[HBR] Re: Linear Capacitor Tuning

[hbr@mailman.qth.net]

I got involved in this about 30 years ago.  I must admit that I never put the 
following into a practical project, but here is the theoretical shape of the 
plates of a linear-with-frequency tuning capacitor:

R=SQR((-4*K)/(H*(K*A+F2)^3)+C^2)

Where:
R == Radius of plates as a function of rotation (inches)
A == Angle of rotation (radians) -- the variable in the equation
K == Rate of frequency change with rotation -- (Hz/rad)
F2 == Higher frequency (freq with plates unmeshed) (Hz)
C == Radius of cutout in stator to clear shaft (inches)
H == Ck/(F1^2*C1)
       Where: Ck == Farads per square inch of capacitor used -- this accounts 
for the plate spacing and number of plates
                F1 == Lower frequency (Hz)
                C1 == Capacitance at F1 (Farads)

The equations look much simpler when you put them in standard math notation.

Since this is only theoretical, fringing of the electric field is neglected, 
but this should have only a minor effect.

Now, does someone know how to build a capacitor once you design it?

Anyway, it is fun to see what the capacitor you want looks like.  Remember I 
did this back before home computers.  I had a TI SR-10 calculator which was 
great because you could do square roots on it!

Dan K9WEK


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