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# [SOLVED]Why -3dB frequency is used as the reference for the cut-off frequency of a filter?

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#### cannibol_90

##### Member level 5
Hi,

I have observed that -3dB is usually taken as a reference point to denote the cut-off frequency of a filter. What is the significance of this -3dB point? Why not -5dB or -10dB?

I believe there are many previous threads dealing with this topic.

-3 dB isn't used in all cases. For filters with passband ripple (e.g. Chebyshev), the reference point is usually set by the ripple magnitude. But - 3dB is mostly used for smooth filters like butterworth. The most simple foundation is that it refers to half-power point and in case of a first order filter, you have ωc = 1/RC.

cannibol_90

### cannibol_90

Points: 2
-3dB frequency is a point in transfer function where power of signal drops to half of power at maximum of transfer function. It's a convention.

cannibol_90

### cannibol_90

Points: 2

Is it because S11 and S21 cross each other at -3dB, that the cut off frequency is chosen here?

Or is it because for AC, RMS Voltage = Vmax. / sqrt(2) = Pmax. /2, that the cut off is chosen here?
Or is it that the system response is not important beyond this point? The response drops fastly after this point, right?
Or is it that at this point there is Maximum Power Transfer?
Or is it because we Human Beings are only able to sense a change at Half Power Point?
Or is it that the Band-width of a filter can only be defined at -3dB?

Finally, is -3dB just an arbitrary point?

Its the value of 1time constant i.e. the signal strength has dropped to 63% i.e. 1 time constant

cannibol_90

### cannibol_90

Points: 2
Hi,

Its the value of 1time constant i.e. the signal strength has dropped to 63% i.e. 1 time constant
I know what you mean, but your description is not easy to understand for a beginner.

Klaus

cannibol_90

### cannibol_90

Points: 2
Its the value of 1time constant i.e. the signal strength has dropped to 63% i.e. 1 time constant

Consider what that might mean for highpass, bandpass filters.

3dB (actually 3.010dB) is the frequency at which power has dropped by 50%.

No sir, not 50%, to be precise its 63%

No sir, not 50%, to be precise its 63%
You're confusing time-domain with frequency domain filter behaviour. -3 dB actually corresponds to 1/2 power.

vishnuknair

### vishnuknair

Points: 2
Hello!

Why 3dB and why not 5 or 10? I think we can say that since a filter doesn't cut exactly
at one frequency, then there was a need to decide upon a cut-off frequency. And half of
the power seems to be consensual:
- Optimistic people will consider that half of the power is still there
- Pessimistic people will consider that half of the power is lost

Dora.

cannibol_90

Points: 2