertical
axis should be though of as 20 dB/division. As we see, reading the log
amplifier's output too quickly can cause major amplitude errors.
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Here's a similar view of the rise and fall times for
the log amplifier output with the 200 Hz filter.
Note that the rise and fall times are significantly
longer. Hence, it will be necessary, if an accurate amplitude reading is
to be taken, to allow for longer waiting time after moving to a new
frequency step.
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| The Z90's dwell time is set
via the "Scan Speed" setting. It is settable in values of 1 through 5 and
"auto." In auto, the Z90 firmware selects an appropriate dwell time based
upon the selected RBW. You may override this
setting by entering one of the manual values 1...5. These values represent
the approximate time in milliseconds the Z90 waits to take a reading after
jumping to a new frequency during scanning. There is certain overhead
associated with other functions performed by the firmware, so the actual
dwell time may be somewhat longer than the manually selected value. |
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Here's the 1 KHz AM modulated signal, 10 KHz span, 200
Hz RBW.
Dwell (Scan Speed) is set to "Auto"
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Rather than show all five possible manual Scan Speed
settings, I'll instead just show the effects of setting the Scan Speed to
the lowest possible value, 1.Notice how the
peaks are shifted to the right, as the signal does not have sufficient
time to reach it near its steady state value at what should be the peak
point. Also note the resolution is not as good.
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Skip is a measure of
how many data points (frequency steps) are taken for a particular span.
The Z90 steps at a maximum of 240 discrete intervals for
one complete span, corresponding to the Z90's LCD graticule display area
width in pixels. Under certain settings of skip, span and RBW, the Z90's
firmware will take fewer data point.
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Let's consider first the effect of stepping upon
amplitude accuracy and resolution. The illustration shows a series of
stepped measurements with the blue line indicating the amplitude error due
to the frequency step not necessarily being coincident with the spectral
line being measured.
In our simple example, suppose we take 20 data
points, with each data point 1 KHz from the next, for a total span of 20
KHz.
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If we take half as many points (skipping every other
one), the amplitude error increases. In this hypothetical, we step the
frequency 2 KHz and have 10 data points to cover the 20 KHz span.
In addition to increased amplitude error, we have
also increased the frequency resolution error.
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| OK, you're probably thinking.
Seems simple enough, we should always take the maximum number of data
points.
And, yes, that is the correct answer if the objective
is to minimize amplitude error and maximize frequency resolution. But,
remember that measurements have a minimum time for filter stabilization
(plus the general overhead in stepping the frequency synthesizer and in
drawing lines on the LCD or outputting data over the serial port.
Hence, the fewer the sample points, the faster we can
complete a frequency sweep.
Let's take a few concrete examples.
First, let's compute the minimum number of frequency
steps required to cover our span selections, assuming the maximum safest
step interval--where we step exactly one filter bandwidth with each step.
This gives us an expected amplitude error of 3 dB. (The filter bandwidth is
the width of the -3 dB points, so with a step spacing equal to the 3 dB
bandwidth point, no spectral line will be more than the 3 dB bandwidth from
a frequency step.) |
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Span (KHz) |
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RBW (Hz) |
5 |
10 |
20 |
50 |
100 |
200 |
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200 |
25 |
50 |
100 |
250 |
500 |
1000 |
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1000 |
5 |
10 |
20 |
50 |
100 |
200 |
The shaded cells require more frequency steps than we
have pixels for display and hence should be avoided.
This table suggests we might use aggressive frequency
stepping for some spans and bandwidth combinations. |
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Here is our 1 KHz modulated AM signal again. 200 Hz RBW,
10 KHz span, with skip set to None; the data presented uses 240 samples,
so each frequency step is 20 KHz / 240 = 83.3 Hz.
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The same settings, except skip factor is set to "norm"
which implements a light form of skipping. [I'm being intentionally vague
on the number of points displayed here and in the later plots.] Notice
that the display is more angular, due to linear interpolation between data
points. But, the overall view is not too bad and there is a noticeable
speed increase by implementing light point skipping.
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With the skip factor at "med" the lines are even more
pointed. Also note the reduced resolution. In the full 240 point case, the
sidebands are resolved to about 36 dB measured to the carrier. In the
"norm" case, that resolution has dropped to about 30 dB, and for "med"
it's under 30 dB.
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With the skip factor set to max, the sideband
resolution is about 20 dB. There's also an error in the amplitude as the
sidebands are closer to 4 dB below the carrier instead of 6 dB.
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to the skip setting you use. The more aggressive the setting, the faster the
scans are, but with increased error and unpleasing display shapes.
You should also be aware that the Z90 firmware decides
how many points should be skipped for each of the settings "norm", "med" and
"max" based upon the span and RBW. Hence the exact number of points taken is
not directly settable by the user. In some cases, the Z90 firmware will not
allow any points to be skipped, e.g., 200 Hz RBW with 100 KHz span.
In general, if you stick with "norm," the Z90's
firmware will do a decent job at balancing speed versus resolution. |
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Video Averaging allows the ADC
converter to take multiple readings after each frequency step, instead of
the normal one reading per frequency step. Video Averaging is settable in
steps of powers of 2, i.e., 1, 2, 4 ... 64. In most cases, the video
averaging should be set at 1. Why use video
averaging? Video averaging is most useful with a time-invariant signal, such
as a steady carrier signal in the presence of random noise. Since the
time-invariant signal remains constant, its average is equal to its
instantaneous (average = 1) reading. The random noise, however, is reduced
by averaging, thereby improving the displayed signal to noise ratio.
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Here's a steady carrier with a fair bit of noise
visible. Video averaging is set at 1. The noise level is approximately 10
dB peak-to-peak
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I've set video averaging at its maximum value, 64 to
illustrate how it reduces noise. The carrier is unchanged in amplitude, as
its amplitude is time invariant. The noise, on the other hand, has been
averaged down to a peak-to-peak value of about 4 to 5 dB, a useful
improvement.
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What happens if the signal is not time invariant? SSB
voice, for example, does not have a constant amplitude with time.
The short answer is that video averaging will reduce
the apparent ampitude of observed SSB signals. Likewise, there's a power
density issue that suggests you should use the Z90's widest feasible
bandwidth for a given span to observe SSB signals. (A different set of
factors apply for detailed measurement of SSB signals and will be discussed
later.)
Let's look at some sample SSB signals. The sample
signals are generated with a Telulex SG-100 function generator in USB mode,
with audio being supplied by a CD-ROM player playing sample spoken text from
a standard text corpus used for speech quality comparisons. The resulting
bandwidth is significantly greater than that of a typical amateur SSB
transceiver, but the concepts discussed apply mutatis mutandis to an
amateur SSB signals. |
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This is my preferred setting for SSB viewing, RBW set
at 1 KHz, Video Averaging set at 1 and span at least 20 KHz. The signal
peaks about 40 dB above the noise level and can be seen to be USB, as the
energy is distributed to the right hadn side of the screen.
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Applying video averaging = 64 reduces the amplitude
about 10 dB and also drops out a lot of the fine detail seen in the
earlier image. Still, video averaging may be useful to see the gross
shape of the voice spectral waveform.The
amplitude is reduced because SSB has a rather low peak-to-average power
ratio and by increasing video averaging to 64, the display now shows the
average power in each bandwdith.
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Here's the SSB signal viewed with 200 Hz RBW. Note the
amplitude reduction from the 1000 Hz RBW images.
This is because the power in the SSB signal is
spread over a certain bandwidth. The 200 Hz RBW filter intercepts 20% of
the power that the 1000 Hz filter does, which results in a 7 dB power
loss. Then, the 200 Hz filter has about a 5 dB excess insertion loss, so
an SSB signal viewed with the combination of 200 Hz RBW and video average
= 1 will show about 12 dB less signal than with the 1 KHz filter. (This
analysis is highly simplified, but the numbers are "close enough for
government work.") This extra 7 dB bandwidth loss is as a result of the
laws of physics.
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If we turn on video averaging with the 200 Hz RBW, we
reduce the signal level even more. than for the 1 KHz case. This is
because the voice energy peak to average is even more pronounced when
looked at with a narrow band filter. Hence, the averaging process greatly
reduces the signal level in any 200 Hz bandwidth window.
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Some receivers (Kenwood at least) apply automatic gain
control to the RF amplifier. The block diagram section below shows the
TS-830S arrangement (one of the Z90 beta testers has a TS-830S) and my
TS-940 has a similar arrangement. Kenwood brings out a broadband 8830 KHz IF
sample, suitable for use with the Z90, from after the RX Mixer (Q3,4) and
ahead of CF1.
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Elecraft's K2, in contrast, applies AGC only to the IF
amplifier, with the RF amplifier and post-mixer amplifier running at maximum
gain all the time. (The K2's RF amplifier can be switched in and out, of
course.) The recommended Z90 connection point in the K2 is after the post
mixer amplifier and before the crystal filters.
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| The panadapter's display will
behave differently between receivers with AGC applied to the stages ahead of
the IF connection point and receivers without AGC.
With AGC applied, the broadband IF sample output level
depends upon the strength of the signal received. Suppose you set your
receiver to a spot on the band where there are no signals, just the normal
background noise. The receiver AGC increases the overall gain to maximum.
Signals up and down the band are amplified by the receiver's RF amplifier,
mixed with the LO and output to the Z90 at maximum level.
Now suppose a strong signal lands on the frequency you
are tuned to. The receiver's AGC will immediately reduce gain of all stages
by an amount proportional to the strength of the received signal. Since the
RF amplifier stage is also subject to AGC, its gain will also be reduced and
thus signals fed to the panadatper (even those far away from the one the
receiver is tuned to) will also be reduced in level. Thus, the signal level
the panadapter shows is dependent upon the strength of the signal at the
frequency to which the receiver is tuned.
Fortunately a good receiver is designed so that the
AGC gain reduction is distributed over multiple stages, and a signal that is
40 dB over S-9 won't reduce the RF amplifier gain by 90 dB. Indeed that
degree of gain control must be spread over several stages, perhaps 6
amplification stages, each reduced by 15 dB. And, many receivers are
designed so that AGC is applied preferentially to later stages, with the RF
amplifier only having its gain reduced for relatively strong signals (so
called "delayed AGC") Still, you will see the panadapter's level change as
you tune across the band and the received signals go from weak to strong.
A receiver without AGC applied to the RF stage will
not exhibit this same variation, and the strength of the signal being
received will not affect the panadapter's displayed amplitude of other
signals. |
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Here's an analogy to the receiver AGC amplitude issue.
Suppose you are copying a CW station with the receiver bandwidth set to 20
KHz (not too likely but bear with me). Your faithful CW second operator,
pictured at right) is copying a second, much weaker, station, with a beat
note of 18 KHz, far above your hearing range, but not a problem for your
CW second op.
To make the listening easier for you, as the station
you are listening to is very strong, you turn down the volume control.
This also reduces the audio level of the station 18 KHz away and the
second op can no longer copy it.
[Thanks to my beta tester for the photo of his
faithful CW second op!]
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