Not often that maths formulas excite me, I must say - but I came across these simplified formulas for resonant circuits, and it got me thinking..
Perhaps folks could share simple stuff like this here (Thierry presented beautifully simple calculations in the Antenna tuning thread recently) which makes life easier for the stupid or lazy or those like me who dont understand why they dont understand! (or, even though they believe they understand, always get the answers wrong!)
So, heres the "awkward" resonance formula:
f= 1 / (2pi * Sqrt(L*C))
where f = frequency in Hz, L = inductance in Henrys, C is capacitance in Farads.
And here's what I found:
L*C*f*f = 25330 .... This applies for ALL values of L,C and f, AND L = uH, C=pF, f= MHz.
From this we get:
Given C and L : f = Sqrt (25330 / (L*C))
Given C and f : L = 25330 / (C*f*f)
Given L and f : C = 25330 / (L*f*f)
f = MHz
C = pF
L = uH
I have no real understanding why this should be true, but it certainly seems to be - and (to me) is a lot simpler to enter into a spreadsheet than the other way - yeah, still have a constant instead of 2pi, and essentially the above is not much simpler than the original - but it sure looks simpler! ;-)