Some years back I was involved in experiments directed at making a very
fast voltage step by using a transmission line periodically loaded with
diodes. While this structure can be made with packaged diodes and
twinlead, the structures we were working with were balanced microstrip
on a GaAs substrate, with integrated diodes. (Stanford University had
some patents for this implementation.) It used exactly the principle
Sverre is speaking of -- the velocity factor was altered by the diode
capacitance, which in turn was a function of the wave amplitude. The net
result is that one edge of a pulse was made sharper and the other more
gentle as the pulse propagated along the line. Harmonics are generated
by this nonlinear operation.

You might be confusing this with dispersion, which is different
frequencies traveling at different velocities. This commonly occurs on
microstrip lines due to some of the field being in the dielectric and
some in the air, with the relative proportions changing with frequency.
(It's also common in waveguides and, I believe, optical media.) This is
a linear effect and doesn't generate harmonics, and in fact can be
produced by linear lumped components in what's known as an allpass
filter. The time-domain waveform distortion it causes is due solely to
differing phase shifts, or delays, of the constituent frequency-domain
components. That's different from the amplitude-related velocity
dependence of the nonlinear lines.

Intutitively, a test for harmonic-causing distortion might be to see
what happens when you apply a single sine wave. Dispersion and other
linear phenomena will change the amplitude and phase of the waveform,
but not the shape. But a nonlinear phenomenon like the diode-loaded line
or other amplitude sensitive properties will change the shape and,
therefore, create new frequencies. It's pretty easy to show that the
amplitude related velocity property doesn't satisfy the classical
definition and requirement for linearity that the response to the sum of
two excitations is the same as the sum of the responses to the
individual excitations, while a property like dispersion does.

Roy Lewallen, W7EL

Dave Shrader wrote:
If I understand what you are saying then a vertical EM ground wave
suffers from non-linear [distortion], as you define it.

The surface component of the wave is in a dielectric media, earth
ground, with a propagation constant less than the velocity of light.
While the top of the EM wave is propagating in a 377 ohm medium, air,
with a velocity of propagation close to the velocity of light. So, the
top of the wave travels faster than the bottom and the wave tilts in the
direction of propagation and ultimately 'falls' to earth.

You are implying that a wave from a single source but traveling in two
or more different mediums suffer non-linearity. Doesn't that mean that
non-linearity is applicable to all EM waves involved in different media?

I believe that Maxwell-Heaviside's Curl equations at the boundary
conditions can be solved for this condition. [It's been over 40 years
since I tried it though!]

I have a problem with the words 'non linear as used in this thread.
'Non-linearity' is generally understood to introduce harmonics, i.e.
distortion.

For an EM wave sharing a common boundary in different linear media I
offer that the wave 'rolls' in the direction of propagation but does not
create harmonics from some non-linear process.

Deacon Dave, W1MCE
+ + +

[SNIP]


Nonlinearity is if the velocity varies with the amplitude of the wave.
Like
in acoustics where the positive (high-pressure) peaks propagate faster
than
the negative peaks. It leads to waveform distortion and creation of
harmonics. The modern cardiology ultrasound scanners ( 5 years old)
usually
default to this mode these days, transmitting ultrasound at about 3 MHz,
receiving at 6 MHz, as it gives better image quality than the fundamental
mode.


Sverre
www.qsl.net/la3za