Modeling TL "dielectric" loss
 

I am trying to reconcile the following in respect of for practical low
loss RF transmission lines:

In the RLGC model for Zo and gamma, it is generally accepted a good
approximation is that R=c1*f**0.5, G=c2*f, and L and C are constant.

If the term (G+j*2*pi*f*C) can be rearranged as
(2*pi*f*C(G/(2*pi*f*C)+j)), and substituting c2*f for G, written as
(2*pi*f*C(c2/(2*pi*C)+j)).

If we regard G to be principally the loss in the dielectric , then
c2/(2*pi*C) should give us the dielectric loss factor, D, 1/Q,
tan(delta), dissipation factor, power factor, whatever you want to
call it.

alpha= 0.5*R/NomZo+0.5*G.NomZo
It also seems generally accepted that Matched Line Loss (MLL) can be
modeled well by the expression MLL=k1*f**0.5+k2*f.

(Remember that alpha= 0.5*R/NomZo+0.5*G.NomZo)

It follows then that c2=k2/(10*log(e)*Ro), and that (G+j*2*pi*f*C)=
2*pi*f*C(k2/(10*log(e)*Ro)/(2*pi*C)+j) which implies that D is
k2/(10*log(e)*Ro)/(2*pi*C).

Problem is, that whilst PE has D somewhere about 2e-5 up to 1GHz, the
loss model for RG58CU (PE dielectric) indicates D of 2e-3, much much
worse than would be expected from D of the PE dielectric alone.

Any thoughts. Is there an inconsistency between the explanation that G
is principally due to D of the dielectric material, or I have I messed
the maths up?

Owen
--

On Thu, 30 Jun 2005 22:46:39 GMT, Owen wrote:


alpha= 0.5*R/NomZo+0.5*G.NomZo
It also seems generally accepted that Matched Line Loss (MLL) can be
modeled well by the expression MLL=k1*f**0.5+k2*f.

(Remember that alpha= 0.5*R/NomZo+0.5*G.NomZo)

Sorry, I mixed the notation using . for multiply operator instead of
*.

the first quoted line should have been deleted, and the second should
read:

(Remember that alpha= 0.5*R/NomZo+0.5*G*NomZo)


--

I saw this apparent discrepancy many years ago, and wondered the same
thing. I've come to believe that the extra loss is due to the braided
shield, not some unknown additional dielectric loss. There's very little
quantitative information about that loss mechanism, but from time to
time I've come across comments that it can be substantial.

Roy Lewallen, W7EL

Owen wrote:
I am trying to reconcile the following in respect of for practical low
loss RF transmission lines:

In the RLGC model for Zo and gamma, it is generally accepted a good
approximation is that R=c1*f**0.5, G=c2*f, and L and C are constant.

If the term (G+j*2*pi*f*C) can be rearranged as
(2*pi*f*C(G/(2*pi*f*C)+j)), and substituting c2*f for G, written as
(2*pi*f*C(c2/(2*pi*C)+j)).

If we regard G to be principally the loss in the dielectric , then
c2/(2*pi*C) should give us the dielectric loss factor, D, 1/Q,
tan(delta), dissipation factor, power factor, whatever you want to
call it.

alpha= 0.5*R/NomZo+0.5*G.NomZo
It also seems generally accepted that Matched Line Loss (MLL) can be
modeled well by the expression MLL=k1*f**0.5+k2*f.

(Remember that alpha= 0.5*R/NomZo+0.5*G.NomZo)

It follows then that c2=k2/(10*log(e)*Ro), and that (G+j*2*pi*f*C)=
2*pi*f*C(k2/(10*log(e)*Ro)/(2*pi*C)+j) which implies that D is
k2/(10*log(e)*Ro)/(2*pi*C).

Problem is, that whilst PE has D somewhere about 2e-5 up to 1GHz, the
loss model for RG58CU (PE dielectric) indicates D of 2e-3, much much
worse than would be expected from D of the PE dielectric alone.

Any thoughts. Is there an inconsistency between the explanation that G
is principally due to D of the dielectric material, or I have I messed
the maths up?

Owen
--

On Thu, 30 Jun 2005 21:07:20 -0700, Roy Lewallen
wrote:

I saw this apparent discrepancy many years ago, and wondered the same
thing. I've come to believe that the extra loss is due to the braided
shield, not some unknown additional dielectric loss. There's very little
quantitative information about that loss mechanism, but from time to
time I've come across comments that it can be substantial.

Roy,

I thought about the effects of through braid loss. I guess any loss
that increases proportionately to f will be captured in the loss model
and allocated against k2.

Below are k2 factors for a few cables of interest. The first three use
PE dielectic, and there is a big difference between RG58 and RG213
where the dimesions of the dielectric are quite different. A small
difference between RG213 and RG214 with similar dielectric size, but
214 has double braiding, suggesting that braid loss / leakage may one
of the factors.

Belden 8262 (RG58C/U) 2.95e-10
Belden 8267 (RG213) 8.23e-11
Belden 8268 (RG214) 7.17e-11

The next bunch don't use braid, but use a corrugated solid outer
conductor. Not a dramatic change in k2 considering how much larger
6-50 is compared to 4-50.

LDF4-50 6.15e-12
LDF6-50 4.60e-12

Could the distribution of the electric field intensity in the
dielectric be a factor, will the dielectric exposed to the highest
field intensity dissipate the most power?

Owen

--

On Fri, 01 Jul 2005 04:30:00 GMT, Owen wrote:

On Thu, 30 Jun 2005 21:07:20 -0700, Roy Lewallen
wrote:

I saw this apparent discrepancy many years ago, and wondered the same
thing. I've come to believe that the extra loss is due to the braided
shield, not some unknown additional dielectric loss. There's very little
quantitative information about that loss mechanism, but from time to
time I've come across comments that it can be substantial.

Roy,

I thought about the effects of through braid loss. I guess any loss
that increases proportionately to f will be captured in the loss model
and allocated against k2.

Below are k2 factors for a few cables of interest. The first three use
PE dielectic, and there is a big difference between RG58 and RG213
where the dimesions of the dielectric are quite different. A small
difference between RG213 and RG214 with similar dielectric size, but
214 has double braiding, suggesting that braid loss / leakage may one
of the factors.

Belden 8262 (RG58C/U) 2.95e-10
Belden 8267 (RG213) 8.23e-11
Belden 8268 (RG214) 7.17e-11

The next bunch don't use braid, but use a corrugated solid outer
conductor. Not a dramatic change in k2 considering how much larger
6-50 is compared to 4-50.

LDF4-50 6.15e-12
LDF6-50 4.60e-12

Could the distribution of the electric field intensity in the
dielectric be a factor, will the dielectric exposed to the highest
field intensity dissipate the most power?

I'm a little late on this as my news service just hiccupped.

Without wading throught the ASCII math, a couple of thoughts.

1. As Tom said, most references give the D of poly as 0.0002,
although the "Handbook of Coaxial Microwave Measurements" by General
Radio gives it as 0.0003.

2. Again, without having followed the derivation, I find the k2
values to be different from those given by the handiwork of Dan,
AC6LA, in his XLZIZL.xls workbook or his TLdetails program. Dan used
published attenuation values and Excel regression analysis to
determine the values of k1 and k2. See:

http://www.qsl.net/ac6la/bestfit.html

3. Also, General Radio says, "alpha(diel) does not depend at all on
the dimensions of the line..." This suggests that there should be no
difference in k2 between LDF4-50 and LDF6-50. Dan's numbers show that
to be the case.

4. Any loss that doesn't follow the sqrt(f) rule (radiation,
wire-to-wire resistance of braid?, etc) as you suggest falls into the
k2 term.

5. High-quality, high-frequency (microwave) flex cables do away with
braid, or at least solder fill it, and use tape-wound shields.

On Fri, 01 Jul 2005 20:56:25 -0700, Wes Stewart
wrote:


Without wading throught the ASCII math, a couple of thoughts.

I see someone else grizzling about the "ugly maths". Oh well...


1. As Tom said, most references give the D of poly as 0.0002,
although the "Handbook of Coaxial Microwave Measurements" by General
Radio gives it as 0.0003.

Ok, as I posted in another msg, my figure came from the ITT Ref Hbk,
and even at 2e-4, it comes short of being the entire explanation of G
derived from published loss figures. I accept that the ITT book is
much lower than others.

Just Googling, I see Reg's site shows 2e-5,

2. Again, without having followed the derivation, I find the k2
values to be different from those given by the handiwork of Dan,
AC6LA, in his XLZIZL.xls workbook or his TLdetails program. Dan used
published attenuation values and Excel regression analysis to
determine the values of k1 and k2. See:


Dans k2 figures are based on units of MHz and feet, mine are Hz and
metres, and when you allow for the units base, they reconcile to
within 1%.

http://www.qsl.net/ac6la/bestfit.html

3. Also, General Radio says, "alpha(diel) does not depend at all on
the dimensions of the line..." This suggests that there should be no
difference in k2 between LDF4-50 and LDF6-50.

I believe that is true, my derivation is that k2=9.09e-8 * D /vf (for
units of Hz and metres). So, the "leakage" loss depends on D and 1/vf
(or permittivity**0.5), and dimensions don't enter the equation.

What sent me down this track is trying to reconcile this with the
published specs which claim more loss than is explained by the
dielectric.

Dan's numbers show that
to be the case.

Dan's figure (in my ZLZIZL) is, like mine, a little lower (25%) for
the larger line. It is the observation that it varies that suggests
there is more to it than D alone.


4. Any loss that doesn't follow the sqrt(f) rule (radiation,
wire-to-wire resistance of braid?, etc) as you suggest falls into the
k2 term.

5. High-quality, high-frequency (microwave) flex cables do away with
braid, or at least solder fill it, and use tape-wound shields.

Yes, see my other post regarding the LMR cables which, like the LDF
series, show much less variation in k2 with cable size than moving
from RG58C/U to RG213.

Thanks for the thinking Wes, Owen

--

The fact is nobody knows the dielectric loss of polyethylene. It is
too small to measure samples in a bridge. The materials of which the
bridge is made have losses of the same order.

The slightest unavoidable impurities and contamination during
production cause wide variations in D.

Coaxial line Attenuation = A*Sqrt(F) + B*F

The most accurate way to estimate D at HF is to measure attenuation
versus frequency over a wide frequency range on several miles of solid
polyethylene coaxial line.

Then separate the constants A and B by plotting on graph paper
Attenuation/Sqrt(F) versus Sqrt(F). and then do a few simple
calculations.

I have performed this operation several times during acceptance tests
on newly laid cables. The cable insulation was mainly air-spaced with
the inner conductor being supported by polyethylene disks at 1.5"
intervals.

D can vary noticeably from one length of cable to another manufactured
from a different batch of nominally identical materials.

I have also measured attenuation on many miles of 1" diameter solid
polyethylene submarine cable and determined quality of the insulation
by this graphical means. It is necessary to make attenuation
measurements very accurately by the substitution method against
standard attenuators.

But for comparison, I have never measured the relative junk used by
radio amateurs.
----
Reg.

On Sat, 02 Jul 2005 05:31:02 GMT, Owen wrote:

On Fri, 01 Jul 2005 20:56:25 -0700, Wes Stewart
wrote:


Without wading throught the ASCII math, a couple of thoughts.

I see someone else grizzling about the "ugly maths". Oh well...

I wasn't the only one?


1. As Tom said, most references give the D of poly as 0.0002,
although the "Handbook of Coaxial Microwave Measurements" by General
Radio gives it as 0.0003.

0.0002 is from the ITT Handbook, fourth and fifth editions.

Ok, as I posted in another msg, my figure came from the ITT Ref Hbk,
and even at 2e-4, it comes short of being the entire explanation of G
derived from published loss figures. I accept that the ITT book is
much lower than others.

Just Googling, I see Reg's site shows 2e-5,

2. Again, without having followed the derivation, I find the k2
values to be different from those given by the handiwork of Dan,
AC6LA, in his XLZIZL.xls workbook or his TLdetails program. Dan used
published attenuation values and Excel regression analysis to
determine the values of k1 and k2. See:


Dans k2 figures are based on units of MHz and feet, mine are Hz and
metres, and when you allow for the units base, they reconcile to
within 1%.

Of course. But I said that I didn't wade throught the numbers [g].


http://www.qsl.net/ac6la/bestfit.html

3. Also, General Radio says, "alpha(diel) does not depend at all on
the dimensions of the line..." This suggests that there should be no
difference in k2 between LDF4-50 and LDF6-50.

I believe that is true, my derivation is that k2=9.09e-8 * D /vf (for
units of Hz and metres). So, the "leakage" loss depends on D and 1/vf
(or permittivity**0.5), and dimensions don't enter the equation.

What sent me down this track is trying to reconcile this with the
published specs which claim more loss than is explained by the
dielectric.

Dan's numbers show that
to be the case.

Dan's figure (in my ZLZIZL) is, like mine, a little lower (25%) for
the larger line. It is the observation that it varies that suggests
there is more to it than D alone.

I admit I discount the last digit of preceison in the values. As Dan
says so well in a note on his web site:

"Caution: The computed values for K1 and K2, like all computed results
in both the XLZIZL package and the TLDetails program, are shown with a
precision of a few digits beyond what is reasonable in normal
engineering practice. This is done to allow you to spot trends and do
theoretical studies. Don't allow yourself to become overly concerned
with the exact values for K1 and K2. The loss characteristics for any
transmission line will vary with manufacturing tolerances, age,
bending, exposure to heat and sunlight, and even changes in the
ambient temperature. The values used here, and indeed in any modeling
package, must be considered as "best guess" estimates of the actual
attenuation for any given line."


Yes, see my other post regarding the LMR cables which, like the LDF
series, show much less variation in k2 with cable size than moving
from RG58C/U to RG213.

Another cautionary note:

While Dan was working on his programs we corresponded a lot via email.
In one instance, he said "X" and I said "Y" about Heliax.

After some fussing around, we learned that my paper Andrew catalog no.
35 has different loss figures for the LDF series than does the "new"
online catalog no. 38. As we would say in America, like trying to
shoot at a moving target.

Also, from my catalog 35, Vp is given as:

LDF3-50 88%
LDF4-50 88%
LDF5-50 89%
LDF6-50 89%
LDF7-50 88%

So even that varies in a random fashion.

Regards,

Wes

"Wes Stewart"wrote:
After some fussing around, we learned that my paper Andrew catalog no.
35 has different loss figures for the LDF series than does the "new"
online catalog no. 38. As we would say in America, like trying to
shoot at a moving target.
________________

Yes, and Andrew sometimes changes their philosophy about specs to meet
certain marketing realities. I was involved in a competitive situation
where my proposal for an offshore broadcast RF system included some Andrew
HeliaxT. The tender spec called for a certain power rating for the coax,
which by its published catalog, Andrew did not meet for the line size they
proposed to us as compliant. A similar line size by an EU Andrew competitor
had been bid to the end user by another tenderer, which by their spec was
compliant to the tender. The customer asked for clarificatication from
us/Andrew. The difference was due to Andrew's inclusion in the spec of a
solar derating value for their cable, where the competitor's did not.
Andrew proved their point (through us), and my proposal won.

Not long after that, Andrew changed all the power ratings for their cable,
removing the solar derating factor, and advising users to apply their own
based on derating information they added to the catalog (similar to derating
for SWR).

Also note that cable attenuation and power ratings are dependent on, and
stated by most OEMs only for specific ambient temperatures and a specific
load SWR (1:1 in the case of Andrew).

RF

On Sat, 02 Jul 2005 07:54:12 -0700, Wes Stewart
wrote:

On Sat, 02 Jul 2005 05:31:02 GMT, Owen wrote:



0.0002 is from the ITT Handbook, fourth and fifth editions.

Rechecking my sixth edition, it is 2e-4 at 100MHz, I need new glasses
for these books with tiny print.

Thanks... Owen
--

On Sat, 2 Jul 2005 11:15:29 +0000 (UTC), "Reg Edwards"
wrote:

....

Noted.

The most accurate way to estimate D at HF is to measure attenuation
versus frequency over a wide frequency range on several miles of solid
polyethylene coaxial line.

Then separate the constants A and B by plotting on graph paper
Attenuation/Sqrt(F) versus Sqrt(F). and then do a few simple
calculations.

Ok, as I stated earlier, I am working from published specs rather than
my own measurements, and I understand there are issues about the
reliability of published specs.

I didn't plot the values on graph paper to find A and B (or k1 and
k2), but used a least squares regression to find A and B (and r**2,
the correlation coefficient as an indicator of the quality of the
fit).

What I was trying to do was to develop an RLGC model for the line from
published figures (attenuation at spot frequencies, nominal Ro, vf),
and I can do that. The issue about the dielectric came up in trying to
reconcile the G / D / k2 figures with the knowledge that the cable had
PE dielectric and should have had D=2e-4 (I stand corrected on my
misreading of the value 2e-5 from my ITT Handbook by Wes - thanks).

The purpose of the model and validation are for my online transmission
line loss calculator.

The notes to the calculator show the modelled loss vs the data points
in one of the graphs at http://www.vk1od.net/tl/tllc.php .

D can vary noticeably from one length of cable to another manufactured
from a different batch of nominally identical materials.


Ok, noted. I have added a few words to the explanatory notes on the
calculator.

Thanks for the help all.

Owen
--

Owen,

Are you aware of programs -

RJELINE2, RJELINE3, for balanced pair lines,

and COAXPAIR, COAXRATE for coaxial lines ?

These are based on exact, classical transmission line formulae and
will tell you all you could wish to know about behaviour of
transmission lines versus any complex termination from open circuit to
short circuit. No approximation of critical parameters.

However, in the coaxial case, dielectric loss is an input quantity.
;o)
----
.................................................. ..........
Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
.................................................. ..........

On Sun, 3 Jul 2005 06:26:57 +0000 (UTC), "Reg Edwards"
wrote:

Owen,

Are you aware of programs -

Yes, of course, Reg, they and the rest of the suite are interesting...

In validating my calcualator, I have compared it to yours, Dan's
XLZIZL / TLD, Dean's TLA and Kevin's java applet. They all produce
slightly different results, one of the reasons I have tried to
document the assumptions that underly my calculator.


RJELINE2, RJELINE3, for balanced pair lines,

and COAXPAIR, COAXRATE for coaxial lines ?

These are based on exact, classical transmission line formulae and
will tell you all you could wish to know about behaviour of
transmission lines versus any complex termination from open circuit to
short circuit. No approximation of critical parameters.

However, in the coaxial case, dielectric loss is an input quantity.
;o)

Yes, I played with a model of Belden 8262, it is pasted below, and
will probably be line wrapped by a lot of news readers.

I have plugged in the dimensions from the 8262 spec sheet, and it
produces some results that are inconsistent with the specs. The
insulant diameter from the spec sheet is 4.5mm, loss/Km 13dB. (The
value for O was chosen to calibrate the DC loop resistance.) At 1GHZ,
the calculated loss was 35dB against spec of 21dB.

I played with it for a while trying to calibrate against the B8262
specs, but was unsuccessful.

Owen


N. Nominal Zo, ohms . 50.0 TERMINATION/LOAD -------------
ohms ---
D. Inner diameter, mm 0.889 R. Series Resistance
0.0
O. Outer thickness mm 0.080 X. Series Reactance
50.0
V. Velocity Factor Vf 0.6600 EQUIVALENT TERMINATION -------
ohms ---
T. Loss Factor ...... 0.000200 S. Shunt Resistance
2500000000.0
L. Line Length metres 100.000 Y. Shunt Reactance
50.0
F. Freq, kilo-Hertz . 1000.00
----------------------------- LINE CHARACTERISTICS
---------------------------
Insulant diameter 3.14 millimetres. Total Attn 10.5898
dB/kilo-m
Magnitude of Zo 51.79 ohms. Dielectric Loss 0.0275
dB/kilo-m
Angle of Zo -2.112 degrees. RF Resistance 0.1258
ohms/metre
Relative Velocity 0.6373 Inductance 0.2705
uH/metre
Electrical length 0.523 wavelengths. Capacitance 101.1476
pF/metre
DC Loop resistance 49.063 ohms/kilo-m. Conductance 0.1271
uS/metre
----------------------------- INPUT IMPEDANCE Zin
----------------------------
Series Resistance 16.51 ohms. Equivalent Shunt R 271.28
ohms
Series Reactance 64.86 ohms. Equivalent Shunt X 69.07
ohms
Magnitude of Zin 66.93 ohms. Angle of Zin 75.716
degrees
-------------------------- TRANSMISSION PERFORMANCE
--------------------------
Reflection coeff. 1.0375 Line loss when matched 1.0590
dB
Refl.coeff. angle 92.01 degrees. Actual line loss 70.8624
dB
VSWR at termination 54.296 Actual power loss in line 100.000
percent
VSWR at line input 9.696 Skin Depth 0.066 mm Q 13.5
Length = Q(1/4-wave) A(dd 1/4-wave) 3(dB) 6(0dB) =(.2%) -(.2%)
Hit N,D,O,V,T,L,F,R,X,S,Y to change data. B(egin again), E(xit
program)



--

If you want to work from published specs, you should find this
interesting, from the Belden catalog:

It looks like 8214 and 9913F7 are the same except that 9913F7 has a
solid aluminum shield between the insulation and the braided copper
shield. 9913F7 claims lower loss, amounting to 0.9 dB at 400 MHz. One
might conclude that the difference is due to the extra shield,
presumably because it's smooth and not braided.

It looks like 9914 is the same as 9913F7 except that 9914 has a solid
rather than stranded center conductor. The spec for 9914 shows less
loss, amounting to 0.4 dB less at 400 MHz. One might conclude that the
difference is due to stranded vs. solid center conductor.

I think your analysis isn't valid for two reasons. The first is that
you're relying on published specifications. (For example, I just
measured the Z0 of ten "50 ohm" cables of different brands and types I
have on hand -- it ranged from 44.6 to 56.8 ohms. I already reported a
loss measurement that was quite different from the spec.) The second is
that your model is overly simplified. It looks like you're trying to
account for all the loss mechanisms in a coax cable by considering only
the dielectric and conductor losses in idealized materials, or at best
two factors which are proportional to F and proportional to the square
root of F. In order to get a decent fit, I think you'll have to include
additional factors for such things as the effect of stranding the center
conductor and the extra loss associated with a braided shield, which
might well be different functions of frequency. Of course, tinned
conductors, which are very common, will alter the loss characteristics
depending on the composition of the plating, and change the shape of the
loss vs. frequency curve at a frequency depending on the depth of the
plating. Once you start really digging, I think you'll find other
mechanisms, such as perhaps how tight a woven shield is -- it wouldn't
take much of an air gap between the shield and the insulation to have
some pretty noticeable effects.

I went through this excercise of attempting to predict coax cable loss
many years ago (my notes say 1991) and abandoned the effort as being too
time consuming. I hope you'll be willing to devote the time and effort
necessary to come up with a reasonably accurate model.

Roy Lewallen, W7EL

Roy said -
I think your analysis isn't valid for two reasons. The first is that
you're relying on published specifications. (For example, I just
measured the Z0 of ten "50 ohm" cables of different brands and types
I
have on hand -- it ranged from 44.6 to 56.8 ohms. I already reported
a
loss measurement that was quite different from the spec.)

========================================

The greatest source of divergence between manufacturers'
specifications and what you think you've actually got is due to
manufacturing variation in cable dimensions.

Such as :

Inner coaxial wire diameter as it is drawn through diamond dies.
Ovality of wire drawn through worn dies.
Tightness of stranded inner conductors affecting diameter.
Diameter over the extruded polyethylene insulant. Affected by
temperature.
Off-centre eccentricity of inner conductor within the insulant.
Ovality of the polyethylene extrusion.
Diameter of braiding wires.
Tightness of braid over polyethylene.
Longitudinal tension in braid.
Tightness of copper or aluminium tapes over polyethylene.
Tightness of PVC jacket or other protection over braid or tapes.

- and a dozen other dimensional factors which I have long forgotten.

There's also variation in the conductivity of annealed copper wire and
contaminants in polyethylene due to lack of cleanliness in storage.

During manufacture, as the product is drawn through machinery,
electrical characteristics change. They can become cyclic. When
measuring long lengths small reflections can accumulate causing
attenuation versus frequency curves to exhibit a slow ripple about the
average slope of A*Sqrt(F)+B*F dB.

( The most unreliable manufacturer's specification I have seen,
associated with attenuation and power rating, allowed cable to be used
at a temperature of the melting point of polyethylene. Would burn the
skin off your hands. Testing equipment???? )

Important factors are the inevitable errors in all measuring
instruments, especially so-called SWR meters, and the delusions of
accuracy usually suffered by everybody involved. It's so easy to draw
the wrong conclusions!
----
Reg, G4FGQ

On Sun, 3 Jul 2005 11:20:01 +0000 (UTC), "Reg Edwards"
wrote:

Roy said -
I think your analysis isn't valid for two reasons. The first is that
you're relying on published specifications. (For example, I just
measured the Z0 of ten "50 ohm" cables of different brands and types
I
have on hand -- it ranged from 44.6 to 56.8 ohms. I already reported
a
loss measurement that was quite different from the spec.)

========================================

The greatest source of divergence between manufacturers'
specifications and what you think you've actually got is due to
manufacturing variation in cable dimensions.


Thanks Roy and Reg,

I understand your point that the calculation engine is more precise
than the model accuracy (against specs), and the product manufacturing
tolerances introduce an even larger error in the predictions. Not
mentioned, but installation and through life degradation introduces
yet another uncertain and possibly greater issue.

Appreciate all the input.

I am sure you are right Roy, this could go on indefinitely. I think I
have gone far enough for the purpose, probably too far, but that is
the cost of confidence that I have gone far enough!

Thanks again.

Owen
--