In article , "Reg Edwards"
writes:

Just a comment.

Even such a thing as a small 1/2-watt resistor has distributed R, L and C.

L and C can be calculated from physical dimensions.

A resistor can be treated as a helically-loaded transmission line in exactly
the same way as a helically-loaded antenna. If the frequency is high enough
the radiation resistance can be taken into account.

Just calculate the input resistance of the line with a short circuit at the
other end and the job is done. The performance of dummy-load resistors can
be determined in the same way.

If you (in the plural) are unable to do this then you are unworthy to call
yourselves engineers. Whatever happened to your education? ;o)

Reg, with all due respect, I think most of the newsgroup readers
are HOBBYISTS in radio and electronics, not engineers. I happen
to be both, a design engineer for 4 decades and a hobbyist for over
5 decades of experience.

I'll just say that I disagree with your hypothesis of "helically loaded
transmission line" doesn't quite jibe with the basic question of
trying to model a film resistor. Case in point: I have four 1000
MegOhm IRC resistors having 61 "turns" of what appears to be
carbon film under the clear conformal coating, wound on about a
5/16" diameter, 5 inches long form (substrate material unknown).

For a two-port structure, the series inductance equivalent is only
about an eighth of the apparent inductance based on visual
examination and dimensions of a good conductor made with flat
wire to the same dimensions. To find out what electrons thought
of it, I hooked them up as a reactive voltage divider (analogue to
the capacitive voltage divider common to oscilloscope inputs)
and examined a square wave output versus input. Why such a
gross dissimilarity?

For one thing, the resistance helix is a DISTRIBUTED thing, not a
convenient discrete lump collection. The substrate material is
unknown, maybe something equivalent to light-colored Bakelite?
There's a further complication of the fringing capacity of each of the
61 turns to the adjacent turns or the end caps. The spacing of the
film "turns" is about twice that of the film width. That adds a
capacitance component (equivalent to the distributed capacity of
a solenoidal-wound inductor). The clear conformal coating may add
to the "inductance" loading. Who cares? The one-evening
experiment of about four decades ago showed I could make a HV
voltage divider for a voltmeter at rather high input resistance up to
about 16 KHz, my intent at the time. It worked.

Did I check for higher LF effects? MF? HF? No. Could that be
arranged? Yes, with some slight loss of accuracy; R component
was rated +/-5% and that would be the baseline for any wideband
application, reference point at DC.

I could have gone nuts on the theoretical analysis, spending many
nights in rigorous mathematical whatsis to satisfy some school
instructor's "theoretical" demands on paper. I took a more practical
engineering approach of DIRECT APPLICATION that would resolve
the apparent two-port model equivalent. [I'd already learned that
electrons, fields, and waves don't obey all human notions of how
they work...:-) ]

TIME is the most precious commodity we all share...at work as well
as in hobbies. That applies to everyday practical engineering where
it is quicker, cheaper, and more realistic to MEASURE some unknown
rather than go through a school exercise of "analysis" taking hours
and hours from First Principles on up...or argue excessively in some
newsgroups on the whichness of the what. :-)

Based on some practical experience getting HF through microwave
region range electronics to work, I'd have to agree with all those
who pooh-pooh all the "deleterious effects of parasitic elements"
of components. Those don't appear to be enough to worry about
on film resistors on up into VHF. If there's a concern about it, then
those concerned should MEASURE it if they can't find data to suit.