I just meant that you've commented a few times over the years that putting a pot (with limit resistance and wiper to ground) between inverting and non-inverting inputs of the first amp is generally the lowest noise way of accomplishing a wider Q range.I didn't know that I had a preferred Q adjust....
Shelf/bell topologies in SVF parametric EQs
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that is correct for using conventional components, there may be other options like using DPOTS.
JR
yes, or cap switching on the integrators. BP in parallel, LP in series. I suppose one could implement that with a simple DPDT toggle, relay, or two SPST CMOS switches where one is NC and one is NO. it’s a little non-intuitive because the switches are doing opposite things. but easier for the majority of designers…there don’t seem to be a lot of people doing things with Dpots. i considered that in the thing I’m working on, but I’ve already got cap switching happening to enable a low noise broad frequency range, so it would mean a little too much state-dependent automation.
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I finally figured out the PQ1549 magic and ported it over to a Net EQ topology. Here are 6dB boost traces for band pass, single pole LP, and single pole HP responses; cut traces are the same but inverted. Single pole LP and HP have the LP integrator capacitor shorted, boostrapping its input resistor and bringing its output to 0V. No ripple! For reference, the last screencap is the two-pole HP response.
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Attached are phase plots for the band pass and single pole low- and high pass responses, measured at the output of the boost amp.
I see that with one integrator shorted, the -3dB crossover point of the LP and HP doubles in frequency. Easier to see on the middle two pics of the post above. Going from bell to shelf seems to work pretty well for the low shelf, but the high shelf looks like it would be noticeably higher. Hm. I suppose you could double the capacitance for the remaining integrator in high shelf mode...wouldn't be too difficult with small caps. Not gonna happen at 100Hz! [EDIT: Yeah that works well at 10KHz. Still a little smoother than the bell, about 4dB at ƒc vs 6dB at ƒo, but hey, that's why you hit the shelf button in the first place.]
I see that with one integrator shorted, the -3dB crossover point of the LP and HP doubles in frequency. Easier to see on the middle two pics of the post above. Going from bell to shelf seems to work pretty well for the low shelf, but the high shelf looks like it would be noticeably higher. Hm. I suppose you could double the capacitance for the remaining integrator in high shelf mode...wouldn't be too difficult with small caps. Not gonna happen at 100Hz! [EDIT: Yeah that works well at 10KHz. Still a little smoother than the bell, about 4dB at ƒc vs 6dB at ƒo, but hey, that's why you hit the shelf button in the first place.]
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Actually, using the conventional definition of shelf EQ, which is estimating the point where about 80% of the max boost/cut is achieved, both the low and high shelf EQ are shifted about an octave apart, i.e. the low shelf is an octave below the bell and the high shelf an octave above. It wouldn't be an issue at all operationally, but in comparison with a standard Baxandall type, there would be considerable difference.
Another solution is to have different scales for bell and shelf. Not very clever!
Some are willing to accept the ripple for the benefit of a more pinpointed action. AFAIK, the only notable commercial product is the K+H UA series, which uses S&K filters, not SVF.
Actually, when it comes to such resort, it is often preferrable to cascade two EQ's, one in shelf and the other in bell, about one octave apart.
That's what insert points and patchbays are for.
See attachment.
Green is shelf alone, red is shelf and bell cascaded.
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I’ll have to post the traces later, but i removed the short across the LP cap and turned the output inverter into an equal value differential amp. Then i hooked up first the LP output and then the HP output into its non-inverting input. The resultant low shelf showed up the exact same as the single pole trace, and the high shelf (surprise) crossed over at the same point— i.e. no frequency shift due to mismatched rolloff. So that lends credence to the combine-two-outputs approach, at least for a fixed value of input attenuation and matching gain via Q adjust.
These are set up for easy toggling in the viewer, LP-BP-HP. 4dB is 80% of 6dB. [EDIT: I ran the same thing in cut for both derived shelves, and got the expected -4dB at ƒc.)
In band pass, the filter section output amp is back to being an inverter with 2x gain. For bell/shelf, that's a SPST for Rf and a SPDT to engage or disable the voltage divider. Two sections of a changeover switch, or 3/4 of a CMOS quad SPST, or one DPDT relay/toggle/pushbutton, whatever.
Is phase of each response at the boost amp output (dark blue, ±18°ish) about what one might expect from an additive parametric?
In band pass, the filter section output amp is back to being an inverter with 2x gain. For bell/shelf, that's a SPST for Rf and a SPDT to engage or disable the voltage divider. Two sections of a changeover switch, or 3/4 of a CMOS quad SPST, or one DPDT relay/toggle/pushbutton, whatever.
Is phase of each response at the boost amp output (dark blue, ±18°ish) about what one might expect from an additive parametric?
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All these EQ's are minimum-phase, hence phase response is bi-univocally tied to amplitude response.
In other words, when amplitude responses are identical, phase responses are also identical.
user 37518
Well-known member
To add a bit more theory, if anyone cares, to what Abbey said.
Minimum phase filters/EQs, are those in which you can determine the magnitude of the filter from its phase response, or the phase response from the magnitude. They are related by something called the Hilbert transform, the dynamics of it are quite similar to the Fourier transform (or the FFT if you are using it in a computer) in which you can get the frequency response from the waveshape (time domain response) and viceversa.
In non-minimum phase filters this doesn't happen, that is, phase and magnitude are not related with each other by means of the Hilbert transform. An easy way to determine if a filter is non-minimum phase is to see if the filter's transfer function has any right hand zeros, if it does, it is a non-minimum phase filter. Since looking at a transfer function is not always a possibility, another good hint that you might be dealing with non-minimum phase filter is if you measure its step response and negative signal values appear before the step ramps up. An example of a non-minimum phase filter is an All-Pass filter.
To illustrate this, the following image shows the step responses of a Bessel low-pass (minimum phase) and a Padé All-Pass (non-minimum phase) vs an ideal delayed step. You can see all that wiggling of the blue trace assuming negative values; that is something characteristic of a non-minimum phase filter.
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Actually, to cut short the protests of the pedantic brigade (which I am part of
), it's the amplitude variations vs. pulsation that allow calculation of the phase angle. Corollary to that, the phase response allows calculating a relative amplitude response. The absolute amplitude is lost in translation.Being older than I care to divulge, I have forgotten the pertaining demonstration. I wish someone could link me to it.
user 37518
Well-known member
Yes, I guess that is the same thing I said. The magnitude response and phase are related by the Hilbert transform and you can switch back and forth, although, as you mention some is 'lost in translation'. A similar effect to what the Fourier transform happens, the Fourier transform when reverted to the time domain (via the inverse Fourier transform) some stuff is lost. For example, if you delay a sine wave in the time domain, you take its DFT, then inverse DFT, you get the same sinewave with a phase change, but the time delay is not recuperated.
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Thanks for the insight, @user 37518
Are there EQs out there that have shelves with 2P cut and 1P boost? Seems like the kind of thing that might be baked in to a stepped cut/boost with asymmetric response, -15dB cut / +10dB boost, that sort of thing. Inquiring because....that's looking pretty doable with this topology.
Are there EQs out there that have shelves with 2P cut and 1P boost? Seems like the kind of thing that might be baked in to a stepped cut/boost with asymmetric response, -15dB cut / +10dB boost, that sort of thing. Inquiring because....that's looking pretty doable with this topology.
Following up on post #68:
Here is (I think) the lowest noise way to do single pole shelves without switching from the SVF to a buffered single pole. 6dB noise penalty? Plus the various series resistance results. Note the lack of feedback from the LP integrator in either shelf mode. This satisfies the 80% of ƒ0 at ƒc rule of thumb that D suggested.
Attachments show the LP to BP transition (3x SPST), then the BP to HP transition (2x SPST, 2x SPDT).
I like the curve of the low shelf using the PQ1549 trick better than this curve, as it’s closer to the bell shape. The easiest way i’ve found to replicate that for the high shelf is to use the same trick, and double the cap value on the integrator-formerly-known-as bandpass.
Here is (I think) the lowest noise way to do single pole shelves without switching from the SVF to a buffered single pole. 6dB noise penalty? Plus the various series resistance results. Note the lack of feedback from the LP integrator in either shelf mode. This satisfies the 80% of ƒ0 at ƒc rule of thumb that D suggested.
Attachments show the LP to BP transition (3x SPST), then the BP to HP transition (2x SPST, 2x SPDT).
I like the curve of the low shelf using the PQ1549 trick better than this curve, as it’s closer to the bell shape. The easiest way i’ve found to replicate that for the high shelf is to use the same trick, and double the cap value on the integrator-formerly-known-as bandpass.
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If anyone wants to play with this thing, the sim is tidied up. Post any interesting findings!
Values adjusted for a little better noise performance. Can't add potentiometers because I'm out of objects in the free version of Multisim. I went with the PQ1549 trick, and doubling of the BP integrator cap in high shelf mode. High or low, it's the least switching and gets you closest to the bell slope without radically reinventing the filter.
Leaving this here too, for anyone doing what I'm doing in the future:
Values adjusted for a little better noise performance. Can't add potentiometers because I'm out of objects in the free version of Multisim. I went with the PQ1549 trick, and doubling of the BP integrator cap in high shelf mode. High or low, it's the least switching and gets you closest to the bell slope without radically reinventing the filter.
Leaving this here too, for anyone doing what I'm doing in the future:
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You wouldn't have this problem if you used LTspice or Kicad...
would you mind putting a representative schematic with switches and pots? its hard to follow the logic of the multisim layout
Glad someone's messing with this!
You have to visualize or reference the NetEQ architecture (thanks @peterc ) while you use it, knowing that an actual application would use those Q, frequency, and gain pots instead of the fixed values presented. As D noted elsewhere, Harpo's simplification of Porter's non-inverting attenuator at the mix amp produces the same results, and a simple resistor from NI input to ground is representative of that.
The generic approach in the sim is inclusive of NetEQ variants that use switched resistors for frequency and Q selection, and eschew the center tapped cut/boost scheme in favor of cut- or boost-only stepped gain. My application is all CMOS switching, so shelving transformations exclusively involve changes at op amp inputs to avoid loading mux and SPST drains, and cut/boost can only be done at the inverting inputs of the cut and boost amps themselves.
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I try LTspice every time you suggest that and haven't been able to make it work for me. I'd like to be using TINA since my gen purp opamp is the OPA2210, and the INA1620 gets a lot of play as well, but I'm on a Mac. I'll look into Kicad.
Makes sense. What about the switching for the shelf? Mind annotating that?
