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.

Owen

On Apr 5, 3:03 pm, Owen Duffy wrote:
Owen Duffy wrote :

...

So for small diameter 50 ohm polyethylene dielectric line at 1.8MHz,
the worst case for most ham applications, Xo/Ro is about .18. For
that, I used 2.7dB/100ft for RG174 type line. That's getting to be

I make the loss/100' of RG174 to be 1.1dB and from that I get Xo=-3.6
ohms. (Did you get loss/100m from somewhere? This is probably the
answer to Cecil's diligent spot of an apparent error.)

Tom, in view of your comment about skin effect not being well developed
in RG174, I went to Belden's data sheet for 8216 (RG174 type) and sure
enough, the loss below 30 MHZ does not track the loss=k1*f^0.5+k2*f
model. Your loss figure of 2.7dB/100' may well be correct, and my line
loss calculator is in error below 30MHz for this particular cable due to
the thin copper plating and steel core of the inner conductor. TLDETAILS
and other calculators based on the same loss model will also be in error.
I note that the ARRL TLW shows 1.8dB/100' for 8216 at 1.8MHz.

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.

Owen


Hi Owen,

Yes, I've played with the same model (k1*sqrt(f)+k2*f) for loss. For
things below 500MHz or so--and generally above--the k2 term seemed to
always be so low as to not be worth including. For one thing, the
high-frequency apparent loss may well NOT be due to increased loss in
the dielectric, but rather to variations in impedance along the line
or some similar phenomenon. Published specs for precision lines seem
to be a lot closer than those for "garden variety coax" to what I'd
expect based on theory and what I believe to be the dielectric's power
factor for polyethylene and PTFE. Assuming that all types of line
from a given reputable manufacturer use the same quality polyethylene
and the same quality PTFE, we should see the same contribution from
dielectric, taking into account solid versus foam, for all types: at
a given frequency, the dielectric loss of the poly or PTFE should be
the same. If that's the case, then for some lines at least, the k2
factor must not be due entirely to dielectric loss.

A note on my simple formula: one of the approximations in it is that
the phase angle of Zo is assumed to be close to zero, so that
sqrt(1+j*x) can be reasonably approximated as 1+j*x/2. For x=+/- 0.2,
the error magnitude is less than 0.005, and the error in the imaginary
part is less than 0.0005. But for line that has a seriously reactive
Zo, the error can be large.

We have Roy to thank for pointing out to me, several years ago, that
characteristic of RG-174. I knew I'd have a chance to thank him in
public for it sometime. ;-)

Cheers,
Tom

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.



Jim

Walter, W2DU wrote:
"The first reference I can give you is in "Theory and Problems of
Transmission Lines" by Robert Chipman, in Schaum`s Outline Series, page
128 Eqs 7.9a and 7.9b."

Alas, I don`t have Chipman`s book. Another source is Terman`s 1955
"Electronic and Radio Engineering". He solves the differential equations
for a transmission line, starting on page 84 for solution of traveling
wave problems.

Best regards, Richard Harrison, KB5WZI

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.

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.

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

The loss of real coax often doesn't fit simplified models for at least
the following reasons:

1. Plated or tinned center conductor, where plating or tinning is
thinner than several skin depths at the lowest frequency of analysis.
2. Roughness of a stranded center conductor.
3. Roughness of a braided shield and the necessity for the current to
migrate from wire bundle to wire bundle.
4. Shield thickness which is less than several skin depths at the lowest
frequency of analysis.
5. Tinned shield.
6. Multiple shields.

Numbers 1, 4, and 5 can be calculated, but require modified Bessel
functions and often some mathematical trickery to prevent truncation or
overflow errors even with extended precision calculation. The remainder
are often empirically determined, are complex functions of frequency,
and vary from one cable type or manufacturer to another. All can be
significant with typical cables at HF.

Roy Lewallen, W7EL

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

Owen Duffy wrote:
. . .
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.
. . .

Unfortunately, manufacturer's published loss data are often quite
different than actual cable loss. Belden RG cable I measured long ago
was routinely considerably better than the spec -- apparently the spec
was dictated by the MIL SPEC, and the cable was manufactured to never
exceed it. More recently, I've found that in trying to convince rather
naive amateurs to purchase their cable, some manufacturers are claiming
considerably lower loss than the cable actually has. So the bottom line
is that manufacturer's published data are just so many numbers, and
don't necessarily have any direct relationship to any real cable.

Careful scrutiny of real cable will also reveal that the characteristic
impedance varies quite a bit, and the velocity factor of foamed
dielectric cable is even more variable.

Roy Lewallen, W7EL

Roy Lewallen wrote in news:131e0pcf2aq4g16
@corp.supernews.com:

Owen Duffy wrote:
. . .
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.
. . .

Unfortunately, manufacturer's published loss data are often quite
different than actual cable loss. Belden RG cable I measured long ago
was routinely considerably better than the spec -- apparently the spec
was dictated by the MIL SPEC, and the cable was manufactured to never
exceed it. More recently, I've found that in trying to convince rather
naive amateurs to purchase their cable, some manufacturers are claiming
considerably lower loss than the cable actually has. So the bottom line
is that manufacturer's published data are just so many numbers, and
don't necessarily have any direct relationship to any real cable.

I understand. One of the cable types that I tried to fit to the loss
model was Davis Bury Flex, and it had the worst regression errors of all
of the 90 line types that I modelled. Of course, some manufacturers data
is an extremely good fit, and I suspect that is a result of fitting their
own measurement data to the same model, then publishing points from the
modelled performance.


Careful scrutiny of real cable will also reveal that the characteristic
impedance varies quite a bit, and the velocity factor of foamed
dielectric cable is even more variable.

Agreed... but you have to start somewhere with design, and the
manufacturer's data isn't such a bad place to start. But, I hear your
point that obsessing about model accuracy isn't wise.

Owen