It's important not to confuse the sort of pulses or steps used in TDR
with transient sine wave conditions.

It's perfectly valid to derive the sinusoidal steady state conditions on
a transmission line by looking at the transient conditions that occur
from the time the source is first turned on. And because of the
transient nature of the signal, the most practical way to approach this
analysis is in the time domain.

TDR also (obviously) involves time domain analysis. But it's quite
different. Sinusoidal transient analysis assumes a sinusoidal source
that stays on once it's turned on. But TDR involves either a pulse type
source that's off when the pulse reflection returns, or a step type
source that provides a DC step to the transmission line. In this case,
the source voltage is a stable DC value from the time of the initial
step. In the case of the sinusoidal source, the source voltage continues
changing while the transients are propagating.

In both cases, the sum of all forward and reflected voltages or currents
have to sum to the correct values at all points, and this knowledge can
be used to derive various wave components. But the results and some of
the methods can be very different for the two cases. For example, when a
reactive load or impedance bump is present, a simple reflection
coefficient can be calculated for the sine wave, based on the reactance
at the sine wave's frequency. The reflected wave will be a simple
replica of the incident wave, altered only in phase and amplitude. You
can't do this with a pulse or step; a reactive load changes its shape,
defying a simply defined reflection coefficient. (Some confusion arises
because of the use in TDR of a reflection coefficient, usually denoted
rho. It's the same as the magnitude of the sine wave reflection
coefficient -- but only if the anomaly or load causing the reflection is
purely resistive and a constant value from DC or a low frequency up to
the equivalent maximum frequency contained in the TDR pulse and viewable
with the TDR system. With some TDR systems having equivalent bandwidths
of over 50 GHz, this can be an onerous requirement.) Another important
difference is what happens to a returning wave when it reaches the
source -- reaction to a source that's off, at a stable DC value, or at
some point in the cycle of a sinusoidal waveform is different.

TDR is a very valuable technique, providing important information and
illuminating insights about transmission line phenomena. But great care
has to be taken in extrapolating TDR observations to what happens in a
sinusoidal transient or steady state environment. As readers have seen,
I'm very wary of explanations of sinusoidal phenomena, either steady
state or transient, that depend on drawing parallels to TDR results. You
should be, too.

Roy Lewallen, W7EL

W5DXP wrote:
Tdonaly wrote:

I would like to know why Cecil, for instance, uses pulses, as in a
TDR, in
order to argue a steady state point.


Do steady-state signals obey one set of laws of physics and pulses
obey a different set of laws of physics? You seem to feel so but
I just don't have that much faith!

The useful steady-state shortcuts have developed into a religion that
has no place in science. I am not opposed to steady-state shortcuts.
I am opposed to the steady-state religion that has evolved based on
faith. "Have faith, there is no such thing as reflected waves."
"Have faith, photons can be exchanged between equivalent inductors
and capacitors in a transmission line so they move sideways at less
than the speed of light instead of lengthways at the speed of light."

Particle physicists would really be interested in any proof of that.

"Have faith, a V/I ratio is identical to a physical impedance because
a source, with an IQ of zero, cannot tell the difference." "Reflections
completely disappear the instant that steady-state conditions are reached."
There are many more faith-based characteristics of the steady-state model.
These are just the ones that come to mind.