Calculating a resonant frequency requires a capacitor and inductor.
I'm trying to figure out the optimal capacitor and inductor values for 49Mhz.
Is it recommended to go for a lower inductor value and higher capacitor value? or vice versa? I'm aiming for best quality.
For example, should I go for 22pF and 480nH inductor or should I go for a 12pF cap and 879nH inductor?
The inductors I will use are premade axial and the capacitors might be ceramic disc.
Best Answer
You have a choice of inductor and capacitor value, that's 2 unknowns. If you know the frequency you want, that fixes their product.
If you are doing a simple school question, job done. Choose the value of one of them arbitarily, and calculate the other.
If the resonant circuit is for a specific purpose however, then you may be able to use other constraints.
The sqrt(L/C) of the components is called the impedance. You may want to control the ratio between your resonant circuit impedance and other components surrounding it. Generally, most transistor/IC applications will end up with a few 10s of ohms to a few kohms impedance, though specialist applications like RF transistor matching or Tesla coils will use lower or higher values respectively.
Closely related is the Q. If you have resistive loading, then the ratio L/R at the resonant frequency will give you the Q. A high Q means a narrow bandwidth, and a very 'ringy' response. A low Q means a wide bandwidth, and a very damped response.
If there is no external resistive loading, and no other constraints, then maximising the Q of the L with respect to its own internal R would be most people's definition of optimal. Go to an inductor catalogue, and tabulate a few Ls and residual Rs, for any given family of inductors. Work out the corresponding C and Q for the target resonant frequency. Warning, the optimum changes with inductor family.
Until you want to control the Q, or the impedance, or the bandwidth of your resonant circuit, you must choose one arbitarily.