From: Scott McMorrow (firstname.lastname@example.org)
Date: Tue Aug 01 2000 - 01:32:21 PDT
abe riazi wrote:
> The critical length Lc (rather than a specific frequency or rise time) is often used as a yardstick for distinguishing lumped and distributed circuit elements and for setting acceptable limits on stub lengths.
> Does concept of critical length break down at frequencies above 1GHz?
Critical length is an interesting approximation. The evaluation of what
is "critical" depends upon how much error can be tolerated in the
result when one is using a lumped circuit approach over a distributed
one. There is always error when using lumped circuits to model
any sort of waveguide. For example, according to Christopoulous
in "The Transmission-Line Modeling Method TLM", page 24, if
lambda/10 is used as the size for lumped elements, there is
still almost a 2% error in the propagation delay of the circuit over
the true distributed circuit. The breakdown comes in the size of
errors we can tolerate at high frequencies and the effects which
are masked by oversimplified modeling.
Several things happen with high frequency signaling:
1) the period is reduced, increasing the chances of intersymbol
interference occurring because of discontinuities in the line.
(i.e. - ringing and jitter spill over into the next bit period.) This
translates into less overall margin.
2) the edge rate is increased to support the higher signaling rate
which increases the bandwidth of the signals.
3) the increased bandwidth of the signals causes a subsequent
increase in sensitivity of the circuit to discontinuities.
4) the increased bandwidth of the signals can excite stubs into
operation at quarter wave resonances. ( large packages
like BGA's make for very nice stubs with a large discontinuity
at both ends. A capacitive discontinuity at the die and a
Z to Z/2 mismatch at the pin breakout when the device is
placed on a line terminated at the far end. This structure
forms a very nice resonator if excited with a high edge rate
source.) Hmmm ... I wonder what might happen at say ...
400 MHz with 800 Mb/s signaling on a bus with a single
parallel end terminator and one BGA driving another? This
might form two resonant circuits ... one from device to
device and the other from trace to package. Like this:
| (package resonance)
|<- resonant circuit ->|
5) these quarter wave resonant stubs can perturb signals
causing excessive jitter.
6) Multiple stubs on a single line with nearly similar resonant
frequencies can form high frequency bandpass filters which
actually amplify the resonances. This will greatly increase
signal jitter and can cause high bit error rates which are
pattern sensitive. (If multiple devices of the same type and
package are daisy chained on a parallel terminated line
then it is most likely that the package interconnects have
nearly the same resonant frequency. This greatly increases
the chances of something bad happening.)
7) Resonant points of all circuits involved can change
due to even and odd mode coupling to neighboring circuits.
This makes it even more interesting to diagnose and track in
8) Unbalanced data coding as used in most computer systems
will cause large average DC level variations dependent upon the
data pattern being transmitted. These DC level variations
translate into decreased eye margin for differential signals
and increased timing jitter (skew) for non differential signals.
9) A capacitor is not just a capacitor any more ... and this
includes die capacitance. Since all include some physical
length of interconnect to get to the capacitance there is a
delay and an associated inductance. Ignore the inductance
and the nifty little trace width impedance compensation circuit
that you might design will not work so nicely.
10) There are little capacitors everywhere ... especially in
device pads and pad stacks. These little capacitors reflect
quite a bit of "stuff" when hit with fast edges. Removing
excessive capacitance in layouts removes a lot of excessive
jitter ... which is just a by product of "stuff" reflecting.
These are some of the interesting effects at high frequencies that
can be easily ignored when moving up from SI engineering at lower
frequencies. The guys who have experience doing RF and Microwave
work have been used to these effects for years.
A frequency domain sweep will uncover unwanted resonances
quite nicely ... and help to better understand what is happening
in the time domain. This is where transmission line simulators
like XTK, SpectraQuest, ICX and Hyperlynx fall short. These can
all do a good job of simulating in the time domain at high frequencies
but can't perform simple AC sweeps. An AC sweep will often
explain why a circuit won't perform beyond a particular frequency
or why jitter can rise to unacceptable levels.
This was a long winded answer to a simple question.
I hope it helps.
-- Scott McMorrow Principal Engineer SiQual, Signal Quality Engineering 18735 SW Boones Ferry Road Tualatin, OR 97062-3090 (503) 885-1231 http://www.siqual.com
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