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 2e-3 much much less
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
--

"Owen"
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
===================================

From where did you obtain D 2e-3 for RG 58 ? That's the most likely
source of the discrepancy.

Also the highest grade polyethylene is unlikely to be used for the
manufacture of RG58.

The only way to investigate is to lay 100 feet on the ground, in the
form of a circle, and measure attenuation vs frequency between the
ends from 1 MHz to 1 GHz.
---
Reg

On Fri, 1 Jul 2005 04:54:35 +0000 (UTC), "Reg Edwards"
wrote:


"Owen"
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
===================================

From where did you obtain D 2e-3 for RG 58 ? That's the most likely
source of the discrepancy.

Also the highest grade polyethylene is unlikely to be used for the
manufacture of RG58.

The only way to investigate is to lay 100 feet on the ground, in the
form of a circle, and measure attenuation vs frequency between the
ends from 1 MHz to 1 GHz.

I took the figures published by Belden for their 8262 cable at
frequencies from 1MHx to 1Gz (9 points) and did a polynomial
regression to MLL=k1*f**0.5+k2*f, then substituted k2 into the
expression described in my original post.

I didn't measure the losses, and I recognise that Belden might have
smoothed their results by an intermediate regression, but I figure
that they are not going to exaggerate the effect of k2 unnecessarily.

Owen

--

My reference suggests that D for PE is 2e-4, but even at that, the
copper loss would be ten times the dielectric loss out to 2GHz, if I
figured it right. It could be difficult to accurately determine your
k2 with such a small contribution from the dielectric. But there are
likely other mechanisms at work...

Roy mentioned the braid. I recall reading a nice article by, I
believe, an engineer with Andrew talking about various loss mechanisms
in coax due to things like braid and stranded inner conductor and
surface smoothness. The article went well beyond the usual theoretical
discussion that assumes smooth conductors and perfectly uniform
construction. I wish I could locate it again! I thought it was in "RF
Design" magazine, but never could find it again there, so perhaps it
was in "Electronic Design" or "EDN".

One mechanism to consider is the effects of a non-constant Zo as a
function of distance along the line. There are undoubtedly small
variations in the manufacturing process. Over a length of line that's
many wavelengths long, even small variations make a noticable
difference. It's not a dissipative mechanism, per se, but will show up
as line attenuation if you put the line on a network analyzer. Small,
flexible lines that are guaranteed to a close tolerance on impedance
are quite expensive.

I don't claim to have any definitive answers for this one, but hope my
comments give you some ideas where to look.

Cheers,
Tom

Owen wrote:

I took the figures published by Belden for their 8262 cable at
frequencies from 1MHx to 1Gz (9 points) and did a polynomial
regression to MLL=k1*f**0.5+k2*f, then substituted k2 into the
expression described in my original post.

I didn't measure the losses, and I recognise that Belden might have
smoothed their results by an intermediate regression, but I figure
that they are not going to exaggerate the effect of k2 unnecessarily.

I didn't realize that was the source of your loss figures. Reg is right,
you have to measure it. Another thing I found long ago is that the
published specs don't match reality. I recall finding Belden to be
conservative with loss, but that sure isn't the case with some others. I
just had occasion to very carefully measure the loss of some Davis RF
"Bury-Flex" which they specify as having 2.9 dB/100' at 400 MHz. It was
4.1 dB/100' at 400 MHz and extrapolated very nicely to at least 3.5 MHz
with a square root rule. (It has a solid aluminum shield under the
copper.) So there's some real specsmanship going on out there.

Roy Lewallen, W7EL

One other thing I did long ago was to check some semi-rigid lines with
solid shield and center conductor and PTFE dielectric, against
theoretical calculations. As I recall, the agreement was pretty good --
much better than the garden variety coax.

And by the way, you'll see a noticeable difference in loss between
RG-58, which has a solid copper center conductor, and RG-58A which is
tinned -- as you'd expect.

Roy Lewallen, W7EL

K7ITM wrote:
My reference suggests that D for PE is 2e-4, but even at that, the
copper loss would be ten times the dielectric loss out to 2GHz, if I
figured it right. It could be difficult to accurately determine your
k2 with such a small contribution from the dielectric. But there are
likely other mechanisms at work...

Roy mentioned the braid. I recall reading a nice article by, I
believe, an engineer with Andrew talking about various loss mechanisms
in coax due to things like braid and stranded inner conductor and
surface smoothness. The article went well beyond the usual theoretical
discussion that assumes smooth conductors and perfectly uniform
construction. I wish I could locate it again! I thought it was in "RF
Design" magazine, but never could find it again there, so perhaps it
was in "Electronic Design" or "EDN".

One mechanism to consider is the effects of a non-constant Zo as a
function of distance along the line. There are undoubtedly small
variations in the manufacturing process. Over a length of line that's
many wavelengths long, even small variations make a noticable
difference. It's not a dissipative mechanism, per se, but will show up
as line attenuation if you put the line on a network analyzer. Small,
flexible lines that are guaranteed to a close tolerance on impedance
are quite expensive.

I don't claim to have any definitive answers for this one, but hope my
comments give you some ideas where to look.

Cheers,
Tom

On Fri, 01 Jul 2005 02:29:31 -0700, Roy Lewallen
wrote:

One other thing I did long ago was to check some semi-rigid lines with
solid shield and center conductor and PTFE dielectric, against
theoretical calculations. As I recall, the agreement was pretty good --
much better than the garden variety coax.


Ok, that is one of the reasons that I looked at how k2 changed with
size of the LDF series.

I have just had a look at LMR200 wrt LMR1700. (They have an aluminium
tape +braid outer.) I do not know the value of D for the closed cell
foam dielectric that they use. The k2 factor (and therefore G) of the
larger cable is about 50% of the smaller cable, though there is nearly
a 1100% increase in diameter. It seems that of the few cables that I
have looked at that ones with better shielding result in less
variation in k2 (and G) with change in diameter ( for Zo and
dielectric remaining constant). That suggests that shielding and loss
effectiveness of the outer conductor is to some extent reflected in G
(proportional to f).

Tom, the D figure I quoted for PE was from the ITT Radio Engineers
Handbook.

G seems not to be solely or principally dependendent on D of the
dielectric in a general sense. It may be with very good lines, but it
doesn't seem to be so with single braided PE insulated coax. It is
clear that using D (even at 2e-4) to calculate G in an RLGC model of
R58C/U will not give a very good fit to published attenuation
characteristics.

Regarding using the published specs, I am trying to glean as much as
is reasonable from the published specs. I note and agree with your
comment Roy about the quality or accuracy of some specs.

Thanks all for the thoughts on possible contributions to G.

Owen
--