# Highest frequency with 0 dB attenuation point

#### atferrari

Joined Jan 6, 2004
3,919
Just for reference, let us say we are talking of a Butterworth low pass filter.

What is the real usefulness of knowing the cutoff frequency value (-3 dB attenuation) for me, when I am interested in designing a filter that would pass UP TO xxx Hz with no attenuation, that is 0 dB?

For this particular case, why cutoff frequency is not expressed as the highest frequency point where attenuation is still 0 dB for that filter?

Other way of asking more or less the same: how can I know for the above filter what is the highest frequency that would pass without being attenuated?

Since we are here, could anyone, after answering that question, extend the concept to all filters?

#### t_n_k

Joined Mar 6, 2009
5,455
The issue when asking about the Butterworth LPF response being 0 dB is somewhat nebulous - how close do you want to be to 0 dB? The LPF gain is always asymptotically approaching the DC gain value. In contrast, the point at which the gain crosses the -3dB point is well defined.

Another issue one tends to overlook is that any practical filter design is a compromise. An ideal LPF would pass a strictly defined band of frequencies (from DC to the cut-ff) without suffering any magnitude or phase distortion. Outside of the pass band (above the cut-off in the LPF) nothing is passed through - the attenuation is infinite.

With respect to the Butterworth LPF, there is a phase displacement of the input signal starting for input signals at frequencies well below the LPF cut-off frequency. This may or may not be an issue having regard to the filter application.

#### atferrari

Joined Jan 6, 2004
3,919
Let us say then, I want to know the -0.1 dB point frequency value. Not nebulous now.

#### Audioguru

Joined Dec 20, 2007
11,249
Like I said ten minutes ago on the other website, .... (why post the same thing on two websites?)

Why did they select -3dB to be the cutoff frequency of a filter?
Because it is half-power and it is just noticeable as a small drop in level (audio or video).

How many people can hear or see a 0.5dB drop in level? Anybody?

#### MrChips

Joined Oct 2, 2009
20,882
What is the real usefulness of knowing the cutoff frequency value (-3 dB attenuation) for me, when I am interested in designing a filter that would pass UP TO xxx Hz with no attenuation, that is 0 dB?
There is no such thing as the 0db point in a filter response. All filters will attenuate the signal at any given frequency.

As audioguru says, at -3db you may just start to notice a difference. This is a good way to characterize the cut-off frequency.

#### kubeek

Joined Sep 20, 2005
5,718
Let us say then, I want to know the -0.1 dB point frequency value. Not nebulous now.
I don´t feel like solving it, but you can find it the same way like you would do with a resistive divider set to 0.1dB attenuation, but you replace one resistor with a capacitor = 1/2.PI.f.C in the equation.

#### Ron H

Joined Apr 14, 2005
7,014
I don´t feel like solving it, but you can find it the same way like you would do with a resistive divider set to 0.1dB attenuation, but you replace one resistor with a capacitor = 1/2.PI.f.C in the equation.
That works well for a single pole RC network. Do the same calculation on a 5 pole Butterworth. It can be done (I think), but it isn't simple.

#### kubeek

Joined Sep 20, 2005
5,718
You´re right, I missed the Butterworth part. For that I would just simulate it and see where it rolls off.

#### hgmjr

Joined Jan 28, 2005
9,029
Just for reference, let us say we are talking of a Butterworth low pass filter.

What is the real usefulness of knowing the cutoff frequency value (-3 dB attenuation) for me, when I am interested in designing a filter that would pass UP TO xxx Hz with no attenuation, that is 0 dB?

For this particular case, why cutoff frequency is not expressed as the highest frequency point where attenuation is still 0 dB for that filter?

Other way of asking more or less the same: how can I know for the above filter what is the highest frequency that would pass without being attenuated?

Since we are here, could anyone, after answering that question, extend the concept to all filters?
Greeting atferrari,

Unlike some members of this forum, I think your consulting multiple websites is always a good idea. It provides you with other viewpoints and it also gives members of this website the chance to learn from the information exchange.

Keep it up.
hgmjr

#### atferrari

Joined Jan 6, 2004
3,919
Greeting atferrari,

Unlike some members of this forum, I think your consulting multiple websites is always a good idea. It provides you with other viewpoints and it also gives members of this website the chance to learn from the information exchange.

Keep it up.
hgmjr
Yes. I get wider exposure of my question with better chances of getting an answer.

For me it is simply as talking about the same subject with different group of friends.

I always do.