Speed of Electrons vs. Speed of Signal Transmission
Reference: Eric Bogatin; Signal Integrity Simplified, Prentice-Hall (Section 7.4, P. 210).

False intuition: In a transmission line the speed signal depends on the speed of
electrons traveling down the wire.

Truth: The signal speed is about several billion times of the speed of the electrons.

We can estimate the speed of an electron in a copper wire with a diameter of 1 mm
and carrying 1 Amp of current.

Sine
I = Q  t = (q n A v t)  t

v = I  (q n A)
where
v is the electron speed,
(Coulomb’s Law)
I is the current,
q is the charge of one electron = 1.6  10-19 Coulombs,
n is the free electron density in copper  10-19/m3
A is the cross-sectional area of the wire  10-6 m2.

v  1 cm/sec

The speed of signal transmission is usually less than but in the same order of
magnitude of the speed of light c ( 12 inches/ns).

vsgl  12 / r1/2 (inches/ns) for non-magnetic materials.

For example, a commonly used substrate material FR4 has an r1/2 of approximately 4
and thus the speed of signal transmission is about 50 % of c ( 6 inches/ns).

In summary, signals travel at several inches per nanoseconds while free electrons
travel less than an inch per second.

The speed of signal transmission an a transmission line can also be computed from
the line parameters:
vsgl = (L C) -1/2 where L is inductance and C is the capacitance of the line.

Since Z0 = (L / C)1/2, we can also use: vsgl = 1 / (C Z0) = Z0 / L.

The speed of signal transmission is directly related to the capacitance and inductance
of the transmission line.

Now we can see that the speed of free electrons has almost nothing to do with the
speed of signal transmission. As a result, the resistance of an interconnect is almost
irrelevant when the speed of signal transmission is considered.

On the other hand, resistance plays an important role in the loss of signal amplitudes.