Electronic – Does Q-Factor matter for low pass and high pass filters

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For band pass and band stop filters, Q tells how sharp the curve is at the centre frequency. I guess in this way it is required to roll-off.

However, low pass and high pass filters do not have centre frequency. So, what meaning does Q factor have for them? Does it matter of it is less than 0.5 or more?

Looking at picture of frequency response, it seems that the high Q filter has a type of hump as it approaches the cut off frequency. Isn't this a bad thing since ripple in pass band is not desired.

Best Answer

Here's a picture (I drag out now and then) that explains the effect of Q on a 2nd order low pass filter: -

enter image description here

The top three pictures show you the effect of varying the Q-factor. Q-factor can also be reduced to make a maximally flat pass-band (aka a butterworth filter).

The picture goes on to explain where the pole zero diagram comes from and how you can relate natural resonant frequency (\$\omega_n\$) with zeta (\$\zeta\$). For your reference, zeta = 1/2Q.

You will also find that the shape of the curve reverses (with a hump) for 2nd order high pass filters: -

enter image description here

The high-pass filter picture came from here.

However, low pass and high pass filters do not have centre frequency.

They have the equivalent of a centre frequency known as the natural resonant frequency and if you think about a series L and C making a notch filter: -

enter image description here

This becomes a 2nd order high pass filter if the output is taken from the junction of the capacitor and inductor. Also if L and C swap places, it's still a notch filter but now if you take the output from across C it becomes a 2nd order low pass filter. Same resonant frequency and Q formulas all apply.