On Tue, Dec 12, 2017 at 8:10 AM, mike.valk@gmail.com mike.valk@gmail.com wrote:
2017-12-11 11:53 GMT+01:00 Luke Kenneth Casson Leighton lkcl@lkcl.net:
On Mon, Dec 11, 2017 at 7:25 AM, mike.valk@gmail.com mike.valk@gmail.com wrote:
Just a small question. Why not deviate from the 45 degree angle? So you end up with converging lines, instead of the stepped approach?
because the steps are a close approximation to the original 1956 paper which ensures that there is a smooth transition of the impedance.
I think we're on different tracks here. ;-)
We have different types of impedance and capacitance going on.
- Single trace (of a pair)
- capacitance to other traces/planes such as GND/PWR
- impedance due to trace geometry
- Intra differential trace (between two line of the same pair)
- capacitance to the differential trace
- Impedance due to the parallel nature of the trace pair
- Inter differential trace (between different pairs)
- capacitance to the differential trace
- Impedance due to the parallel nature of the trace pair
So for matching impedance on a single trace you can do a taper. To match different incoming outgoing impedance requirements or to nullify impedance mismatching parts such as vias.
right, this is inter-pair, and also the keep-out area which must also be tapered. we're leaving individual traces @ 5mil and the calculations that richard's done are all based on traces being fixed @ 5mil.
In an inter pair you'll the steps on the outside so the width between the two lines of a pair remains as smooth as possible.
right. ok. so the paper from 1956 explains that it is REALLY IMPORTANT that you NOT do a straight (linear) taper. the shape of the steps is VERY specific, and is based on studies (many decades later) that explain that you can EMULATE the curving shapes of required tapering from the original paper by deploying a CHAIN of DISCRETE steps.
these discrete steps are what richard went to the trouble of outlining in that table.
For narrowing multiple pairs, I cannot see the benefit of a stepped approach. See the left side drawings. Just more work.
more work with a very very specific and specifically designed outcome, based on a paper that has been demonstrated mathematically to be very specific and precise in how it gradually changes impedance from one value to another whilst GUARANTEEING that at no time will there be ANY reflections back down the line.
a linear step approach such as the one that you outline in the drawing is GUARANTEED 100% to cause reflections.
the gradual change outlined in the 1956 paper is similar to an S curve (not exactly, but close enough). i'm drawing it (attached) freehand on gimp - really badly - so it may not be totally clear. the black lines are supposed to be the smooth S-like tapers of the "ideal" case. the purple one is supposed to be the 45-degree multiple individual steps.
so by doing this series of steps the inter-pair impedance changes from its (appx).... 110 ohms by virtue of the distance being 15mil to each pair and also to the keep-out area, down to something closer to 50 ohms by the time we get to the end of the set of 8 steps, by which point the inter-pair spacing is 5mil, as you have to have, because of the distance between the pads on the ESD and the JAE DC-3 HDMI connector.
if we followed the "straight line" inter-pair approach that you're advocating, the change from the 110 ohms to 50 ohms using linear spacing between 45-turn steps OR a straight 1-line arbitrary-angle taper is *GUARANTEED* to result in reflections back down the line(s).
btw numbers (110, 50) above are not wholly accurate, richard calculated them correctly, i am just substituting convenient indicative numbers from my vague and non-specific memory.
l.
