[hsdd] High-Speed Digital Design Newsletter - - Adequate Bandwidth -
- From: "Dr. Howard Johnson" <howie03@xxxxxxxxxx>
- To: <hsdd@xxxxxxxxxxxxx>
- Date: Mon, 19 May 2008 16:59:31 -0700
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<http://www.sigcon.com/seminars/seminarHSDD.htm> High- Speed
Digital Design:
Integrity Seminars
taught by Dr. Howard Johnson
<http://www.sigcon.com/seminars/oxford.htm> Oxford Univ.
<http://www.sigcon.com/seminars/SanJose.htm> San Jose, CA
June 23 <http://www.sigcon.com/seminars/oxford.htm> - 24
October <http://www.sigcon.com/seminars/SanJose.htm> 27 - 28
<http://www.sigcon.com/seminars/seminarAHSSP.htm> Advanced
High-Speed Signal Propagation: June 25
<http://www.sigcon.com/seminars/oxford.htm> - 26 October
<http://www.sigcon.com/seminars/SanJose.htm> 29 - 30
<http://www.sigcon.com/seminars/seminarHSNG.htm> High-Speed
Noise and Grounding: November
<http://www.sigcon.com/seminars/SanJose.htm> 3 - 4
Adequate Bandwidth
HIGH-SPEED DIGITAL DESIGN - online newsletter -
Vol. 11 Issue 03
I just heard from Istvan Novak, who follows the world of power
integrity as closely as anyone I know. I wrote to him about a new
TDK capacitor type recently mentioned on the SI-LIST:
http://news.thomasnet.com/fullstory/540513
It is available in a range of specific ESR values. That's good
for controlling resonance in certain power supply applications.
I asked Istvan if he were aware of any others, or if it is the
first of its kind.
Istvan replied, "I think it is great to have this choice, so that
people can make a conscious decision in optimizing their power
distribution network. [Regarding the question of being "first"]
it depends how we define being first. This TDK part is the first
mass-produced controlled-ESR ceramic capacitor. However, in
experimental sampling, controlled-ESR MLCCs have been produced by
at least three other capacitor vendors since year 2000, but for
various reasons those have not been put into volume production.
Also, volume-produced controlled-ESR capacitors (other than
ceramics) became available in recent years before the TDK
controlled-ESR ceramic.
"POSCAPs and tantalums were actually the first bypass capacitors
with guaranteed plus and minus tolerance for ESR. A [short]
history of the developments and the available volume-produced
controlled-ESR parts were documented in last year's DesignCon
paper, posted on http://home.att.net/~istvan.novak/papers.html ,
"History of Controlled-ESR Capacitors at SUN" in TecForum TF-MP3
"Controlled-ESR Bypass Capacitors Have Arrived".
If you are not following the controlled-ESR topic, it's worth a
look.
By the time you get this I'll be preparing for my annual journey
to the U.K. to visit Oxford University and other sites in Europe.
In my experience, June is the best time to visit. The weather's
fine, and all the businesses are still open.
The technical note below results from some good questions I
received recently about the meaning of scope bandwidth, and its
effect on signal measurement accuracy. Thanks to all for your
good questions
_____
Adequate Bandwidth
by Dr. Howard Johnson
The waveform in figure 1 had its tips clipped by a low-pass
filter.
The source signal comes from a DS25BR100 LVDS-style differential
driver. The driver is designed to work at speeds up to 3.125
Gb/s. This particular driver provides adjustable pre-emphasis. In
making this waveform I set the pre-emphasis feature to its
maximum setting.
The driver outputs run through SMA connectors, 24-in. RG-316DS
cables, and DC blocking capacitors straight into CH1-CH2 of a
LeCroy SDA 6020 6GHz digital scope. The scope computes the
difference between channels 1 and 2, showing the differential
result in purple, labeled "6 GHz".
The "1 GHz" waveform uses the low-pass filtering function
available on my LeCroy scope. That function selects the
equivalent bandwidth of each input channel.
Analog scopes have long been available with a 20-MHz
bandwidth-limit feature. That feature can be quite useful when
looking at small signals.
A bandwidth-limit feature performs a service somewhat like
vertical averaging in that it reduces random noise, but it does
not require a repetitive signal. It's just an analog filter, so a
bandwidth-limit feature works on single-shot acquisitions. The
feature applies a moving-weighted-average function to the
incoming waveform, smoothing the peaks and edges. Properly used,
it can reduce the level of random white noise or short impulsive
noise present in a signal at the expense of a slight degradation
in the rise/fall time of the measured waveform. The exact
frequency response of the filter function is determined by the
particular profile of moving-weighted-average function used.
Early implementations implemented with analog filters had only
one choice: 20 MHz.
Nowadays, digital scopes do an even better job. Using digital
signal processing techniques a good digital scope can apply a
very nice Gaussian, linear-phase filter to the input signal with
a variety of different bandwidth limits.
The LeCroy SDA 6020 can do both digital and analog filtering. It
offers front-end analog bandwidth selections of 6 GHz (full
bandwidth), 4, 3, 1, 0.2, and 0.02 GHz. In addition, it can
implement arbitrary filter functions in DSP software
post-acquisition.
The effect of the filter depends on the speed of the signal to
which it is applied. In general, a low-pass filter rounds the
sharp corners of a square-edged waveform. If the waveform has
sharp peaks, the filter clips them off, as shown in Figure 1.
<http://www.sigcon.com/images/news/11_03Fig-1-chops-peaks.jpg>
In signal-processing terminology, the high-bandwidth LeCroy SDA
6020 scope, combined with a 1 GHz low-pass filter function, makes
a 1-GHz instrument. In other words, the figure shows what signal
you would have seen with a 1-GHz instrument.
That's an interesting way to think about the issue, because it
means you can explore signals using the high-bandwidth scope to
see how they would be distorted if viewed through the eyes of an
instrument with inadequate bandwidth.
In the case just presented, the bandwidth-limit effect clipped
only tiny peaks from the signal. The remaining portion of the
waveform, being fairly slow-moving, was unaffected. If you only
cared about the gross ups and downs of the waveform, in effect
just looking for 1's and 0's, the 1-GHz bandwidth limit makes
almost no difference. On the other hand, if you are trying to
accurately measure an exact degree of transmit pre-emphasis, the
low-pass filtering effect of a limited-bandwidth instrument
distorts your view.
Figure 2 illustrates an even more dramatic case. It depicts the
common-mode output of the same differential signal, using the sum
of the two input channels (CH1+CH2). The vertical scale has been
enlarged to 50 mV/div. As you can see, the common-mode signal
harbors some very tall, narrow peaks. Many signals, like
crosstalk and skew, have a similar appearance.
<http://www.sigcon.com/images/news/11_03Fig-2-atten-pulse.jpg>
With the 1 GHz input bandwidth setting the short pulses rise to
only half their correct amplitude. That's a 50% error. The 6 GHz
bandwidth setting shows you the whole signal.
How do I know that 6 GHz is enough? Might there not be even more
to this signal at even higher bandwidths?
I know there is not because I checked that. I pushed the 3 GHz
button and saw the same result at both 3 and 6 GHz. That's a cute
trick you can use to make sure your scope has adequate bandwidth.
You can rarely increase the bandwidth of your instrument, but you
can artificially reduce it. If the reduction makes no observable
difference, then you probably have adequate bandwidth headroom
[see <outbind://21/#note> note 1]. If the reduction makes a
noticeable difference, then a higher-bandwidth instrument might
reveal even more of the signal you are trying to measure.
The most commonly used rule of thumb for determining the
bandwidth you need depends on the effective rise/fall time of the
measuring instrument. To determine whether your instrument is
adequate, given no other information but the 3-dB bandwidth of
your scope, first figure its effective rise/fall time:
t[scope] = 0.338/f[3dB]
Compare that time with the rise/fall time of the signal you need
to measure, t[signal]. The waveform-reproduction accuracy of the
measured result will fall in line with this table:
Ratio t[scope]/t[signal]
General accuracy
< .1
better than 0.5 %
1/3
5%
1/2
12%
1
40%
>1
do not attempt
Keep in mind that your measuring system comprises a probe (or at
least a probe cable) and a sampling unit. They affect each other.
The overall bandwidth of the combination is never as great as
either of the individual pieces. To figure the overall effective
rise/fall time of your combination, first determine the rise/fall
time of each piece and then combine the pieces:
t[overall] = sqrt{ t[scope]2 + t[probe]2 }
These simple equations assume well-damped Gaussian filters in
both the scope and probe. In some cases, especially for digital
scopes at 6 GHz and above, that assumption may not be correct. In
that case the equations will be indicative of behavior, but not
precise. Check your scope manufacturer's web site for more
precise information about the equivalent rise/fall time of
various instrument/probe combinations.
Best Regards,
Dr. Howard Johnson
_____
[NOTE 1-I said your bandwidth is probably adequate because there
are some pathological cases for which my simple test would not
return the correct answer. For example, take a square wave with
10 ns rise/fall times, and superimpose upon that signal a 70 GHz
sine wave. Any scope with a bandwidth greater than 100 MHz would
show the square wave part of the signal with crystal clarity, but
unless your scope goes all the way to 70 GHz, you would probably
never notice the sine wave component.]
Join me at my upcoming seminar at Oxford University, U.K., June
23-27, 2008. A full schedule of cities and dates appears at:
www.sigcon.com <http://www.sigcon.com/seminars.htm> .
If you have an idea that would make a good topic for a future
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