Optimization Problem with an RC BP filter

[NascentOxygen]

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.)

 

[NascentOxygen]

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.

 

[The Electrician]

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:

 

[donpacino]

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.

 

[BiGyElLoWhAt]

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.

 

[The Electrician]

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?

 

[NascentOxygen]

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.

 

[BiGyElLoWhAt]

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.

 

[tech99]

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.