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Q&A

Comments on Design high -pass filter with 2 points of the bode plot

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Design high -pass filter with 2 points of the bode plot

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Im designing a high-pass filter which has a gain of -8dB at half of the roll-off frequency and I am stuck ,I dont know how to continue the design.

In the bode plot of that filter we have 2 points:1 is at (fc,-3dB) and the other is at (fc/2,-8dB).What information must I extract to find the transfer function of the filter?

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It sounds like an [XY problem](https://xyproblem.info/#). What is it for? (5 comments)
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You still haven't said why you need, or even what order, type, etc. Assuming it's a 2nd order, an exact solution involves creating a generic transfer function and then solving a system of equations with imposed conditions (use squared to get rid of radical):

$$\begin{align} H(s)&=\dfrac{s^2}{s^2+as+b} \tag{1} \\ &\begin{cases} |H(j)|^2&=\dfrac12 \\ |H(j/2)|^2&=\left(10^{-8/20}\right)^2 \end{cases} \end{align}$$

You wil get four solutions (4 combinations): $$\begin{cases} a_{1,2,3,4}&=[+,-,-,+]0.33035 \\ b_{1,2,3,4}&=[+,+,-,-]0.47976 \end{cases} \tag{2}$$

Since the denominator needs to be a Hurwitz polynomial only the positive values are chosen (the 1st pair), which results in a perfect match:

$$\begin{align} |H(j)|&=0.70711\space(0.70597) \\ |H(j0.5)|&=0.39811\space(0.39165) \end{align}$$

In parenthesis are the results of @TonyStewart's solution, tweaked to have $f=0.42\space(2f=0.84)$. And these are the plots (Tony's is dashed):

matches, as prescribed

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1 comment thread

interesting analysis +1, close enuf for gov't work. (2 comments)
interesting analysis +1, close enuf for gov't work.
TonyStewart‭ wrote over 2 years ago

interesting analysis +1, close enuf for gov't work.

a concerned citizen‭ wrote over 2 years ago

TonyStewart‭ Thank you for returning the favour. You had a nice "back of the envelope" approach.