# $Q$ factor refers to what on a lowpass filter? (EE kind of definition)

For what I'm learning, the bandwidth (of a BPF, for example) refers to the $\Delta$ between $f_L$ and $f_H$ at (usually) $-3\textrm{ db}$ from the $f_0$ (from wiki). For a peaking filter instead, $f_L$ and $f_H$ are situated (usually) at the peak $\textrm{dB Gain}/2$.

Q Factor become $f_0 /\Delta$. It's clear till here.

• Now, if I take a lowpass filter, how is calculated $Q$ Factor?
• I have $f_0$, but how would I calculate the $\Delta$ of a lowpass?

There is no a "peak" as reference, so $-3\textrm{ dB}$ (or $\textrm{dB Gain/2}$) make no sense as references points for the "created" bandwidth.

• Can you please clarify if you are referring to low pass filters with resonance?. In that case, perhaps the points you are looking for are apparent from its frequency response (?)
– A_A
Nov 21 '16 at 11:37
• actually paizza, the definition of Q for the peaking filter is more of a cookbook thing than it is "usually". we had a discussion about this not too long ago. Nov 22 '16 at 17:06
• Not sure if its really only a "cookbook" thing :) From this : The threshold value is often defined relative to the maximum value, and is most commonly the 3dB-point, that is the point where the spectral density is half its maximum value (or the spectral amplitude, in V or V/Hz, is more than 70.7% of its maximum). It also seems that "your" dbGain/2 band edges (for the Peaking filter) refers to Half power point (which is again -3db to the peak). It looks like all is related. Nov 22 '16 at 17:48
• Here (more or less) I'm asking if a Low Pass Filter's band edge are situated at -3db as for a Band Pass Filter (for the standard convention). I see this "-3db" only when talking about band pass (or notch)... Nov 22 '16 at 17:49

For lowpass and highpass filters, Q factor is not well defined. What is defined is the cutoff frequency and bandwidth.

Q factor is useful for bandpass or bandstop (notch) filters as it shows the selectivity of the BPS. Quantitatively Qf is the ratio of the center frequency of the pass-band to the bandwidth of the pass-band. Assuming the system has only a single pass band.

For a highpass filter, since the bandwidth is infinite, this Q will be zero. And for a lowpass filter it will always be 1/2. As a result, Q is not used for HighPass or Lowpass analog filters.

• So you are saying that for low (and high) pass, Q become "resonance"? Nov 21 '16 at 11:27
• @paizza yes, kind of. Q is for Quality (of resonance)! From wikipedia's Q factor article's headline: Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, and characterizes a resonator's bandwidth relative to its center frequency. Nov 21 '16 at 11:41
• the relationship between the terms resonance and Q is another concern, that would typically not apply for LowPass and HighPass filters. What I said was Q is not applicable for LPF and HPF systems. (note: the resonance refers to the condition of a match between an input driving sinusoidal frequency and a natural oscilllation frequency of a system) Nov 21 '16 at 11:45
• Oh ok, so also on Low/High Pass filter the bandwidth across the resonance refers to -3db to the peak (a peak that increase when resonance increase). Nov 21 '16 at 14:24
• god, he will kill me :D I stressed him a lot days ago... Nov 21 '16 at 20:14