# What bandpass Q factor do I want for 12dB/octave roll off?

Sorry for what may be a dumb question. I'm used to thinking about low and high pass filters in terms of db/octave (e.g. 6db for passive RC filter).

Whats the equivalent Q factor for a bandpass filter that would give me 12dB rolloff per octave in either direction from the centre frequency?

e.g. Fc = 150kHz At f = 75kHz and 300kHz, signal should be 12dB down.

Is there a simple conversion?

Simple? Δf=fc/Q (-3dB BWp)

Q of 3 at fc = 150kHz gives ;

• 3dB @ BWp = 50kHz max (27kHz, 76kHz)
• 6dB @ BWp = 77kHz max ( 123kHz, 200kHz )
• 12dB @ BWp = 193kHz max (82kHz, 275kHz )

(using a model for linear phase Multiple Feedback 0.05 deg; )

so maybe Q=3.1

So what's all this Stuff About Filter Specs and tolerance error?

Maybe you want a flatter passband and and a steeper stopband?

Then a Chebychev BPF staggers higher Q poles to make the ripple small e.g. 0.1, 0.5 or 1dB in the PassBand and thus higher Q yields steeper skirts in the StopBand.

Maybe you want linear phase or maximally flat Group Delay?

Like Bessel filters then using lowest Q staggered poles in the PB it minimizes excessive group delay in the pass band.

Or maybe some other characteristic such as phase shift sensitivity or maybe stability with tolerance using 0.5% tolerance stackup or 5% tolerance parts..

So the usual specs to define any simple filter as follows;

• Gain (Ao):
• Center Frequency (fo):
• Allowable Passband Ripple (Rp): [dB]
• Passband Bandwidth (BWp @ -3 dB):
• Stopband Bandwidth (BWs @ -Asb dB):
• Stopband Attenuation (Asb):
• Filter Order (optional): with -6dB*n per octave slope

More complex filters are defined by scattering paramters for input and output impedance s11,s22 and transfer function s21.

The roll-off characteristic of a band pass does NOT depend on the Q-value.

At first - the Q-value Q=wo/dw is defined for the lowest-order bandpass (n=2) only (dw: 3-dB bandwidth). It is identical to the quality factor of the corresponding pole Qp=Q)

Secondly, the roll-off value does depend on the filter order only. Therefore, a roll-off of 12dB/octave is equivalent to a second-order roll-off - to be achieved with a 4th-order bandpass only. (Note that we have a minuimum of n=2 for the most simple bandpass; the filter order is identical to the order of the denominator).

Comment: As you are asking for a specific attenuation at a certain frequency, it seems that you are mixing stopband attenuation and roll-off characteristics.