# [TowerTalk] 75 or 70 Ohm twinlead or ladderline cable - does it exist?

Wed Mar 26 10:01:01 EDT 2014

```On 3/26/14 6:13 AM, Steve Hunt wrote:
> Jim,
>
> They do, by virtue of the way the data is derived!
>
> I make Open-Circuit and Short-Circuit S11 impedance measurements of the
> line; from which Zo=SQRT(Zoc.Zsc).
> Loss is determined from the input resistance at frequencies where the
> line is multiples of a quarter-wave long.
> Vf is determined by comparing the physical length with the
> multiple-quarter-wave electrical lengths.
>
> At that point the loss model is assumed to be of the form:
>
> Total Loss = k1.SQRT(F) + k2.F
>
> k1 is a coefficient representing the copper loss and k2 represents the
> dielectric loss; the two coefficients are determined by best fit to the
> measured total loss. As a check, k1 can be calculated directly from the
> known RF resistance of the conductors.
>
> Some of the underpinning maths here:
> http://www.karinya.net/g3txq/wet_ll/tl_formulas.pdf
>
> Hope that helps,
> Steve G3TXQ
>

OK.. so you didn't actually independently measure the copper and
dielectric loss (I haven't had my coffee yet, and I'm not sure how you
would do that other than by how you did it); You fit the measured data
to the standard square root and linear model, so of course, the data
matches..

One catch, for others thinking of trying this approach, is when the wire
is small enough that the assumption of it being a thin tube is violated.
Two ways I know that can happen are if the skin depth is a significant
fraction of the diameter or if the wire is plated (e.g. silver over
stainless steel, used for cryogenic coax to minimize heat leakage),
particularly if the materials involved are magnetic. [Yes, indeed, I've
been caught by the latter...]

At 1 MHz skin depth in copper is  2.5 mil/65 micron.  AWG 24 wire is 20
mil/511 micron diameter, which is 8 times the skin depth. Start going
much lower, or using AWG 40 wire, and that thin tube assumption breaks down.

>
>
> On 26/03/2014 12:31, Jim Lux wrote:
>>
>> An interesting test would be to see if the copper losses go as the
>> square root of frequency (skin effect) and dielectric losses go
>> linearly with frequency.
>>

```