- #1

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Where BW=bandwidth, fr=resonance freq and Q is Quality factor.

I understand this relationship suppose to hold, I just don't understand why.

I basically am looking for a proof.

thank you all a priori.

drforbin

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- Thread starter merlyn
- Start date

- #1

- 20

- 4

Where BW=bandwidth, fr=resonance freq and Q is Quality factor.

I understand this relationship suppose to hold, I just don't understand why.

I basically am looking for a proof.

thank you all a priori.

drforbin

- #2

Bystander

Science Advisor

Homework Helper

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http://en.wikipedia.org/wiki/Q_factor

Origin rather than proof enough?

Origin rather than proof enough?

- #3

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http://en.wikipedia.org/wiki/Q_factor

Origin rather than proof enough?

Thank you so much for your reply.

Unfortunately I already read that Wiki page.

I'm really looking for a proof and I can't seem to find one ANYWHERE.

I understand intuitively how the relationship could work (or does work) but I really would like to see the math.

- #4

NascentOxygen

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Start with the general 2nd order transfer function for a bandpass filter,

remember Q = 1/(2ζ )

replace s by jω

calculate ω where the magnitude of the real part equals that of the imaginary part,

you should be close to getting your answer

http://thumbnails112.imagebam.com/37333/0363e9373324851.jpg [Broken]

remember Q = 1/(2ζ )

replace s by jω

calculate ω where the magnitude of the real part equals that of the imaginary part,

you should be close to getting your answer

http://thumbnails112.imagebam.com/37333/0363e9373324851.jpg [Broken]

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- #5

meBigGuy

Gold Member

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Googled q factor proof:

This may answer your question.

http://ocw.mit.edu/courses/electric...pring-2006/lecture-notes/resonance_qfactr.pdf

Your problem will be dealing with this:

"By combining Equations (1.9), (1.10), 1.11) and (1.18) we obtain the relationship between the bandwidth and the Q factor"

which, of course, he does not do in the paper.

This paper has some proofs, but I didn't go through it rigorously to see if it actually answered your question. It takes a different approach.

http://www.lightandmatter.com/html_books/lm/ch18/ch18.html [Broken]

This may answer your question.

http://ocw.mit.edu/courses/electric...pring-2006/lecture-notes/resonance_qfactr.pdf

Your problem will be dealing with this:

"By combining Equations (1.9), (1.10), 1.11) and (1.18) we obtain the relationship between the bandwidth and the Q factor"

which, of course, he does not do in the paper.

This paper has some proofs, but I didn't go through it rigorously to see if it actually answered your question. It takes a different approach.

http://www.lightandmatter.com/html_books/lm/ch18/ch18.html [Broken]

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