# [SI-LIST] : SYNTHETIC INDUCTOR USING SHORTED TX LINE

From: Steve Rogers ([email protected])
Date: Tue Feb 20 2001 - 04:40:28 PST

I have been looking into the use of shorted transmission line 'stubs' as
synthetic inductors. In particular I hoped that this approach could yield a
high Q factor inductor at VHF.

Shorted stubs made using semi-rigid coaxial line seem to be popular for low
phase noise oscillators at UHF frequencies which suggests a high Q structure
be possible by this method. I had an attempt at producting a synthetic
inductor for VHF using a length of semi-rigid coaxial line shorted at one
end the result was poor to say the least. Details below:-

Line length 0.7 metre
Resonant frequency approx 80 MHz
Q: approx 50

I wonder why the Q is so poor?

My analytical attempts.

My first stab at attempting to justifiy the loss assumes that the cable loss
given by the manufacturer may be used together with the line length and the
driving impedance to calculate the loss due to the inevitable multiple
reflections between the source and the load (Basically use of complex power
flow with masons rules). At first this seemed to be the way to go but then I
thought about the loss value for the line. The loss given by the
manufacturer only applies to a matched line! So what is the loss for a
shorted line???? The V:I ratio will clearly vary along the line length being
min V max I at the short. The loss of the line will thus be a function of
the position of the section of line in question with respect to the short
circuit (at and near the short where currents are max the i squared R losses
must be dominant, at and near the V maximum points the dielectric losses
must be maximum).

Is my thinking taking me off on the wrong path here (is there an easy answer
to this problem?)

IF ANYONE CAN SUGGEST HOW TO SOLVE THIS ONE IT WOULD BE VERY MUCH
APPRECIATED?