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
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
Q&A

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?

Why does this post require moderator attention?
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)

3 answers

+2
−0

Miss Mulan - I am a bit late with my answer. Nevertheless - there is formula which gives you the necessary filter order "n" - as a function of two frequencies and both associated damping figures. If applied to the most simple case (Butterworth approximation) the result is

n>1.2

Hence, a 2nd-order filter topology is required. This sounds plausible because a 1st-order filter has a damping characteristic of 6dB/okt. - however, you require 8 dB.

Why does this post require moderator attention?
You might want to add some details to your flag.

0 comment threads

+1
−0

Filter design 101

  1. given hypothetical high-pass (HPF) filter -3dB gain HPF at fc

  2. attenuation of -8dB at fc/2

  3. Assumptions gain = 0 dB at f>> fc

  4. Ripple between -3dB and 0 dB is unknown but assume 0dB max for simpler case.

  5. steepness of skirts << fc is unknown but we know 1st order slope is 6 dB/octave maximum

  6. the attenuation at fc on a 1st order filter at fc/2= -7 dB which almost satisfies -8dB so is slightly greater than 1st order, which means another 1st order filter that results in -1dB at fc/2 may be added to solve this problem. That frequency might be computed from impedance ratios to obtain the final transfer function, but I can tell you -1dB is about 2xfc.

  7. There are also an infinite number of other solutions if the assumptions change above.

    The breakpoint is defined as the half-power point where the voltage drop is 0.707 or -3dB approx.

Using my assumptions in 6. above I declare the 2nd order HPF transfer function is;

$$H(s)=\dfrac{s^2}{(s+\omega_0)(s+2\omega_0)}$$

See if that suits your specs.

Why does this post require moderator attention?
You might want to add some details to your flag.

0 comment threads

+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

Why does this post require moderator attention?
You might want to add some details to your flag.

1 comment thread

interesting analysis +1, close enuf for gov't work. (2 comments)

Sign up to answer this question »