Picking up on a comment in a previous thread on coax traps

The type of trap I am discussing here is one where a coil is formed of
a length of coax, the outer conductor of one coax end is tied to the
inner conductor of the other coax end, and the remaining connections
(outer at one end and inner at the other) form the terminals for the
trap.

I have drawn a diagram of the configuration at
http://www.vk1od.net/lost/coil.gif .

I am unsure of who originated this design, so until I determine that
reliably, I will refer to the design as the "bootstrap" type, as the
inductor is connected in parallel with one end of the transmission
line, and the outer of the other end of the line is connected to the
end of the inductor so as to bootstrap the pair.

I have seen explanations of the operation of this circuit, and those
that I have seen seem unsound.

Let me propose an explanation of how this trap works.

With reference to the diagram, I1 is the current into terminal A and
the inner conductor of the coax. Lets designate V1 as the voltage
beween the inner and outer of the coax at that point.

I2 is the current out of the other end of the coax inner conductor,
and lets designate V2 as the voltage beween the inner and outer of the
coax at that point.

The outer conductor of the coax forms a coil with and equivalent
inductance and series resistance.

The current that flows on the outside of the coax outer conductor is
I1+I2.

V1, I1, V2, and I2 have a relationship given by the common
transmission line equations, given gamma (the complex propagation
constant) for the transmission line, and its length.

The impedance between terminals A and B is given by (V1+V2)/I1.

The values for V1, V2, and I1 can be found by solving the set of
simultaneous equations that describe the system.

It seems to me that an explanation that considers that I1=I2, or that
propagation time on the coax is zero, or that the inner conductor
forms a inductance with mutual coupling to the outside of the outer
conductor is flawed.

Owen

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