How do I normalize angular frequency for circuit optimization?

[anothnagle]

Hey all,

This question may sound daft, but how do I normalize angular frequency? For a little background: I'm trying to optimize some circuits, and I've managed to write some successful code using the "Design of Ultra Wideband Antenna Matching Networks" book, but the code requires normalized angular frequency, whereas what I have are data for the normal frequency response of our circuits. I imagine I should be normalizing to radians/second, but I could be wrong. What would I do for this?

Thanks

 

[OldEngr63]

"To normalize" usually means to divide the actual value by some characteristic value. Is there a natural frequency associated with this system? If so, normalized frequency might mean omega/omega_nat.

 

[anothnagle]

What can I do if I don't know the natural frequency? Can I normalize it at all?

 

[Baluncore]

For a broadband network that has no obvious centre frequency I would find the frequencies of some reference level such as the -3dB points and use the geometric mean of those as the reference. It does not matter if you use radians or hertz, normalisation will reduce them to the same values.
F_ref = Sqrt(F_min * F_max)

 

[alphy]

for your question. Normalizing angular frequency means converting it to a dimensionless quantity by dividing it by a reference frequency. This is commonly done in circuit design to make calculations and comparisons easier. In your case, if your circuit data is in normal frequency response (in Hertz), you can normalize the angular frequency by dividing it by the reference frequency, usually the center frequency of your circuit. This will give you a dimensionless quantity that can be used in your code. If your circuit data is already in radians/second, then you can skip this step. I hope this helps.