# RE: [SI-LIST] : the old high-frequency return current model

Eric Bogatin ([email protected])
Mon, 4 Oct 1999 11:40:21 -0500

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The recent discussion on the impact on differential pairs in crossing a
split in a plane has gotten me thinking about how we could do a quick
simulation, in the absence of doing a 3D FDTD simulation of the actual
currents and voltages. This was a very good suggestion, and I also await to
see the film.

Here's one approach that I tried and would like folk's opinions on. It has
certainly opened my eyes a bit at how robust differential pairs are.

Consider a coupled, microstrip differential pair that is 7 inches long. At
the three inch point, the plane on the back side is etched off for a length
of 1 inch. This is an extreme case of a differential pair passing over a
split in the ground plane.

For the special case of lines 5 mils wide, 5 mil spaced, with a 2.9 mil
thick dielectric to the return plane, the matrix elements of the two lines
are: Z11 = 52.4 Ohms and Z12 = 5.2 Ohms. I got these from my trusty Ansoft
Maxwell 2D Extractor, 2D field solver. This gives a diff Z0 of 2 x
(52.4 -5.2) = 94.6 Ohms.

In the region where the plane has been removed, the single sided Z0 is 160
Ohms. It is interesting to note that the field pattern of the single ended
coplanar lines is the same as the differentially driven coupled microstrip.
The difference, of course, is that the presence of the return plane
dramatically changes the specific value of the characteristic impedance of
the differential pair vs the single ended. From
the differential signal's perspective, it will see an impedance
discontinuity of 95 Ohms in the microstrip area and then 160 Ohms for the 1
inch distance, and back to 95 Ohms. The common mode will see an impedance of
57 Ohms in the microstrip region and infinite in the coplanar region. I
think this is how the gap will "block"
common mode signals, as D.C. was alluding to. Basically, the common mode
impedance is open in the gap region, but the differential mode impedance is
only about 80% larger in the gap.

To first order, this will be the main effect the signal sees in crossing the
gap. We all agree that there will be mixing of the return paths in the plane
within a few line widths of the traces, at the edge of the gap. This is
probably on the order of 20 mils. I think this discontinuity will be small,
compared to the 1,000 mil discontinuity of the 95 Ohms to 160 Ohms
transition. If this is the case, we can simulate the common and differential
mode signals with a tool like Hyperlynx to look at the magnitude of the
signal degradation. A number of folks pointed out that yes, there will be a
discontinuity, but if you keep the lengths short compared to a rise time, it
might not affect the noise margin much.

In order to use Hyperlynx to simulate this structure, we have to trick it
into seeing the coplanar region as a coupled microstrip region, as it
assumes perfect planes as return paths for all signal lines. We do this by
using a 2.9
thick dielectric for the differential sections and using a 50 mil thick
dielectric for the coplanar region. Using my trusty Ansoft 2D field solver,
I found that for two coupled microstrips, as long as the dielectric to the
return plane is thicker than 15 mils, the differential impedance saturates
at 140 Ohms. The common mode impedance continues to rise, however, as the
plane is lowered.

This is a bit lower than the 160 Ohms of the single ended line with no
return plane, and the dielectric 2.9 mils thick, since in the case of just
thicker dielectric over the plane, there is field in the thick dielectric
and higher capacitance, and hence, lower impedance. The difference is small,
and I went ahead and used the two coupled microstrip, with 50 mil thick
dielectric, as my gap region. The common mode impedance was 320 Ohms- large
compared to the 57 Ohms common mode impedance of the front of the line.

The Hyperlynx circuit I set up has three diff pairs in series. The first
section is 3 inches long, 95 Ohm. The next section is 1 inch long, 140 Ohms
and the third is 95 Ohm, 3 inches long. Each trace is defined by its cross
section, taking advantage of the built in field solver to calculate the
matrix elements. I have independently verified the Hyperlynx field solver to
be within 1-2% of the Ansoft tool. I used a differential TDR as the source,
with a 100 psec rise time. (The 1 inch gap is about 130 psec long) The end
of the lines are differentially terminated with 95 ohms.

Slide 1, in the attached file, is the near end response of one channel
of the TDR and its far end response, TDT, and the differential signal at the
far end. I compare the response of the differential pair with a 1 inch gap
and a 0.1 inch gap. You see the impedance discontinuity of the gap in the
TDR, as you expect, a little distortion in the TDT, and very little effect
in the differential response. The impact from a 0.1 inch gap, maybe more
realistic even with 100 psec rise times, is almost non existent. This
suggests that the differential signals are not impacted much by the gap.

However, as many have pointed out, the real problem with differential lines
is when there is an asymmetry, as with driver skew. In Slide 2, I compare
the same traces, with a delay of 50 psec in the second driver, but recorded
at the far end. The two unmarked scope traces are the + and - signal lines.
The green is the differential signal. The skew is 1/2 a
rise time, and might be a common magnitude of delay. Again the differential
signal is not degraded very much- at most, its rise time is slowed down a
bit, but the signal quality is good. The big impact is the generation of
common mode voltages (and currents) on the other side of the gap. I can't
plot common mode voltage in Hyperlynx, but you can see it clearly in the
ripples that move in step at the receiver side. Note that without a gap, you
still get some common mode generated from the driver skew, its just cleaner.

I looked at the near end waveforms, at the source, with and without a skew,
and these show the generation of large common mode noise with the skew, and
low values without the skew. I would have appended this figure, but this
list allows a max posting size of 60k, and I couldn't fit it in this note.

Conclusion: The gap will be an impedance discontinuity to the differential
signals, and the common mode signals. The differential signals in passing
over the gap are relatively clean, as they see a short, series,
discontinuity. Unavoidable asymmetries in the lines and
drivers will cause larger common mode voltages, since the common mode
impedance discontinuity is larger. The reflected signals will scale
with the TD of the gap. If the skew is ever comparable to the rise time,
series
termination might be needed to dampen the reflected common mode signals. The
quickest way to get an intuitive and quantitative feel for the behavior of
the differential and common mode signals is to look at the size and length
of the differential and common mode impedance discontinuity a gap or other
uncontrolled effect presents.

The recent discussion on this topic has been very timely for me, as I am
working on a paper for DesignCon with Mike Resso of HP and Steve Bird of
Hadco, on differential impedance analysis with TDR. Based on the last few
weeks' discussions, I am adding a test structure to our board that has a
split plane.

--eric

Eric Bogatin
BOGATIN ENTERPRISES
Training for Signal Integrity and Interconnect Design
26235 W. 110th Terr.
Olathe, KS 66061
v: 913-393-1305
f: 913-393-1306
pager: 888-775-1138
e: [email protected]
web: www.bogatinenterprises.com

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