Help frequency to dB relationship

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Discussion Overview

The discussion revolves around designing a filter with a specific frequency response, particularly focusing on the relationship between frequency and decibels (dB). Participants explore how to determine the -6dB point for a filter with a 24dB/oct slope, starting at 0dB at 90Hz, and consider various filter topologies such as Butterworth, Chebyshev, and Elliptical.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Exploratory

Main Points Raised

  • One participant seeks guidance on finding the -6dB point for a filter designed to have a 0dB response at 90Hz.
  • Another participant suggests using different filter topologies and plotting their frequency responses to understand the behavior of the filter at the -6dB point.
  • There is a mention of potential disadvantages of sharper filters, though the specific disadvantage is not agreed upon, with suggestions including size and added complexity.
  • A later reply emphasizes the importance of considering real-world component tolerances when simulating filter responses.
  • One participant notes that different filter topologies exhibit varying characteristics in passbands and stopbands, highlighting the trade-offs between flatness and sharpness of the knee in the frequency response.

Areas of Agreement / Disagreement

Participants express differing views on the disadvantages of sharper filters and the implications of filter topology on design choices. No consensus is reached regarding the main disadvantage of sharper filters.

Contextual Notes

Participants mention the need to consider real-world factors such as component tolerances and the characteristics of different filter topologies, which may affect the design and performance of the filter.

frogdogbb
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Hello all, I am having trouble figures out the following filter I am designing. I to use a filter with a 24db/oct slope I want 0dB@90hz. So if I want the knee of the cuttof curve to start at 90Hz how do I find the -6dB point so I can design the crossover, by the way this filter uses -6dB as the crossover point as opposed to the usual -3dB.
Thanks
 
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It depends on the topology of your filter. Cheby, Butterworth, etc. Just put a generic form of the candidate polynomials into Mathematica or even Excel, and plot out the frequency response. That will start to show you how close you can get a 0dB flat spot to the -6dB point with each polynomial. It's way different for the different filter topologies. Keep in mind that in the real world, there can be some disadvantages to the sharper edged filters. Quiz question -- what is generally the main disadvangate of the sharper filters...?
 
I don't know what is the main disadvantage? Size, added complexity? It is an active filter so componet losses are not really an issue.
 
frogdogbb said:
I don't know what is the main disadvantage? Size, added complexity? It is an active filter so componet losses are not really an issue.
Nope. Hint -- you need to order the resistors and capacitors from Digikey to build your filter. Read the datasheets from digikey for the real components, and resimulate the filter response, based on the published tolerances. See any problems?
 
frogdogbb said:
Hello all, I am having trouble figures out the following filter I am designing. I to use a filter with a 24db/oct slope I want 0dB@90hz. So if I want the knee of the cuttof curve to start at 90Hz how do I find the -6dB point so I can design the crossover, by the way this filter uses -6dB as the crossover point as opposed to the usual -3dB.
Thanks
BTW, keep in mind that the different topology filters have different characteristics in the passbands and stop bands, as well as different knee sharpness characteristics. The Butterworth is flat and slow, the Cheby is better if you can tolerate some ripple in the passband (not 0dB all across), and the Elliptical is better yet in terms of a sharp knee, if you can tolerate gain ripple in both the passband and stopband.

But the quiz question that I posed above would also factor into your decision for a real world filter (another hint here), especially if you plan on building them in the millions...
 

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