Jim Lux wrote in
:

Jim,

Comments noted.

My objective isn't so much trying to build a better loss model, but
rather to use a simple loss model and build the coefficients from
manufacturer's published data and make that available in the calculator.

Although I calculate the correlation coefficient when do the regressions
on the manufacturers freq/loss tables, and had not used models with poor
r^2, I hadn't explored the lower frequency data points for fit. I did
just that a day or so ago, and interestingly the cases where low
frequency points were not a good fit were all non-homogenous centre
conductors.

I had previously explored thin homogenous centre conductors, and they
should not be an issue for practical cables down to 0.1MHz.

I am also not obsessing about accuracy, because real cables have
tolerances that set a limit to necessary accuracy.

So, to try and persevere with the simple model, I have excluded data
points that appear to be a result of departure from the simple model due
to composite conductor effects, and show the lower frequency that bounds
extrapolated / interpolated results. Extrapolated results are always a
risk, the user must make their own judgements about the applicability.

I noted Roy's comments on braids and composite conductor issues, and I
thank him for his response. I may include some similar explanation in the
calculator's usage notes.

It also occurs to me that some cable construction intended for 500MHz and
above use a plastic film with a very thin metallic coating, and I wonder
about its performance at low frequencies. Perhaps yet another departure
from a simple loss model.

As noted above, the largest departures at low HF frequenciesfrom the
simple loss model were all cables with steel cored inner conductors.
There is a salutory lesson that when buying RG59 or RG6 for HF use, those
cables with 100% copper inner conductors are likely to be better at the
low end of HF. The same may apply for use of such cables for baseband
applications like video.

Owen


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