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LF: Re: Re: Low loss inductors

To: [email protected]
Subject: LF: Re: Re: Low loss inductors
From: "Dick Rollema" <[email protected]>
Date: Mon, 28 Feb 2000 15:28:39 +0100
References: <[email protected]> <[email protected]> <[email protected]>
Reply-to: [email protected]
Sender: <[email protected]>
To All from PA0SE

Bob, ZL2CA, wrote:

I am strongly of the view that coaxial cable with the far end either short
or open
termination is mostly reactive at LF when "looking" in to the near end
of the cable.  The main issue is the loss factor (or Q).  Which has the
higher Q, a coil or a shorted end coaxial cable?

>From an intuitive point of view, I would think a purpose built coil
would give lowest losses for a given value of inductance needed.  The
designer is in full control of countermeasures for skin effect,
proximity effect, voltage gradient and can select the best length to
diameter ratio for a given frequency band.  On the other hand, coaxial
cable is widely used at VHF/UHF for "stub matching", however it does not
appear to be technique that has been used on lower bands, where lumped
components are generally preferred, and can be variable (variable
capacitors and variometers) and so are more useful for "tuning up" or
adjusting for a good match to 50 ohms.
Using N6BV's transmission line  computer program TLA  I have inserted
different
lengths of RG-213 coax, terminated in a short circuit.

Starting from zero length the inductive reactance "seen" at the input of the
cable starts to rise and reaches a maximum at about 1130 ft (344 m) of
cable.
There Zin = 435 +j 334 Ohm.  When the length increases further X decreases
and reaches zero when quarter wave resonance is reached.
X = j 334 Ohm corresponds to an inductance of 388 microhenry. Apparently
that is the maximum "coil" that can be constructed this way. But Q = 334/435
= 0.76.
So it just does not work.

That an "inductor" made this way  has so much loss is not so difficult to
explain.
In a normal coil at LF the current has the same value at all points. The
(I squared  *  R) loss per cm of wire is the same throughout the coil.

But in an inductor made of a piece of coax, shorted at its end,  current
rises from the value at the input to a much larger value near the end. As
loss is proportional to current squared the contribution to the loss in the
pieces of coax near the end is very much larger than the loss near the
beginning of the cable. The end result is a much larger loss than in the
case of  uniform current distribution and this translates into a larger R
component in Zin = R + j X.

At VHF the story is different.

For instance a 23 cm long piece of RG-213 coax, shorted at its end, has at
145 MHz an input impedance of Zin = 0.78 + j 88.99 ohm. This looks like an
inductor of
0.1 microhenry with  Q = 88.99/0.78 = 114.
Although the loss/100 ft of the cable at 145 MHz is very much higher than on
137 kHz this is more than compensated for by the small length of the cable.
Therefore shorted (open) stubs as inductors (capacitors) can be used
succesfully at VHF and UHF.

73,

Dick Rollema, PA0SE





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