Ian White GM3SEK wrote:
In that case, I suggest you stop making constant references to "1/4WL
self-resonance" and "1/2WL self-resonance". If you don't mean it
literally, it's a very misleading metaphor.
All of those concepts are explained at:
www.ttr.com/TELSIKS2001-MASTER-1.pdf
in an IEEE sponsored paper by KB1EUD and K1AON. The first high
impedance self-resonance point of a coil, where the phase angle
changes sign, is called "quarter-wave resonance". (The self-resonant
frequency for a 75m bugcatcher loading coil *IS* the 1/4WL self-
resonant point.)
Under "III. TRANSMISSION LINE MODELING", it says:
"By means of conventional distributed-element theory, a thorny
boundary value problem has been reduced to a very simple RF
transmission line. In fact, the entire design and tuning
exercise ... can now be performed conveniently on a Smith Chart."
"There are a great number of formulae for coil self-capacitance.
None are of particular value for quarter-wave helical resonators
anywhere near the 90 degree point."
A coiled coax choke operated at its self-resonant frequency *IS*
being operated at the quarter-wave (90 degree) point.
I doubt that the IEEE would publish a "very misleading metaphor".
I have graphed the |Z| data for all the chokes (see link to spreadsheet
below) and there is no consistent trend. In the following table, Fmax is
the frequency of maximum impedance, and Fmin is the frequency of any
minimum observable within the frequency range (the 8t 1 layer choke has
two very small minima). Ratio is Fmax/Fmin.
What we are looking for is the phase shift from negative to positive.
That would indicate the 1/2WL point.
Choke Fmax Fmin Ratio
6t 1 layer 24 none -
The 1/4WL self-resonant point is at 24 MHz. 48 MHz data is not
given. There is no phase shift from negative to positive in the
given data. The 1/2WL resonant point is not contained in the
data so this set of data is useless for finding the 1/2WL point.
12t 1 layer 15 31 2.1
2.1 is approximately 2
4t 1 layer 21 34 1.6
8t 1 layer 12 19 1.6
Round the 1.6 to a single digit - that's approximately 2
8t bunched 12 32 2.7
Bunched isn't well behaved enough to count.
beaded 6 36 6.0
Beaded isn't a coil so doesn't count.
Judging from the shapes of the graphs and the table above, I would say
that "twice the frequency" is not even valid as an approximation.
Someone needs to explain to mathematicians that rounding 1.6
to an integer isn't equal to 2. If I said it was an extremely
rough approximation, would that be better?
Across the whole 1-30MHz band, the bunched choke behaves as an almost
perfect L-C circuit, free from any unwanted resonances.
Which means it is not behaving as a slow-wave coil structure.
One might say it is misbehaving and is a very poor design.
If you say "the length of wire is irrelevant to this discussion" - with
which I most strongly agree - why do you persist in using these terms
"1/4WL" and "1/2WL" - what dimension of the choke are they referring to?
I'm using them because the IEEE uses them. I keep telling you
that they do not refer to a physical dimension! They refer to
a measurable condition. The first self-resonance is obviously
the 1/4WL point.
I did make a mental slip-up in my previous posting. I forgot
that the VF of the coil changes with frequency. That would
help explain the deviation away from the times two value for
1/2WL resonance. To illustrate the transmission line
characteristic of the choke, the frequency needs to remain
constant while the number of turns is varied.
--
73, Cecil
http://www.w5dxp.com