Trying to understand Baxandall EQ

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CurtZHP

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Well, I've managed to get in over my head again, sort of. Fortunately, this time around I haven't actually started soldering anything together.

I've been wanting to learn how to build an EQ circuit, so I started reading up on them. Bought a copy of Self's "Small Signal Audio Design" and found a pdf of Lancaster's "Active Filter Cookbook."

One circuit that really interested me was found in Self's book. I've attached a picture below. It's a 4-band EQ that is basically two 2-band Baxandall tone controls in series. I'd like to build something similar, but I'm trying to get my head around a few of the component choices. How are the different frequency bands determined in a circuit like this? Obviously, it has a lot to do with capacitor values, but I'm having a time figuring out how. It's one of those situations where you're trying to find something, and it's right in front of you.

Take the LF section for starters. I get that C4 essentially shorts out RV1 at high frequencies, taking it out of the circuit as far as they are concerned. But at what frequency does this start to happen? I know that a low pass filter is basically frequency-dependent voltage divider with the cap as the shunt element. But I can't quite figure out which resistor(s) to include in the calculation.

It gets even more fun when trying to figure out the HM or LM sections, since they are bandpass filters, and now you're dealing with the interaction between two capacitors, I assume. The "bottom" frequency seems like it would just be a matter of calculating a high pass filter comprised of, say, C5 and RV2. Or is it C5 and R11? C5, and the combination of RV2 and R11?

I know I'm missing something simple here. Just need another pair of eyes on the problem. (And a smarter brain behind them....) Maybe I have a lot more to learn before trying this.
 

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JohnRoberts

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Baxandall EQ topologies are popular for their symmetrical boost cut EQ curves. The reason those 4 bands are split up into two op amps sections is to reduce interaction between bands.

In general the HP and LP skirts for EQ bands are defined by simple RCs. A capacitor across a boost/cut pot will effectively defeat that pot as the cap shunts signal across it. RCs in series with the boost/cut pot wipers defines when that section becomes active. The fact that the HF boost/cut pot does not have a cap across it means the HF response will be shelving. It is pretty common to also make LF sections shelving.

This topology has multiple benefits beyond this simple discussion.

JR
 
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CurtZHP

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A capacitor across a boost/cut pot will effectively defeat that pot as the cap shunts signal across it.

That part I think I get. High frequency content of the incoming signal bypasses the pot, so the pot has no effect on it, because the capacitor's impedance(?) goes down as frequency goes up, and vice versa. My question is how do I determine at what frequency that starts to happen?


I think the other thing that's getting me lost in the weeds is that all this is happening in the feedback loop of the op amp.
 

JohnRoberts

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That part I think I get. High frequency content of the incoming signal bypasses the pot, so the pot has no effect on it, because the capacitor's impedance(?) goes down as frequency goes up, and vice versa. My question is how do I determine at what frequency that starts to happen?
1/ (2pi x RC)
I think the other thing that's getting me lost in the weeds is that all this is happening in the feedback loop of the op amp.
The magic of Baxandall is that it is both in the input and feedback path of a gain stage, which is why the boost/cut is symmetrical. This topology was developed long before op amps were commonly used, but negative feedback is over a century old. .

JR
 

Bo Deadly

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This circuit is not as simple as understanding RC filters and such. But you can break it down a little.

Obviously the two sections are completely independent because they're just in series with one another. So you can evaluate each independently.

But the two bands of each section can also be evaluated separately because the virtual ground will effectively separate the two bands. The op amps are going to simply source or sink current as necessary to make the inverting input match the non-inverting input and because the non-inverting input is at ground, the inverting input will always be driven to be at ground. If you look at the voltage at the inverting input it will look like there's no signal at all. So the nets between R3 R4 and between R9 R10 are effectively "grounded" and separate the two bands.

Now consider that each section has input and that the output of the op amp is inverted. With all controls in the center position, the components and values and therefore impedances on either side of the wiper are the same. And so when you mix the source with inverted signal through symmetric networks, they exactly cancel out.

Now consider the LF band. Signal through R8 is being mixed with inverted signal through R7. With the wiper in the center position, these signals exactly cancel. However, if the LF band is in the full boost position, you now have 3K3 on one side and 100n in series with 3K3 on the other. These signals are not canceling. At high frequencies the capacitor is low impedance and so they do cancel because it looks like just 3K3 on either side. But at low frequencies, the 100n is not low impedance and therefore the op amp gets more positive signal than negative and thus that low frequency signal is boosted.

How do you figure how what the frequencies are? For the LF band this is just an RC of 100n / 3K3 which is a corner of 482 Hz. Although the impedance of the pot and other parts of the circuit might skew that a little. And the boost / cut bands with their two capacitors are more complicated still. This is when I just punt and drop down into LTSpice. Then you can use .step commands and see pretty plots like you see in product documentation and know exactly what it's going to do. Yes this makes me soft but life is easier if you're particularly handy with the computer regardless of just about any endeavor from making circuits to installing kitchen cabinets. Save yourself a lot of grief and let your computer do the work for you.
 

CurtZHP

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But the two bands of each section can also be evaluated separately because the virtual ground will effectively separate the two bands. The op amps are going to simply source or sink current as necessary to make the inverting input match the non-inverting input and because the non-inverting input is at ground, the inverting input will always be driven to be at ground. If you look at the voltage at the inverting input it will look like there's no signal at all. So the nets between R3 R4 and between R9 R10 are effectively "grounded" and separate the two bands.

I actually stumbled into this point on my own from a different direction, when I realized that, once I stripped away everything having to do with tone control, the left half of this thing is just an inverting input buffer comprised of A1, R5, and R6. That puts the "virtual ground" at the same point you suggested for R3 and R4.


Now consider that each section has input and that the output of the op amp is inverted. With all controls in the center position, the components and values and therefore impedances on either side of the wiper are the same. And so when you mix the source with inverted signal through symmetric networks, they exactly cancel out.

Now consider the LF band. Signal through R8 is being mixed with inverted signal through R7. With the wiper in the center position, these signals exactly cancel. However, if the LF band is in the full boost position, you now have 3K3 on one side and 100n in series with 3K3 on the other. These signals are not canceling. At high frequencies the capacitor is low impedance and so they do cancel because it looks like just 3K3 on either side. But at low frequencies, the 100n is not low impedance and therefore the op amp gets more positive signal than negative and thus that low frequency signal is boosted.

Now THAT makes sense!


How do you figure how what the frequencies are? For the LF band this is just an RC of 100n / 3K3 which is a corner of 482 Hz. Although the impedance of the pot and other parts of the circuit might skew that a little. And the boost / cut bands with their two capacitors are more complicated still. This is when I just punt and drop down into LTSpice. Then you can use .step commands and see pretty plots like you see in product documentation and know exactly what it's going to do. Yes this makes me soft but life is easier if you're particularly handy with the computer regardless of just about any endeavor from making circuits to installing kitchen cabinets. Save yourself a lot of grief and let your computer do the work for you.

That was the final sticking point for me, at least as far as that stage was concerned. Namely, which R gets plugged into the RC formula. From here, I ought to be able to decipher the HF stage. Like you said, the two midrange stages are going to take some outside help. I guess I'll have to break down and teach myself LTSpice!

Thanks!
 

JohnRoberts

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I try to avoid subjective judgements, EQ come in many flavors. I have my favorites but not for debate today.

A real benefit-improvement delivered by the Baxandall vs the prior state of the art is that the Bax topology eliminates the need for a following make up gain stage (a source of extra noise and distortion). Baxandall is arguably the best shelving EQ.. :cool:

I have designed too many parametric EQs to dismiss them, but I have seen lots of dubious parametric topologies. There are multiple ways to screw up EQ designs, but that is not unique to parametric.

JR

PS: I advised on the feature set for Peavey's well respected tube mic pre (VMP). I had them limit the maximum boost/cut range in the Baxandall tone controls to make it hard for users to get bad sounds. (y)
 

CurtZHP

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I feel like I'm getting my head around it a little better. I think I might just need to breadboard at least half of the suggested circuit and experiment with it a little.

I really like this design because the whole thing can be built around a single op amp chip and doesn't invert the polarity of the whole circuit.
I had another idea involving building three stages of fixed bandpass (multiple feedback) with maybe the middle one having switchable frequencies, and putting them in the feedback loop of an op amp stage. (Saw a similar circuit in the EQ stage of an old reverb unit...) But that would require an additional stage to "flip" the polarity back.

One of the things I'd like to try, taking another cue from Self's book, is figuring out how to switch the HF stage of the Bax circuit between shelving and peak. That might be a little overly ambitious, though...
 

JohnRoberts

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I feel like I'm getting my head around it a little better. I think I might just need to breadboard at least half of the suggested circuit and experiment with it a little.

I really like this design because the whole thing can be built around a single op amp chip and doesn't invert the polarity of the whole circuit.
I had another idea involving building three stages of fixed bandpass (multiple feedback) with maybe the middle one having switchable frequencies, and putting them in the feedback loop of an op amp stage. (Saw a similar circuit in the EQ stage of an old reverb unit...) But that would require an additional stage to "flip" the polarity back.

One of the things I'd like to try, taking another cue from Self's book, is figuring out how to switch the HF stage of the Bax circuit between shelving and peak. That might be a little overly ambitious, though...
It's not an accident that it restores polarity. In a console you don't want the EQ bypass switch to reverse polarity.

To switch the HF stage between shelving and peaking you merely need to add a capacitor across the HF boost/cut pot to shunt it at HF and defeat the shelf. This cap could be switched in and out.

I wouldn't try to make a (good) three band EQ using only one op amp, the different bands tend to interact with each other. You will note that the HF section in that posted schematic is paired with the low mid, and LF section is paired with the hi mid to keep them as far apart as possible.

JR
 

CurtZHP

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It's not an accident that it restores polarity. In a console you don't want the EQ bypass switch to reverse polarity.

To switch the HF stage between shelving and peaking you merely need to add a capacitor across the HF boost/cut pot to shunt it at HF and defeat the shelf. This cap could be switched in and out.

I wouldn't try to make a (good) three band EQ using only one op amp, the different bands tend to interact with each other. You will note that the HF section in that posted schematic is paired with the low mid, and LF section is paired with the hi mid to keep them as far apart as possible.

JR
That's exactly why I like it.

Thanks for that suggestion. Looking forward to trying it. Self's idea seemed a bit more complicated.

I neglected to adequately explain that three-band idea I was toying with. Each band is a bandpass filter (not Baxandall) built around its own op amp, so three in total. But, all their outputs would be inverted. Then again, the summing stage would invert them again, so this might not be a problem, right?
 

abbey road d enfer

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I neglected to adequately explain that three-band idea I was toying with. Each band is a bandpass filter (not Baxandall) built around its own op amp, so three in total. But, all their outputs would be inverted. Then again, the summing stage would invert them again, so this might not be a problem, right?
There are many traps on the road to additive EQ's. Don't expect summing three BP filters to sum linearly.
Ancients have burnt the midnight oil over EQ's; we have the benefit of simulation software, which allows us to make the same mistakes as the giants on which shoulders we pretend to stand.
 

CurtZHP

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So, I slapped something together on the breadboard that involves a Baxandall stage to handle high and low shelves, and another stage to handle a sweepable midrange involving a Wien bandpass. Only real problem I've run into so far is that all my available pots were log taper. Ordered some linears and a few other parts to try. Tested it with the logs anyway and it seems to behave somewhat.

By the way, have any of you ever tested something like this by running pink noise into it and connecting the output to an RTA like the one in Room EQ Wizard?
 

abbey road d enfer

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By the way, have any of you ever tested something like this by running pink noise into it and connecting the output to an RTA like the one in Room EQ Wizard?
Testing EQ's and filters with an RTA is a bad idea. Why? Because the BW of the analyzer filters add to that of the DUT, resulting in a graph that is wider than it should be. In particular, measuring a 1/3 octave graphic EQ with a 1/3 octave RTA gives very wrong results.
This is true not only of RTA but also of FFT. High-resolution FFT is OK for measuring filters in the high registers, but at LF, the FFT resolution is not so good.
The resolution of a 20kHz 1024-point FFT is about 20Hz; if you use it to measure a filter at 40 Hz, it gives an error of about half an octave.
Slow sine sweeps is the correct way.
 
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PS: I advised on the feature set for Peavey's well respected tube mic pre (VMP). I had them limit the maximum boost/cut range in the Baxandall tone controls to make it hard for users to get bad sounds. (y)
It's our duty to help prevent over use...
 

JohnRoberts

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I never designed a tilt EQ for use in a primary audio path, but put tilt EQ in noise gate side chains.... It does not take much combined boost/cut EQ to suppress unwanted gate triggering.

JR

PS: at Peavey we had to deal with lots of inexperienced customers. If/when they misuse the gear it creates a negative impression about the brand. I used to find it amusing when people would brag that they could get good sound "even" from a Peavey system. :rolleyes:
 

CurtZHP

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I never designed a tilt EQ for use in a primary audio path, but put tilt EQ in noise gate side chains.... It does not take much combined boost/cut EQ to suppress unwanted gate triggering.

JR

PS: at Peavey we had to deal with lots of inexperienced customers. If/when they misuse the gear it creates a negative impression about the brand. I used to find it amusing when people would brag that they could get good sound "even" from a Peavey system. :rolleyes:

Not to go off on a tangent, but I still have an old Peavey Century solid state instrument amp that just will not die! I've had it since I was in high school, and I love it!
 

CurtZHP

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Testing EQ's and filters with an RTA is a bad idea. Why? Because the BW of the analyzer filters add to that of the DUT, resulting in a graph that is wider than it should be. In particular, measuring a 1/3 octave graphic EQ with a 1/3 octave RTA gives very wrong results.
This is true not only of RTA but also of FFT. High-resolution FFT is OK for measuring filters in the high registers, but at LF, the FFT resolution is not so good.
The resolution of a 20kHz 1024-point FFT is about 20Hz; if you use it to measure a filter at 40 Hz, it gives an error of about half an octave.
Slow sine sweeps is the correct way.
What about an RTA where the octave can be adjusted, like on the REW RTA? For me, it was just an attempt at seeing if the controls were actually doing what they were supposed to be doing. (Does the graph change when I turn this knob? Good, at least I hooked it up right!) Couldn't really tell using just a scope.
Wasn't really looking to publish specs based on what I was seeing. I will most certainly do some proper sweeps once I get to that point. (Gotta get the right parts first...) Pretty sure REW does sweeps, but I'll have a look at AudioTester, as Jakob suggested.

Thanks!
 
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