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Design >> Analog Design >> How these LPF are compared?
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Message started by neoflash on Nov 28^th, 2010, 7:39pm

Title: How these LPF are compared?
Post by neoflash on Nov 28^th, 2010, 7:39pm

I'm looking at a chart comparing five types of fifth-order filters.

It is claimed that they are compared at the same corner frequency. How this Fc is defined for different types of filters?

Title: Re: How these LPF are compared?
Post by buddypoor on Nov 28^th, 2010, 11:31pm

1.) Butterworth-, Bessel- and Chebyshev (invers)- response:
Usually the corner frequency is defined at a frequency that has a gain magnitude of 3 db less than at DC.
2.) For all Chebyshev-like responses (including elliptical) with ripple in the passband the corner frequency (in most cases!) is defined at a frequency where the magnitude response leaves the specified ripple area.
That means it is unusual to specify a 3-dB corner for these responses.
_____________

Comment to the attached picture: To me it seems that the Bessel response (yellow curve) has another passband if compared with all other curves.

Title: Re: How these LPF are compared?
Post by carlgrace on Dec 2^nd, 2010, 11:02am

I agree with buddypoor, fc is strictly defined as the frequency at which the gain magnitude has decreased by 3dB. I also agree that the Bessel filter has a different fc from the other filters.

Carl

Title: Re: How these LPF are compared?
Post by buddypoor on Dec 2^nd, 2010, 12:21pm

carlgrace wrote on Dec 2^nd, 2010, 11:02am:

I agree with buddypoor, fc is strictly defined as the frequency at which the gain magnitude has decreased by 3dB. I also agree that the Bessel filter has a different fc from the other filters.
Carl

Carl, I don't completely agree with you; I don`t like the term "strictly" in your answer. A definition is an arbitrary common agreement - nothing else.
And in some cases you are, of course, allowed to specify another "corner frequency", for example only 1 or 2 dB down. But in any case, it should be mentioned clearly as such.

Title: Re: How these LPF are compared?
Post by carlgrace on Dec 3^rd, 2010, 8:19am

buddypoor wrote on Dec 2^nd, 2010, 12:21pm:

Hi Buddypoor,

I guess I agree and disagree with you at the same time. You are quite right that people are free to specify different specifications (for example like you said a 2 dB corner frequency). However, there has to be some agreement to standard specifications or else there will be endless confusion. I think if someone has a circuit and says to you "fc of this circuit is 100 MHz" the person is saying "The frequency at which the output is 3 dB below it's midband value is 100 MHz" and only that. If the person actually means 2 dB or 10 dB down, it is the responsibility of that person to explicitly say "10 dB corner" or something like that. "Fc" without a qualification means 3 dB corner, and only that.

An example where there is a lot of confusion in practice is with Noise Figure. It *is* strictly defined at a 50 Ohm reference impedance but a lot of times people get confused about this, particularly when their gain stages drive high impedances.

So, I spent a lot of time saying: Yes, I agree specifications are arbitrary. However, once we agree they have to be absolute or else they lose a lot of their usefulness.

Perhaps we can agree on this much? :)
Carl

Title: Re: How these LPF are compared?
Post by buddypoor on Dec 3^rd, 2010, 9:36am

Hi Carl,

thanks for your answer and - yes, now I am totally on your line, in particular with the following (quote):

I think if someone has a circuit and says to you "fc of this circuit is 100 MHz" the person is saying "The frequency at which the output is 3 dB below it's midband value is 100 MHz" and only that. If the person actually means 2 dB or 10 dB down, it is the responsibility of that person to explicitly say "10 dB corner" or something like that. "Fc" without a qualification means 3 dB corner, and only that.

My only reservation was in connection with the phrase "strictly".
Thanks and regards
buddypoor
(by the way: Do you know Buddy Rich?)

Title: Re: How these LPF are compared?
Post by carlgrace on Dec 7^th, 2010, 4:21pm

I looked on Google. Buddy Rich is a jazz drummer? I had never heard of him before.