I have an Elenco AM / FM radio kit. For the AM section I am trying to figure out the relationship between the frequency shown on the calibrated dial and the angular position of the dial.
For a capacitor, the capacitance is defined as C = epsilon * A / d, epsilon is the permittivity of the dielectric material between the plates, A is the plate area, and d is the plate separation.
The capacitance seems to be a straightforward linear function of rotation angle. For a variable capacitor like this,
which is representative only, with maximum capacitance being when the rotating blades are all interleaved with the stator blades, I defined the capacitance as C = -k1 * theta + k2, theta being 0 at the maximum capacitance value.
The kit does not specify the inductor value of the ferrite-core antenna and coil, but I estimated it to be about 0.2 mH.
The resonant frequency for an LC circuit is f = 1 / (2 * pi * sqrt(L * C)).
I plotted two lines.
The "Plotted dial data" curve resulted from reading 6 frequencies from the dial and the angles for which they would tune. The "Theoretical Equation data" is the plot of the frequency equation with the linear C equation substituted into it with k1 and k2 being determined so that the curves meet at 540 kHz and 1600 kHz, the lower and upper ends of the AM band. The respective theta is 10 and 170 degrees.
You can see that the two have a superficially similar shape, but I cannot determine why the theoretical curve is not more like the plotted dial curve.
I am missing something.
Thanks for any help.