6 band eq question

[Locrian99]

Hello,

I was looking at some different eq circuits.  And they all pretty much seem the same.   Op amp gyrator thing set your resistance/cap value to the desired hz setting.   I was looking at this one over at pedal pcb and was wondering why there is no gyrator for the 6th frequency which should be 3.2kHz.   I wasn't able to get that number from the AMZ calculators though.   Anyone know what's going on here and why unlike all the other schematics I've seen for these this one doesn't have the op amp on that frequency and what the drawbacks if any are there.   Or am I just looking at this completely wrong (always a possibility).

[Rob Strand]

I was looking at this one over at pedal pcb and was wondering why there is no gyrator for the 6th frequency which should be 3.2kHz. 

In terms of basic equalization there's two types of equalizers peaking and shelving.   You can see the plot in fig 1.   Common bass/treble controls are often shelving.

https://www.soundonsound.com/techniques/using-your-sequencers-equalisers

While it's fairly obvious what to call the "frequency" on a peaking equalizer, it's not so clear-cut what to call the frequency on a shelving equalizer.   Most "frequencies" given to shelving equalizers are imprecise or BS.

One definition is the upper frequency point where the boost starts to get close to maximum and the curve starts to curl over and become flat.    Some people define the point -3dB below the shelf but it's not a consistent point:  Imagine a 6dB boost, -3dB is at 3dB right in the middle of the sloped part, whereas for a 18dB boost -3dB is at +15dB still somewhere near the maximum.

The bottom line is the two equalizers sound different.    The shelving equalizer will boost all frequencies above some point - it kind of has a start frequency but not a boost frequency like a peaking EQ.

The sloped part of the shelving equalize is more or less fixed, it gets less sloped when the boost gets low say less than 6dB.    The fact the slope is fixed means once you set the amount of boost and the upper frequency that automatically sets the lower frequency point where the boost starts to rise up.    The slope of the peaking equalizers get higher as you increase the Q, which generally occurs when you add more bands.

At the low frequency end you can have a band which is missing the cap so there is only a gyrator.  That does the shelving equivalent for bass.

Here's a demo of why the upper frequency doesn't work so well as band frequency spec.    The upper frequency move as the pot is set to difference boost and the lower frequency (where is starts to take off) is the thing that is constant.



At full boost the curve passes through -3dB under full boost (ie. 12dB) at 5kHz.   fhi = 1/(2pi*C*1k) ~ 5kHz

[Locrian99]

As always rob thank you for the thorough response.   

Article was very interesting had no idea there was so many ways of doing this. 

I actually ordered this pcb awhile ago and was getting ready to throw it together when I started looking at them more thoroughly.     

Still not sure why that portion doesn't have the op amp gyrator as the others.   The answer may have been there...

[Rob Strand]

Still not sure why that portion doesn't have the op amp gyrator as the others.   The answer may have been there...

The bottom line is it sounds different.  If you have limited bands a single 3.2KHz band might sound poky and doesn't give the overall brightness of a shelving type 'treble control'.   You could stretch the argument that a shelving last band is like having many bands (3k2, 6k4, 12k8) all coupled together off the same control.   It's only a loose mental picture.     My argument is there's problems giving the last band a correct/consistent frequency as in use all it's doing is adding brightness above some frequency, not at some frequency.

[Locrian99]

Ah ok that makes sense.   I may just end up breadboarding it both ways I suppose and see what I think of the audible difference.  Thank you again. 

[Rob Strand]

Another snippet for designing those gyrator equalizers:
- find an existing EQ design for +/- x dB
- now used an EQ calculator and look at the values for the "470 ohm" resistor.
   You will see the value calculated is somewhat higher than the actual circuit.
- The error lies in the calculators they are not correct for multiple band equalizers.
   While the frequency is roughly correct the Q and amount of boost is incorrect for multiple bands.
 
Look at p31, p32 here,  Third-octave 31 band EQ,

https://worldradiohistory.com/AUSTRALIA/ETI-Australia/80s/ETI%201982-11%20November.pdf

Design targets:   1kHz band, +/-14dB, third-octave implies Q=4.3
Actual circuit values:   RL=220k, Rs=1k, Cs=22n, CL=5n6

Which the calculator will give as:  f0 = 967Hz and Q=7.48

The values in the circuit imply a much higher Q.

Also with Feedback resistors of 10k and for 14dB ( ie gain of 5.01) we would expect the series resistance
to end up at 2.49k ohm  ie.  gain = 1 + 10k / 2.49k = 5.02 = 14dB
but the circuit is using 1k's ie. you would need to enter a lot higher gain into a calculator to get the resisor
used in the actual circuit.

I've posted quite a number of times about the problems with using those calculators on *multi-band* equalizers.
The calculators are usually OK for single bands used in tone controls - sometimes even then pushing their luck.

You really need to use spice to evaluate the Q and amount of boost/cut on these things.

If you are just building an EQ then someone has usually done the adjustments for you.   If you are trying to derive the
design parameters from the circuit value (using a calculator for help) then it will paint very different parameters to reality.

IIRC one of the few places where calculations are given for the adjustment is the old National Semiconductor Audio handbook (I'm nut sure if the calculations appears in both versions or only the later 1977 version.)


Here,
https://archive.org/details/bitsavers_nationaldaAudioRadioHandbook_17034677/page/n71/mode/2up
page 72 (2-59)
I can't see the calculation only the comment on page 2-60  parts imply 17dB Q=1.7 result is 12dB Q=1.414.

[Locrian99]

I was mainly just trying to understand why that band didn't have the gyrator.   Mainly just was fine with building a stock eq for the time being just was trying to wrap my head around what it was doing etc.   Lots of good info here for me.   I'd like to get into doing the spice thing at some point.   I ended up doing the calculator more for the purpose to know which band was the odd man out.   Then noticed that the number for that band from the calculator was way off.  The others were in the ballpark other two I checked were within a couple % of the desired point.   I should have this built tonight was waiting on 2 24k resistors to finish it.   Give it a test run.   I am curious on doing some further exploring of the multi and eq etc and will have to check out that spice program.   Would love to play around more these, still haven't found the big muff with the perfect (we'll to me) tone stack so something I for sure want to dive deeper into.