Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs
Community Proposals
Community Proposals
tag:snake search within a tag
answers:0 unanswered questions
user:xxxx search by author id
score:0.5 posts with 0.5+ score
"snake oil" exact phrase
votes:4 posts with 4+ votes
created:<1w created < 1 week ago
post_type:xxxx type of post
Search help
Notifications
Mark all as read See all your notifications »
Q&A

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

Parent

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

+0
−3

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?

History
Why does this post require attention from curators or moderators?
You might want to add some details to your flag.
Why should this post be closed?

1 comment thread

It sounds like an [XY problem](https://xyproblem.info/#). What is it for? (5 comments)
Post
+1
−0

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

History
Why does this post require attention from curators or moderators?
You might want to add some details to your flag.

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 about 2 years ago

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

a concerned citizen‭ wrote about 2 years ago

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