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## Homework Statement

OK, I have the response function for a notch filter, and I want to find out what the frequency where it has the -3dB response.

## Homework Equations

[tex]H(\omega) = \frac{1-\omega^2LC}{1-\omega^2LC+i\omega RC}[/tex]

This is my response function. My [itex]\omega_0 = \frac{1}{\sqrt{LC}}[/itex]

## The Attempt at a Solution

OK, so I figure that what I am looking for is where [itex]20\log_{10}(H(\omega)) = -3[/itex]. This should be simple enough, but I am having some difficulty and I suspect I am messing up something stupid and obvious.

I am pretty sure that all I need is to have [tex]H(\omega) = \frac{1-\omega^2LC}{1-\omega^2LC+i\omega RC} = \frac{1}{\sqrt{2}}[/tex]. But it's getting there that's the problem and figuring out what my omega ought to be. I tried simply saying that the absolute value of my response function squared should be 1/2, and thereby getting rid of the imaginary component. This is kind of a silly algebra question I suppose, I feel like there is some ridiculously simple thing I am not seeing here.

Looking at it I need something where plugging in [itex]i \omega RC = i \frac{1}{\sqrt{LC}} RC[/itex] yields a square root of 2, or plugging in R/L as my change in omega and multiplying things out, but I feel like I am missing something even simpler than that. Anyhow, any help is appreciated.