Owen Duffy wrote:
Jim Lux wrote in
:


Owen Duffy wrote:

Owen Duffy wrote in
:



This sets me thinking of a way to calculate a lower frequency limit
to the loss model when I generate it, so that I can store that limit
in the database and prevent calculation below that frequency.


I have just analysed the tllc database contents to find cases where
the modelled error is more than 10% different to the data points on
which the regression was based.

There are a few cases, they are all copper clad steel inner
conductors (some of the RG6, RG59, RG174, RG316). I need to implement
a lower frequency limit for model validity for each cable type.

An alternative approach to retain some lower frequency results is to
use a cubic spline interpolation... but it has its own problems.

Not the least of which is that you (philosophically) want a model that
is based on the underlying physics (which the sqrt(f), f model is)..
The problem comes in because sqrt(f) doesn't model skin effect at low
frequencies very well, when the skin depth becomes an appreciable
fraction of the conductor diameter (because the conductor is no longer
a thin wall tube).. the cladding just throws another wrench into the
works.

What might work is if you look at the generic curves for Rac/Rdc for
round and tubular conductors. The analytical formulation is quite
complex, but I'm pretty sure there's a simple polynomial
approximation.


Hi Jim,

I did some playing around comparing spline fits with manufacturers data
points. The underlying problem is that the manufacturer might give a data
point at say 50MHz where the skin effect appears well developed (the data
point is a good fit to the simple loss model constructed with that data
point and the ones at higher frequencies), and only one data point much
lower (eg 5MHz) that is not a good fit to the model and suggests that
skin effect is not well developed at that frequency.

The lack of a good number of data points in the region where resistance
is not proportional to f^0.5 prevents accurate modelling. The loss data
doesn't provide enough information to infer the relative diameters of the
high conductivity coating and the low conductivity core.

Prevents accurate modeling from measured data.. or, more accurately,
prevents you from validating your model with measured data.

I think you could develop the model from physics (which is how the
sqrt(f),f models were developed), and then determine the coefficients
for a particular type coax by measurement.

I would start by looking at Rac/Rdc for the center conductor for low
frequencies. Some reasonable assumptions are
a) dielectric loss is negligble
b) loss in the shield can be modeled by the infinite plane skin depth
formula.

References such as the ITT Reference Data For Radio Engineers have a
short table from which you can build a piecewise model. The analytic
model is a bit complex (hah.. as I recall, it involves Bessel functions
and elliptic integrals)


The approach I have taken with tllc is:
- explain the issue in the usage nots;
- carry into the summarised data, the lowest frequency on which the model
is based so that it can be displayed and users aware when the model
results are an extrapolation;
- the raw data has been analysed to find low frequency data points that
are more than 10% different to forecast by the predicted loss model, and
those points have been excised and the models recreated;

For example, the data for Belden 1189A (a CCS inner conductor) has had a
5MHz data point excised, and the lowest data point used is now 55MHz. The
calculator results shows that frequency, and the user must make his own
mind up about the applicability of an extrapolated result.

I use RG6 coax that has a hard drawn copper centre conductor, and tllc's
results for Belden 1189A (an RG6 type) are probably quite reasonable at
3MHz, but the results would underestimate the loss in real Belden 1189A
because of its use of CCS inner conductor.

An interesting question is ladder lines. Taking Wireman's products, 552
which uses a #16 19 strand copper clad steel conductor or unspecified
coating thickness might well have higher loss than 551 which has a #18
30% single core copper clad steel conductor at sufficiently low
frequency. The question is at what frequency does the effect of the
thinner copper coating of the thicker conductor bundle manifest itself. I
know that Wes measured these lines, and in the article I read he stated
that the measurements were done between 50MHz and 150MHz which would
probably not have shown the effects of the thin coating at low
frequencies.

Stranded copperclad is a very tricky thing (much like measuring the RF
resistance of braid) because you have both the skin effect in a single
conductor issue and the proximity effect of adjacent conductors, and on
top of that, the current flow among conductors (the inner conductors
carry less current than the outer ones).. Much like trying to analyze
Litz wire.

Maybe the thing to do is to actually measure some samples and bound the
error.. (probably not worth going farther if the error is 0.1 dB in 1000
ft, for instance).

I'd start by just running the numbers for solid copper and see what the
difference between the "thin walled tube model" (implied in the sqrt(f)
term) and the actual "solid conductor with skin effect"

Owen