Optimization Problem with an RC BP filter

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Discussion Overview

The discussion revolves around the design of an RC bandpass filter circuit intended to peak voltage at 10kHz while maintaining less than half peak voltage at 3kHz and 30kHz. Participants explore optimization strategies, circuit behavior, and the implications of component selection within the constraints of using only capacitors and resistors.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a complex formula for current in the circuit and expresses uncertainty about the optimization process, suggesting that capacitance ratios may be key.
  • Another participant recommends using programming tools like R, Matlab, or Mathematica for optimization instead of spreadsheets, citing efficiency and ease of use.
  • There is a discussion about the meaning of "optimization" in the context of filter design, with some participants suggesting that achieving a high Q factor is desirable.
  • Participants discuss the behavior of the low-pass and high-pass filter stages, with hints provided about the relative sizes of capacitors C1 and C2 and their impact on circuit behavior.
  • One participant questions the dimensional consistency of the formula presented, suggesting that the terms may not have the same units.
  • Another participant reflects on the challenge of maximizing an RC circuit and discusses the relationships between frequency, resistance, and capacitance in the context of achieving desired voltage levels.

Areas of Agreement / Disagreement

There is no clear consensus on the best approach to optimization, as participants express differing views on the meaning of optimization and the implications of component selection. Some participants agree on the importance of the Q factor, while others raise questions about the assumptions made regarding component behavior.

Contextual Notes

Participants note limitations in their approaches, such as the complexity of the optimization process and the challenges of dimensional analysis in the presented formulas. There are also unresolved questions about the appropriateness of approximations used in analyzing circuit behavior.

Who May Find This Useful

Readers interested in circuit design, particularly those focusing on filter design and optimization techniques in electrical engineering, may find this discussion relevant.

  • #91
The Electrician said:
Here's the un-normalized response of your original circuit using the R and C values I gave in post #25:
Have you determined the Q with those component values?

There's a formula relating Q to the -3dB bandwidth, but do you know any general formula relating Q to the -6dB bandwidth? (The task here specifies the -6dB bandwidth, approximately.)
 
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  • #92
donpacino said:
when analyzing the circuit, the transfer function is found seen below

Vo/Vin = [SC_2R_2 ] / [ S^2C_2^2R_2_2+S(2C_2R_2+C1R1)+1 ]
I have been wanting to reconcile this equation with the plot in #25. Is there an error in this apart from the subscript?

The plot in #25 seems to be exhibiting a Q of around 0.5 or so. (10,000÷19,000) [EDIT: correction]
With the Rs and Cs suggested, I calculate using your equation: Q = 0.333

There needs to be agreement in these figures before developing this further.
 
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  • #93
donpacino in post #32 has the wrong transfer function. The pdf file in post #60 has the derivation of the correct transfer function.

My derivation is the same:

PBP4.png
 
  • #94
The Electrician said:
donpacino in post #32 has the wrong transfer function. The pdf file in post #60 has the derivation of the correct transfer function.

My derivation is the same:

View attachment 106821
Just checked my work. Yes it is incorrect. I now got what the electrcian got. I switched some terms part way through the analysis. 1 am algebra will do that I guess.

the take away: always sanity check your work. In retrospect my answer makes no sense.
 
  • #95
Well, it seems as thought it was merely meant to be a struggle. It wasn't supposed to work, and when I went back, we started messing with bridge filters. Somewhat cruel, but I suppose it was meant to teach us a lesson we won't soon forget LOL.
 
  • #96
Are you saying that your professor is showing you a bridge filter, with only Rs and Cs that will meet the requirements? Or are you saying that your professor expected that you would not be able to meet the requirements with only Rs and Cs?

Did you show your professor that the requirements can be met by the 4 stage R/C filter I showed you?
 
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  • #97
NascentOxygen said:
With the Rs and Cs suggested, I calculate using your equation: Q = 0.333
The figure of 0.33 does seem lower than what I would expect to be achievable.

I added a capacitor parallel to R2 and my calculations (if correct) indicate this can realize a Q of approx 0.88. But I have yet to dertermine whether this would be sufficient to meet this task's specifications.
 
  • #98
I'm saying that we moved directly into discussing bridge filters. I suggested a 4 stage filter, and he said that should work, but that was all the further the conversation went.
 
  • #99
Maybe my simple engineering approach would not satisfy your examiner. However, a simple approach is to draw a phasor diagram for a series circuit consisting of C and R. It is easy to see that if Xc is half R, then the voltage across C is a bit less than half the applied voltage. This is the desired condition.
The high and low circuits are so far removed that interaction will be negligible.
 

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