I'm building an FM radio transmitter kit which includes an LC tank, where C is a tuner capacitor of ~30pF and the resonant frequency is ~100Mhz. The value of the PCB trace inductor, however, is not specified and I want to know what it is.
If I plug:
\$100000000=\dfrac{1}{2π\sqrt{L3\times10^{-11})}}\$
into an equation solver the result is apparently 52771500 Henries. That seems… a little off? Considering most of the FM transmitter examples I've looked at on the net are like, 0.5uH?
How do I work this out?
Best Answer
I think this is a mathematical error as I specified in a comment. To clarify further, rearrange for L as follows.
$$ L = \frac{(1e8*2\pi)^{-2}}{3e-11} = \frac{1}{12\pi^2} \cdot \frac{1e-16}{1e-11} = 8.443e-8 H = 84.43 nH $$
The equation holds and seems to yield a reasonable value.