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# What does 'cut-off frequency' by a low-pass filter mean?

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#### kickbeer

##### Full Member level 3
what does 'cut-off frequency' by a a low-pass filter mean?

low pass filter

The cutoff frequency is where its output level is -3dB (0.707 times the voltage). -3dB is half the power.

### kickbeer

Points: 2
design low pass filter

kickbeer,
In most cases, the cutoff frequency is as Audioguru stated. There are some exceptions. In the case of Chebyshev or Elliptic (Cauer) filters, the cutoff frequency is usually defined as the highest passband frequency at which the response is down an amount equal to the passband ripple. For example, with a 1dB Chebyshev filter, the cutoff frequency would be the highest passband frequency at which the response is down 1dB
Regards,
Kral

Re: low-pass filter

Hi kickbeer !

May be you know these definitions:

# In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at ...
en.wikipedia.org/wiki/Cut-off_frequency

# The point where a lowpass or highpass filter makes a transition from the passband to the stopband. Normally given as a -3 dB point. Also called FC.
www.trilithic.com/RF and Microwave Components/Support/Glossary.html

# the frequency at which the response is -3dB with respect to the maximum response.
www.diracdelta.co.uk/science/source/f/i/filter/source.html

# The frequency that marks the edge of the filters passband and the beginning of the transition to the stopband, usually -3dB relative to filters ...
www.tte.com/glossary.php

One more reason to select the 3dB level is that after that level the characteristics of the filter is easy to approximated with lines. Generally speaking there are no overshoots and undershoots after that level.
But there are some exceptions which are not very interesting.

It is good do define your application and according to the standards in that filed to define the parameters inducing "cut off frequency".
But take the 3dB limit in 99% of the cases and you will be safe.

Please see f Figure 46. Oscilloscope bandwidth is the frequency at which a sinusoidal
input signal is attenuated to 70.7% of the signal’s true amplitude, known as
the –3 dB point.
https://socrates.berkeley.edu/~phylabs/bsc/Supplementary/Lab1/xyz_scopes.pdf
and you will see the characteristic of low pass filter from firs order (RC).
Tektronix: Primer > xyzs of Oscilloscopes

BR

Re: low-pass filter

I completely agree with KRAL, especially to the exceptions mentioned by him (Chebyshev and Cauer/elliptic).
One more exception: For a BESSEL/Thomson filter the cut-off very often is defined in the TIME domain (with respect to the group delay) since this approximation mostly is used to satisfy specifications in the time domain.
Example: cut-off id reached when the group delay differs by 1% or 5% from the basic delay.

Re: low-pass filter

Hello to all!

As I have already posted at

In my opinion the “cut-off frequency” is inappropriate, unclear and misleading term.
In all real cases noting is “cut – off” or at least I don't know similar case.

There are things that are attenuated/modified at some level.
In that cases notations as:
* for positive values Fp1dB, Fp3dB, Fp6dB, etc
* for negative values: Fn1dB, Fn3dB, Fn6dB, etc
are much more appropriate.
Also they could be combined with amplitude and or phase notation.

So why do not we abandon the misleading terms and develop clearer terms and notations?

BR

Re: low-pass filter

Petre Petrov said:
Hello to all!
.................
................
In all real cases noting is “cut – off” or at least I don't know similar case.

.................

So why do not we abandon the misleading terms and develop clearer terms and notations?

Good point ! I completely agree with you, Petre Petrov.
However, how should we proceed to "develop clearer terms" ?
I am afraid, we have to stick with the terminology which has been established within the last 50 years and which is used in most textbooks. But I am open to change my mind.

LvW

low-pass filter

Everybody knows what is a cutoff frequency. It is the frequency you can notice the response noticeably drop-off which occurs at -3dB.

You can call it "The Half-power Response Frequency" if you want.

Re: low-pass filter

Just to say Many thanks LvW and Audioguru for your replay.
I am sure that you are more competent in that field from me.
“Half power frequency” seems good for me.

In my firm opinion:
1.Repeating inappropriate terms is a huge error.
2.That error is damaging the newcomers, students and even experienced people.
3.We are obliged to change everything old and inappropriate: terms, conceptions, theories, standards, laws, etc.
4.F3dB seems better for me that any “cut-off”, “corner”, etc frequency.

In such manner we will progress.
We are not slaves to the past.
The freedom of thought and freedom of speech on technical subjects are largely guaranteed. Or not?
Sorry, some other time I will be happy to discus more the subject with you.
BR

Re: low-pass filter

“Half power frequency” seems good for me.

As mentioned before (kral and myself) there are exceptions from the 3-dB-definition (Chebyshev and elliptical and several other non-standard approximations). Therefore, I don´t think that "half-power-frequency" would be a good term. This is important for my opinion since many people think that the 3-dB-definition is universal! What about "passband edge" or "passband limit" ?

In my firm opinion:
1.Repeating inappropriate terms is a huge error.

But one should be careful, since inventing new terms can lead to "huge" confusion.

2.That error is damaging the newcomers, students and even experienced people.

Damaging ? On the other hand, newcomers can and must learn from the beginning that nothing (really?) is correct by 100%. No terms (linear, sinusoidal, cut-off,....) and no rules resp. equations. Every equation is only an approximation and it is a very important task for an engineer to understand and to decide, if and when an equation can be applied.

3.We are obliged to change everything old and inappropriate: terms, conceptions, theories, standards, laws, etc.

Yes, but with a good feeling for the necessity and the speed of invention.

The freedom of thought and freedom of speech on technical subjects are largely guaranteed. Or not?

Of course !

LvW

low-pass filter

Another motivation for the conventional -3dB "cut-off"-frequency definition, it's also the characteristic frequency of a first order low- or high-pass.

Personally, I don't see sufficient reasons to change the present terminology. Compared to dubious technical terms in some fields of engineering science, it seems nearly self-explanatory to me. You may want to supplement it with explicite pass- and stop-band definitions when you go for a detailed filter specification. The said ripple dependant Chebyshev parameters exactly achieve this.

Re: low-pass filter

kickbeer.
I agree with FvM. In the real world, if you are designing a system that includes a filter, you have an error budget. The filter will contribute to the total error in the system. You would then decide how much error you can tolerate in the passband, and what the minimum acceptable attenuation will be at a specified frequency in the stop band. Based on these parameters, you will decide what type of filter (lag, Butterworth, elliptic, etc.) you need and what the order must be to meet your requirements. The cutoff frequency, if you are interested, will be a result of these decisions, but the cutoff frequency will usually not be part of the filter design specification. It simply falls out as a result of the design parameters required to meet the required filter specifications.
Regards,
Kral

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