# what's the Q factor of a low-pass filter?

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#### cqmyg5

For a band-pass filter, you can calculate its Q factor as f0/BW. For a low-pass filter, its f0 is same as BW, right? But I find some low-pass filter's Q value is 0.5 or 1.5, How it can be?

#### flatulent

Q is a parameter of an individual resonator, not a system of resonators. It is defined as the energy loss per radian of oscillation divided by the total energy stored.

#### cqmyg5

Thanks! I know this Q definition (wl/r), but for BPF we could define Q as f0/BW also.

#### flatulent

The definition for a BPF will be irrelevant. The impulse response will be different for different number of resonators even if the filters have the same 3 dB bandwidth.

More resonators will have a longer ringing time. Also the type of filter shape (skirt selectivity) will have different ringing times.

This reminds me of the British tax system many years ago which taxed automobiles by the piston surface area and not the displacement or power.

#### Davood Amerion

if you consider half of the frequency response for LPF and BPF,
i mean frequency above Fo in LPF (and below Fo in HPF) you will find
efect of Q factor in frequency responce.
see attachment

#### cqmyg5

Davood Amerion said:
if you consider half of the frequency response for LPF and BPF,
i mean frequency above Fo in LPF (and below Fo in HPF) you will find
efect of Q factor in frequency responce.
see attachment

Thanks! That's just what I want!

#### OMEsystem

The Q of LPF can be derived by the biquadric equation, the denominator can
be wrote as (S²+S*ω/Q+ω²). The Q of this equation is what you want.

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