Cecil Moore wrote:
Ian White GM3SEK wrote:
I don't intend to - that quotation is perfectly correct. It means
that in a test-case situation where the lumped model *does* apply,
the distributed model will give EXACTLY the same results.

Ian, you know nothing is "EXACTLY" the same. All you can say is that
the two models give acceptably similar results within a certain range
of accuracy.

NO!

Reality is not on trial here. We are examining your model which is
attempting to describe reality. In a test case where the loading is
DEFINED to be lumped inductance only, agreement with the lumped-circuit
model must be mathematically EXACT.

If one model is a true subset of the other, then as we come closer and
closer to the idealized test case, all the extra terms in the bigger
model will tend to zero leaving only the subset model. In the limit, the
agreement is indeed exact.

(For example, to take up your earlier mis-statement, circuit theory for
DC is a true subset of circuit theory for AC/RF. Set "w" (omega) to zero
and you're left with only the DC relationships. But there is no
discontinuity - as w gets smaller and smaller there is no sudden jump to
a whole new theory. When w is exactly zero, we expect exact mathematical
agreement with DC theory... and of course we get it.)

We do not expect any real-life loading coil to behave exactly like a
lumped inductance, so we cannot physically construct a perfect test
case. But we can envisage a perfect test case in order to test the
model; and for that, we are entitled to demand exact results.

I'm sorry, but all this is Scientific Method 101. Most people don't need
to understand this stuff in detail; though if they do, most people can
also appreciate the compelling logic of it.

You have put yourself in a position where you do need to understand
scientific logic in some detail, and follow the rules that logic lays
down... but you don't.

This is the test case that I'm trying to make you apply, to check
that with a lumped-inductance load, your antenna theory predicts the
correct behaviour, namely no phase shift in the current through a
lumped inductance.

:-) That's like proving there's no loss in a lossless transmission
line, Ian. Please send me a 100 uH lumped inductance and I will
run some tests on it and report back to you. What do you want to
bet the lumped circuit model will be wrong?

Some people have a problem with their model trying to dictate reality.
You seem to have fallen into that trap. Allow me to raise my voice.

THERE IS NO SUCH THING IN REALITY AS A LUMPED INDUCTANCE!!!!


No, of course there isn't. It is either an approximation or - as in this
case - a simplified situation that we can use to check whether theories
make sense.

Remember, it is your theory that we're trying to test. The challenge is
for you to show that your particular application of the distributed
circuit model works correctly.

In a test case where the loading coil comes closer and closer to
behaving like a lumped circuit, your model must do the same as all
successful distributed models do. All the complications must drop away,
giving closer and closer agreement to the behaviour of an antenna loaded
by pure inductance only. In the limit where the loading is pure lumped
inductance, the agreement must be mathematically EXACT.

I am sure this can be done using a standing wave analysis for a
coil-loaded antenna. I am equally sure that you have not achieved that.



--
73 from Ian GM3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek