[SI-LIST] Re: Interconnect Lumped Modelling
- From: "McCoy, Bart O." <McCoy.Bart@xxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Tue, 5 Aug 2003 14:49:38 -0500
Another equivalent way of saying it is that the physical length of the
transmission structure is significantly less than the
How much is "significantly less" is partly a matter of opinion but
mostly a matter of requirements of the system you're designing.
So the requirements are Td << Tr -or- Length << Wavelength
and the time requirement is related to the length requirement by
the the propagation velocity-- so they're both telling you the same thing.
The practical interpretation of those requirements has a lot to do with
disturbances to ideal signals that propagate through the structure.
Suppose the structure in question is a small length of microstrip.
As reflections occur at the load end of your microstrip (unless your system
is perfect with no reflections at all), then those reflected signals will
bounce back to the source, reflect again and bounce back to the load again.
I see it purely as a question of how much the once-reflected or
twice-reflect power
adds out of phase to your rising edges. The bigger the discontinuity,
the more power will be added out of phase with your edge. The question is,
how much of an "out of phase" reflection can you tolerate?
That answer will be in 2 parts:
(1) How much power can you accept out of phase by X degrees with your
rising edge?
(a question of S11/S22)
(2) How much out of phase?
(a question of microstrip length relative to a wavelength).
EXAMPLE:
You have a "short" microstrip structure with pads/probes on both
sides. The pads on both sides cause a non-zero S11 and S22.
S11 = 0.1 across band for simplicity (10% power reflected at input
discontinuity)
S22 = 0.2 across band for simplicity (20% power reflected at output
discontinuity)
Perfect 50 ohm source, 50 ohm load
Rising Edge (10-90%): 25 ps.
Immediately upon launching your rising edge, 10% of your power is
lost and returned
to the source. 90% propagates down your short microstrip. At the
"load" interface,
20% of your signal is reflected. So 20% of our 90% signal is
reflected. That makes
0.2*0.9 = 18% of your original launch power propagating back down to
the source end.
90%*(1 - 20%) = 72% of the power continues on to the load. At the
source interface,
again you have a S11=10% reflection. So 10% of our 18% reflected
wave gets bounced
back to the load. So 10% * 18% = 1.8% of the original power is now
bounced back to
add with your rising edge with some phase delay.
Result: 1.8% of the original signal power is now being added to
your
rising edge out of phase? The rising edge is now only 72% of the
original, so
the reflected wave power is actually 1.8% / 72% = 2.5% of the total
signal power
now. (I hope I went through the math correctly)
Will that much power hurt your rising edge? (question 1)
How much phase delay can you tolerate? (question 2)
If a slower rising edge has barely lumbered itself from 60% to the
75% level
in the time it took for the reflection to go visit the source and
come back
to the load, then you *might* be okay. If the rising edge is at
99% and
before the reflected wave returns, then you might see a different
story.
Talk of whether a transmission structure is long or short relative
to your rising edge
has everything to do with how you answer those questions.
I think that is the practical or physical interpretation of those
requirements.
- Bart
-----Original Message-----
From: Stradlin Donald [mailto:stradlin_03@xxxxxxxxx]
Sent: Tuesday, August 05, 2003 1:56 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Interconnect Lumped Modelling
Hi All:
I was just have a problem comprehend a certain theory practially and
physically. Many theories suggest that a via/transmission line can be
modelled as a lumped element if Tr>>Td where Tr = rise time of the pulse and
Td = propagation delay of the length of via/transmission line.
What might be the physical implications of this comparison ? Does it mean
that before the edge reached 90% of it final value, the interconnect length
should be traversed ?
Is it a faster rise time or a larger rise time ?
-Strad.
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