On Jul 5, 1:26*am, Keith Dysart wrote:
On Jul 1, 8:53*am, K1TTT wrote:



On Jul 1, 12:37*pm, Cecil Moore wrote:

On Jun 30, 11:29*am, Keith Dysart wrote:

Check the a0 coefficient in the Fourier transform. This represents
the DC component of the signal.

And the result is zero EM waves, either forward or reflected, and your
argument falls apart.

Without this, how would you deal with a signal such as
* V(t) = 10 + 2 cos(3t)

If the cosine term is zero, there are zero EM waves, either forward or
reflected, and your argument falls apart.

Incidentally, V(t) = 10, is a perfect way to prove that energy and the
time derivitive of energy are not the same thing and your argument
falls apart.

Alternatively, one can use the standard trick for dealing with
non-repetitive waveforms: choose an arbitrary period. 24 hours
would probably be suitable for these examples and transform from
there. Still, you will have zero frequency component to deal
with, but there will be some at higher frequencies (if you
choose your function to make it so).

Windowing doesn't generate EM waves where none exist in reality and
your argument falls apart.
--
73, Cecil, w5dxp.com

a better argument is that a constant voltage produces a constant
electric field everywhere, since the field is not varying in time or
space there is no time or space derivative to create a magnetic field
so there can be no propagating em wave. *you could do the same with
zero or constant current producing a constant magnetic field.

The same question for you...

With an infinitely long transmission line excited by a step function,
is there an EM wave propagating down the line?

If not, what is it that is propagating down the line? Especially at
the leading edge?

essentially the dc case IS unique in that you must wait forever for it
to reach sinusoidal steady state since the lowest frequency component
is 0hz

You have used similar phrases before. Are you suggesting that an
open circuited transmission line excited with a step function takes
infinitely long to read steady state?

...Keith

'it depends'... in the special case you have concocted where the
signal source has no reflections it only takes one round trip. this
case is very misleading if you try to extend it to cover other cases.
in general it takes infinitely long and you must account for the
infinite series of reflections. that is why the approximations used
to come up with the sinusoidal steady state solution is so useful, and
exactly why it can not be applied to steps and square waves and other
non sinusoidal constant sources.


and in your infinite line example it never reaches steady state so the
step wave propagates forever.