Hi all, I'm in doubt on how to solve for the for any transfer function , and I would like to solve it. My question is not related to 1st order functions, but from 2nd order and so on. For example, suppose I have a simple RLC low pass filter: Solving for the transfer function : for example, I tried to solve for the -3dB frequency But I cannot find the correct result, and I know by simulation and from the first pole that kHz I opened this post here because I think my doubt is more related with math concepts. Thank you in advance.
Hi Mike, It's the second one, but you swapped the values of inductance and capacitance between them. L = 10 uH C = 10 nF From the denominator of the transfer function I know that in this case the frequency of -3dB is 15931 Hz, and for the circuits you posted the -3 dB is 15,915 Hz for the LP and Hp. But I would like to know how to solve the equation analytically, if possible. Thanks !
To solve for ω you would: Substitute the values for R, L, and C. Square both sides of the equation to remove the radical Then solve for ω Check your work by using the value of ω to get a magnitude of 0.707
That's what I have done solving a 4th order polynomial: but I cannot get the correct result, or I cannot recognize it...
If you expand things out you have terms in the fourth, second, and 0th power of ω. That suggests a quadratic polynomial in ω^2 which can be solved with an appropriate substitution.
It really helps if you show your work from beginning to end. Think about it -- you say that you believe the problem you are having is related to math concepts -- so wouldn't the most effective way for people to spot where you are having problems with the math for you to show the math you are doing?
Hi, sorry for my late response. I had to study other things too.. This is the calculation I have done: But no one brings me to the result of 100100 rad/s..
Note that your 0.707 comes from 1/sqrt(2). Leverage that knowledge. Now apply the quadratic formula and see what happens.