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

[mike.valk at gmail.com]

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.

See the left side drawings. The taper can be in steps or smooth. I've
read a, recent, paper that the effect is the same. Indeed don't make
to great steps as they'll create reflections.

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. Skinning effect
in combination with the magnetic fields, which create the capacitance
effect, will draw the signal to travel mostly on the inner edges. So
the steps don't touch the signal to much.

For narrowing multiple pairs, I cannot see the benefit of a stepped
approach. See the left side drawings. Just more work.
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