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
--