# Graphic equaliser design: meaning of Q12dB

#### pleriche

Joined Oct 29, 2017
16
I'm designing an equalised headphone amplifier to mimic the high frequency boost given by my hearing aids. I'm using gyrator-based band-pass/stop filters (essentially the same as "Graphic equalizer using 4558 LF353" at https://www.eleccircuit.com/10-band-graphic-equaliser/).

The LMC835 datasheet gives applicable design equations which I'm using, but these include not only Q (which I understand) but Q12dB, which it doesn't define except by a formula. Could someone please explain what its significance is?

#### KeithWalker

Joined Jul 10, 2017
818
I'm designing an equalised headphone amplifier to mimic the high frequency boost given by my hearing aids. I'm using gyrator-based band-pass/stop filters (essentially the same as "Graphic equalizer using 4558 LF353" at https://www.eleccircuit.com/10-band-graphic-equaliser/).

The LMC835 datasheet gives applicable design equations which I'm using, but these include not only Q (which I understand) but Q12dB, which it doesn't define except by a formula. Could someone please explain what its significance is?
It means that the slope of the filter is 12db per octave.

#### pleriche

Joined Oct 29, 2017
16
Thank you Keith, but I don't think it can be quite that because in this extract from the LM835 datasheet it says it's 1.05, and by fiddling with the values in a spreadsheet I can get it to take various values.

Thinking about it further, since the 3dB bandwidth is f/Q it seems that Q12dB is such that the 12dB bandwidth is f/Q12dB. If each filter in a graphic equaliser has maximum boost of 12dB you need to set the Q such that the 12dB bandwidths of each filter touch but don't overlap in order to get a reasonably smooth response with adjacent filters at max. Or am I talking nonsense?

#### Audioguru

Joined Dec 20, 2007
11,249
I have normal-for-my-age (74) high frequency hearing loss. My hearing aids produce a boost of 12dB per octave which is double a normal treble tone control turned up to maximum. My hearing aids circuit is digital, not analog like in your speaker equalizer circuit.

The boost begins at about 500Hz then 1kHz is at +12dB, 2kHz is at +24dB, 4kHz is at +36dB and 8kHz is at the maximum gain which is a little less than +48dB.

It seems that you are making a speaker equalizer with 7 frequency bands which is completely different.

If I was making a circuit to copy the +12dB per octave boost of my hearing aids then I would make a Sallen-Key second-order highpass filter analog circuit, not a graphic equalizer.

Here is a hearing loss graph:

#### pleriche

Joined Oct 29, 2017
16
I think that might have been the approach taken by older analogue hearing aids, but I think in practice, hearing loss tends not to be quite as simple as a 12dB/octave above a certain frequency. With digital aids I believe they try to match the gain to your hearing loss at a number of frequencies, whether or not it follows a simple law, and this is the approach I'm trying to replicate. (In fact, just with 3 bands at 1.5, 2 and 3kHz, not 7 bands.)

In any case, from my rudimentary understanding, if you think about the Nyquist plot for a 12dB treble boost filter it would seem inevitably unstable. Isn't that essentially what a Wein Bridge oscillator is?

#### Audioguru

Joined Dec 20, 2007
11,249
Few if any people have a hearing loss at certain frequencies and peaks at other frequencies like loudspeakers have. Most older people like me have high frequency hearing loss as showed on the graph I posted. A lousy loudspeaker has a frequency response that a +/- 12dB per octave 7 bands graphic equalizer can make sound better.
My digital hearing aids had their frequency response boost match my hearing loss at all frequencies, not just at a few frequencies.
Deaf people with hearing damage from guns have hearing loss at most frequencies.

Wien Bridge and all other oscillators use a bandpass filter plus positive feedback to oscillate at the frequency peak of the filter. A 12dB per octave highpass filter is not unstable unless something like stray coupling capacitance adds positive feedback.

My digital hearing aids have earmolds and an anti-feedback circuit so that they rarely squeal.