We have two identical opamps with a first order low-pass response. They both have the same 3-dB frequency \$f_1\$.

I need to show that their combined 3-dB frequency (when they are put in cascade) is:

\$f_{3dB} = \sqrt{\sqrt{2}-1}f_1\$.

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    \$\begingroup\$ what did you try? \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Jan 13 at 19:02
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    \$\begingroup\$ Hello, João, welcome to EE Stack Exchange! This appears to be a homework problem. The general rule here with homework problems is that you need to show all the work you've done thus far, and explain where you're getting stuck. This helps us help you develop your understanding. \$\endgroup\$ – Peter Jan 13 at 19:03

The 1st order LPF response is 1/(1+jf/f1). When f = f1, it becomes 1/(1+j) with magnitude of 1/sqrt(2), corresponding to -3dB. When two of these are cascaded, the freq. response becomes, [1/(1+jf/f1)]^2 with magnitude of 1/[1+(f/f1)^2]. Set it to 1/sqrt(2), then 1/[1+(f/f1)^2] = 1/sqrt(2), then solving f gives f3dB = sqrt[sqrt(2)-1]*f1.

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