[Arm-netbook] HDMI High-Frequency Layout: Speed of Propagation

[Richard Wilbur]

HDMI Layout Notes
for EOMA68 Cards
by Richard Wilbur

Speed of Propagation

First let's calculate the speed of electromagnetic wave propagation in
a microstrip differential pair on our circuit board.  Then we can use
that speed to convert the timing tolerances of the HDMI standard into
distance tolerances which will guide our priorities in routing the
differential pairs.

Electromagnetic waves travel at the speed of light.  But since the
electromagnetic fields of these signals extend between the conductors
into both air and the FR-4 substrate of our printed circuit board
(PCB), they will not travel at the same speed as if they were
travelling through a vacuum.

Speed of light in a vacuum: c = 3.00e8 m/s
Speed of light in some other substance:
    v(wave travelling in substance) = c / sqrt(relative permittivity
of substance)

Since the electromagnetic waves in question propagate partly in air
and partly in the PCB substrate (FR-4), we estimate their governing
permittivity to be between that of air and FR-4.

Speed of propagation for signals conducted in differential microstrip
on the PCB:
    relative permittivity of FR-4 = 4.4 [1]
    relative permittivity of air = 1
    v(in FR-4) = 3.00e8 / sqrt(4.4) = 1.43e8 m/s
    v(partly in FR-4, partly in air) ~= 3.00e8 / sqrt(4) = 1.5e8 m/s =
150um/ps[2]

References:
[1]  https://en.wikipedia.org/wiki/FR-4
[2]  Toradex, page 21

Bibliography:
http://docs.toradex.com/102492-layout-design-guide.pdf