Hi, good day, i am new to electronics, and have recently learned the formula

fr = 1/2PI SQRT(LC)

However, i also understand there is a formula

fr = 1/2PI SQRT(LC) * SQRT(1 - (r2C/L)

the second formula, i learned, is used when Q, that is the reactance of the inductor / the dc resistance of the inductor is more than 10.

is the second formula applicable for both series RC circuit as well as parallell RC circuits? or is it just for parallel RC circuits.

In the event that i do not have the Q factor, is it safe to assume that i can use the 2nd formula to cater for the worst case scenario.



finally, can i also enquiry on the graph of reasonant frequency. freqencies that are half bandwidth away from reasonant frequency have 0.707 times the voltage of the reasonant frequency,

however, i do not understand how frequencies that are 1 bandwidths away have a value of 44.7 percent of the voltage of the reasonant frequnecy.

how is 44.7 percent derived? i tried 70.7 percent of 70.7 percent, but i only could get 49 percent instead of 44.7 percent.


Appreciate any help in understanding this. thank you in advance.

 

The formulas you quote are derived for specific circuit configurations. You cannot apply one formula for all situations. You have to look at each circuit configuration.

The attenuation of a low-pass or high-pass filter changes with the order of a filter.
For a 1st order filter, the roll-off is -6dB per octave. The -3dB point is where the amplitude falls to 0.707 of the initial amplitude. At one octave higher in frequency, the frequency doubles.

Hence for a band-pass filter, the -3dB points would be half bandwidth away from the center frequency. The -6dB points would be one bandwidth away from center frequency. -6dB is 50%.