[Arm-netbook] HDMI High-Frequency Layout: Recommendations--Taper

[Luke Kenneth Casson Leighton]

On Tue, Dec 12, 2017 at 8:10 AM, mike.valk at gmail.com
<mike.valk at gmail.com> wrote:
> 2017-12-11 11:53 GMT+01:00 Luke Kenneth Casson Leighton <lkcl at lkcl.net>:
>> On Mon, Dec 11, 2017 at 7:25 AM, mike.valk at gmail.com
>> <mike.valk at 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.
> 1. Single trace (of a pair)
>  - capacitance to other traces/planes such as GND/PWR
>  - impedance due to trace geometry
> 2. 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
> 3. 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.
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