I have some questions about this problem about a L.P. (low pass) filter:

"Determine n, the order of a lowpass Butterworth filter, and the corresponding cutoff frequency wc, required to satisfy the following lowpass filter specifications. Find both the values of wc, the one that oversatisfies the passband specifications, and the one that oversatisfies the stopband specifications.

The gain at 3wc is required to be no greater than -50 dB."

For the lowpass filter, I think that for frequencies w < wc, the gain is 1 (no amplification or attenuation of the signal), and after that, the gain quickly drops to 0 (unity). I need to identify the minumum passband gain (at frequency wp) and maximum stopband gain (at frequency ws) to use the equations in my text for n and wc, but I'm not certain how those were given in the problem. Specifically, where is 3wc in relation to wp and ws? Intuitively, would 3wc = ws since the gain there is no greater than -50 dB? But then, what simplifying assumption(s) determine(s) where wp is?

Thank you for the help,

Sincerely,

J_Rod