Help With High-Pass Filter

[fobits]

Here's a question which I hope will be simple for all the EE types out there.

I fitted my guitar with a pair of Musician's Friend Duncan Performer Scorchers, mainly because they are the cheapest rail-type humbuckers available. These are overwound pickups (about 12k resistance per coil) which put out a very strong bass and much less on top.

I can't imagine wanting less treble, so I was thinking of substituting a bass-cut tone control for the usual treble-cut, like so:



The problems are that I don't know the load resistance or what would be a good cutoff frequency. I have a vague memory that a standard audio input impedance is 47k, but that seems rather low. It could be that my memory is off by a couple of orders of magnitude.

I'm guessing that a 1 meg pot would be needed to get much roll-off. As for the capacitor, how does 680 pF sound? That should give a leveling-off frequency of around 230 Hz. I have no idea what the cutoff frequency would be, since that depends on the input impedance of the amp.

Any suggestions?

[UnklMickey]

Fobits,

your suspicion is right. loading your pup with 47k would decimate the top end, due to their inductance.

i have to run right now, but i guess 1Meg might be a good place to design around. more thought should be put into this though.


see you tomorrow.


hope you get a more complete answer tonight.



unk

[ChrisK]

pSpice it.

The generator is AC.

The generator output resistance is 12 K Ohms.

The generator inductance in series w/ the generator is the PU inductance (needed).

The generator inter-winding capacitance is 100 - 200 pF in parallel w/ the inductor.

The amp input resistance is around 1M Ohms to common.

The tone control is ?250K into ?0.022uF (near off assumed) to common.

The hidden tone control (the cable) is 1,000 to 3,000 pF (or more) to common.

Run freq sweeps for different settings on the the pot and then you'll see (and later hear).

This is actually a very easy thing to try. Just sacrifice a cable and do the component selection/testing "out of body".


pSpice is available free from Linear Technology masked as "switchercad" (it has a pSpice engine). It's also available elsewhere for free, just search this site for it, others have found it already.

[fobits]

Hi, ChrisK

The amp input resistance is around 1M Ohms to common.

That sounds more reasonable than my guess. So even under ideal circumstances, a 1 meg pot can't reduce the output voltage by more than half, -6 dB.

The hidden tone control (the cable) is 1,000 to 3,000 pF (or more) to common.

Oof, I forgot about that. Now there's a real killer. The more that I think about it, the more I think that the whole idea just went down in flames.



This is not good. Even at high frequencies, 75% of the voltage would appear over the small cap. Now I know why this isn't a common modification, and why there aren't drawing of it all over the net.

Just sacrifice a cable and do the component selection/testing "out of body".

Thank you! Here I was racking my brains trying to think of a way to test a half-dozen capacitors without tearing it all apart each time. The answer is so simple. Just put on a couple of jacks and use it as an effects box.

I don't think I'll be testing this one, unless somebody can find a way around the cable problem, but it's a good method to keep in mind.

[sumgai]

fobits,

What I'm seeing here is the same thing as a volume control with a small cap across the two control lugs to maintain some treble when the control is turned down. The difference here is that the third lug is ungrounded. So, what happens to the tone?

If the control is rotated to fully bypass the cap, then we have the full tonal range going through to the output (all frequencies are present) . If we rotate in the opposite direction, we introduce an RC circuit, the action of which is complex, but the gist of it is, we don't change the overall tonal characterics at the output. Why? Because you can't change a capacitor's sensitivity to frequency by merely shunting it with a resistor. (More on this in a moment.....)

"But we do this all the time in a treble cut circuit!" you say. Ah, you've momentarily forgotten that a treble-cut circuit places the capacitor in series with the resistor, not in parallel. Big difference there, I'm sure you'll agree. To be sure that I'm not off my rocker, try this yourself: wire the cap of your treble-cut tone control in parallel with the pot. What happened? Right, the tone stayed almost unchanged no matter where the pot was rotated to. (But the control now acts as another volume control, so it's worthless to us.)

As you shake your head, wondering how this can be, I'll close with this thought.... A parallel RC circuit does work as a frequency filter for a current source. And I'm sure by now, you're guessing that pickups are voltage sources. And your guess is correct.

For more on this topic, you can visit the WIKI site on filters in general at: WIKI - RC Filters, or go here for some basic undestanding of filters: Play Hookey - Filter Basics When you've read this page, follow the links at the top to more in-depth filter topics. (Hell, follow all of them, they cover a wide range of good stuff that can underpin what we're all talking about here.) This is all math intensive, but the prose in between the math spells it out in laymans terms, so you can pretty much brush by that stuff.

I see that while writing this, ChrisK has contributed. Chris, have you pSpice'd this thing yet? At the risk of sounding pompous, might I suggest that you look to make sure your pSpice "generator is AC" is indeed a voltage source?

OK, my crash helmet is on, let the flames flare up! ;D


sumgai

[ChrisK]

Nah,

I opened pSpice today and had to (re)remember how to use it!

Yeah, it's a voltage source. For God's sake, I'm not modeling Lace sensors (ooooh, inference afoot?).

RC circuits are indeed complex, just not hard to understand.

[sumgai]

Chris,

Nah,

I opened pSpice today and had to (re)remember how to use it!

Yeah, it's a voltage source. For God's sake, I'm not modeling Lace sensors (ooooh, inference afoot?).

RC circuits are indeed complex, just not hard to understand.

So what was your result? Inquiring minds want to know!

I don't often have a problem with RC, LC, or RCL circuitry. Sometimes, but not often.


sumgai

[JohnH]

I think this might work better with the third pot lug grounded. Ie, exactly like a volume control with a treble bleed cap. Ive played with different values of bleed caps, and if you get it too high, as you turn the volume down, the mids and treble stay the same and only the bass is cut ie just what we want here!

First pass guess: a 1M pot and a 2nF or 3nF cap. Ive done pSpice sims of these types of things, but although it helps in understanding the principles, I can never quite pick the values that sound best without listening to a physical mock-up.

John

John

[fobits]

sumgai

A parallel RC circuit does work as a frequency filter for a current source.

Thanks for the links, there's some interesting stuff there.

I found a drawing on the WIKI site with a sentence very much like yours: "The parallel RC circuit is generally of less interest than the series circuit. This is largely because the output voltage V_out is equal to the input voltage V_in — as a result, this circuit does not act as a filter on the input signal unless fed by a current source."

But look where they are measuring the voltages - this is quite a different case. Here's a direct link:

en.wikipedia.org/wiki/RC_circuit#Parallel_circuit

ChrisK, sumgai and JohnH

This is going well beyond my knowledge, but if even you guys have to use computer models to figure out what it does, I can't feel too bad.

I've been trying to remember s-domain analysis and basic algebra, which I used to know, but your method will probably be quicker.

Thanks for all the help. I thought that somebody could toss off an answer or a few equations and that would be it. Now it has turned into a whole project.

[UnklMickey]

hi John,

i think i understand what you're suggesting here.

would there also be a resistor from the low end of the pot to ground, to keep from shutting off the signal when the bass is at zero?


unk

[JohnH]

unklmickey said:

hi John,

i think i understand what you're suggesting here.

would there also be a resistor from the low end of the pot to ground, to keep from shutting off the signal when the bass is at zero?


unk

yes, good point - My thought came from testing volume controls with treble bleed caps that were too large, but we don't want this really to be a volume control as well!

John

[ChrisK]

sumgai, fobits,

I opened pSpice and futzed around w/ some older models to relearn how to use it. I didn't model this thread.

I had done the TeleBlender and was disappointed by the lack of diversity available within the stated PUs, so I decided that I wanted to do something meaningful w/ a StewMac MegaSwitch "E" in a Tele copy. Needless to say, my thinking has run amok (as always) in directions blending and high/low pass tone circuits..

I think that the best thing to do is to build a test kit. The first thing that you want is a group of pots such as 500K, 250K, 100K, 50K, 25K. One might question the low values, but we're looking at series here. You could also use a resistor substitution box.

You also need an assortment of caps such as 0.001uF thru 0.33uF (yep, a capacitor substitution box). Also get an old air gap three section variable cap if you can find one. The ones that I have go from about 30 to 1,400pF for all three sections in parallel.

And, go out of body (it's series after all).


Actually, all of this "stuff" can be done the manual way. Like all true engineers tho, anytime that there's a chance that we'll have to do the same thing again, we automate it. I initially was hated in college since I had the money to buy one of the first programmable calculators (I went when I was 23, so it wasn't just 13th grade to me) and the proclivity to write an AC circuit analysis toolkit. Finals took 10 minutes for me, but 2 hours for others. Next year, everybody had one!

One doesn't have to have the more esoteric SW packages to do this tho (Mathematica is $1,800 list, a pSpice plug-in with most integrated design environments is around $5K), but can use Excel (with some extensions). An excellent book is "Excel for Engineers and Scientists" by S. C. Bloch, which includes reasonable complex math support.

The big issue tho is to ensure that complex impedance is fully considered (vector sums rule). It's NOT intuitive to the unexposed.

[JohnH]

Fellow Nutz,
I got intrigued by this, so couldn't resist having a go. Heres my pSpice efforts.

On the left, Ive put in a 12k pup with an inductance of 6H, for a humbucker. and some self capacitance. On the right, the cable and amp is modelled as a 1M resistance, and a 1nf cap , representing about a 20' cord.

Im thinking of a IM pot, with 100k on its ground leg, and a 5nF cap. Here it is with full bass and no cut:



You can see a linear reponse, then a peak and a fall at high frequency, associated with the pup interacting with the cable capacitance.

Here it is with full bass cut:



which shows a roll off at low frequencies:

Now again, without the pot grounded leg:



This seems not so effective however.

pSpice can be quite educational!

cheers

John
ps having set this up, it is easy to try variations, so any sugestions from EEs or wannabEE's, I can try.

[fobits]

Hi, JohnH... and all

pSpice can be quite educational!

Indeed it is. The first thing that caught my eye was the high end. I hadn't seen a graph like this, and was surprised at how early the roll-off starts. This is a vivid argument for using decent quality cables, as short as possible.

The idea of semi-grounding the other pot leg was clearly a good one. Without it, there is little effect at all. Now I'll have to do some thinking to try to understand why it makes such a big difference.

having set this up, it is easy to try variations, so any suggestions from EEs or wannabEE's, I can try.

Heh. That wouldn't be a dig at me, would it?

Actually, since you offered, would it be a lot of trouble to model my original version? That would be an ideal voltage source, a pure load resistance and about 680 pF in the cap. I'm curious to know if it was just over-simplified or completely off base.

I did work out the network function for that version. Since it has one reactive element, you would expect a maximum of one pole and one zero, and that's what it has. According to my work, the numerator is sCR_F+1, giving a zero when X_C=R_F. The denominator is sCR_F+R_F+R_L+1, giving a pole when X_C=R_F||R_L.

That agrees with my original equations and graph, taken from some old notes from many years ago. The notes didn't include any derivation or explanation, but it does work out.... according to wannabEE muddling, anyway.

[JohnH]

Fobits - no dig intended. I just thought that wannabEE was a cute term, and in any case, I'd put myself in that category. After sunrise I revert to being a structural engineer.

Hence Ill leave things like transfer functions and complex numbers to others.

As I understand it, the first circuit you posted had a 1M pot and a 680pf cap. So I think it is this, with other values as before:



Here is the same again, with the extra grounded leg:



These runs may be under specifying the pup. It is a 12k pup, where I think you said yours are 12k per coil. However, the principles should be OK.

On cable length, I only use short cables to reduce that roll off, or preferably and active buffer inside the guitar (see the LP max on the schematics page) - something like that might add the zing that you are possibly losing.

cheers

John

[fobits]

JohnH

Hmmmm.... With the extra resistor on the pot terminal, it seems to work even better with a small cap.

The other one doesn't do much of anything. That's what I expected, after ChrisK pointed out the capacitance in the cable. According to his numbers, some cables could have as much as 3 nF, which would be even worse.

The original version was simplified to the point that the voltage source was ideal, with no internal resistance, capacitance or inductance at all. I also forgot about the cable capacitance, so the load was a pure resistance. I believe that you would get a roll-off with those assumptions, but not in the real world.

On cable length, I only use short cables to reduce that roll off, or preferably an active buffer inside the guitar

Early on in this discussion, the advantages of an onboard preamp became clear. With one of those, all of the problems would be over. The design could be taken right from The Op-Amp Cookbook or any book on audio amplifiers. I really don't want to get into that, though.

I just thought that wannabEE was a cute term

No offense taken. I thought it was funny too, and even considered adopting it as my username.

Hence Ill leave things like transfer functions and complex numbers to others.

<chatty mode on> S-domain analysis is pretty cool stuff. I found it in a book called Basic Electric Circuit Analysis, which I believe is a University textbook for first-year EE students. After struggling through chapter after chapter of complicated mathematics, full of calculus, infinite series and numbers raised to imaginary powers, you get to the chapter on s-domain analysis. Then all of the complications vanish and you're back to Grade 9 algebra. For people like me, who just want handy equations to use without worrying too much about how they are derived, they should put that chapter first.

Unfortunately, when a circuit becomes at all complex, the equations become long and unwieldy, and it isn't so simple anymore.

<back to topic> I have a 1 meg pot on order from Stew-Mac, along with some other supplies for a different project (a custom pickguard). The plan is to solder a couple of alligator clips on the pot, so it will only take a few seconds to change caps.

After I get the pot and fool around with this a bit, I'll let you (plural) know how it went.

[fobits]

Well, I finally spent a long evening fooling around with (aka scientifically testing) this tone control. In fact, two different versions of it.

The Mark I Model

This is a redrawing of the bass-cut control, in a way that may be a bit easier to understand. I built it as an effects box, with input and output jacks, but without the box. The components were just connected with short pieces of hookup wire, with small alligator clips to hold the capacitor and resistor.

Early in this discussion it became clear that it would be sensitive to capacitance in the cable. It's relevant that I used two Precision Instruments cables, of 4 feet and 12 feet, of the same type. In the first round of testing, the long one was between the control and amp.

For those who want it short and sweet, I couldn't get it to work worth a dam.

I lined up 5 capacitors, of 470 pF, 680 pF, 1 nF, 4.7 nF and 10 nF.
There were 3 resistors, of 68k, 100k and 150k.

In theory that would be 15 combinations to test, but I was sure that some of the caps would prove to be much too big or much too small, and could be eliminated quickly. I was right about that. All of them were quickly eliminated!

The 1n cap, with all of the resistors, made it act strongly as a volume control. When it was turned down, everything was turned away down.

The 4.7n cap had the opposite problem. With all of the resistors, it had hardly any effect at all.

Soooo, into the collection to dig out 2.2n and 3.3n capacitors to fill in the gap. The combination that gave the best results was:

C_f = 3.3 nF R_f = 68k

Those were the best, but it still wasn't very good. When I tested individual notes, it was acting as a high-pass filter. It had quite a strong effect on the sixth string and a small effect on the first string. When I went up to the 12th fret on the first string, the control didn't make any difference that I could hear. So it was reducing the low frequencies while allowing the high ones to pass, just as it should.

The effect on the overall tone, especially on open chords, wasn't so good. The goal was to suppress some of the lower frequencies in order to make the tone brighter. For some reason, which I don't understand, it sounded dull and muffled. That's a subjective impression, but it wasn't what I was looking for or expecting.

The next step was to swap the cables around. Even this relatively small change in capacitance made some difference. With the short cable between the control and the amp, I could go down to a 2.2 nF cap without having it act strongly as a volume control. It didn't sound any better, though.


The Mark II Model

While I was working up the gumption to test it, I made up a small output buffer. After trying the control alone, I could unsolder and solder a few wires to turn it into the New & Improved version.

This is JohnH's buffer from the LP Maximizer in the schematics section. I don't know enough about JFETs to calculate the exact input impedance, but it's around one megohm or more, and it's constant. The control always "sees" the same impedance no matter what is plugged in downstream.

That made a big difference. Now the best combination was:

C_f = 1 nF R_f = 100k

When the control was driving directly into the cable, the 1 nF cap turned the sound almost off. With the buffer added, it became the best one.

The tone also became just plain better, not nearly so dull and lifeless. The control made the sound thinner and brighter, as it should. It didn't turn fat humbuckers into the bridge coil of a Strat, but it was brighter.

Conclusion

So, is it a useful control to have? I can only say that I'm not planning to add it to my guitar. It needs a buffer and a battery to sound half-decent. There are easier ways to get a brighter sound, and probably a better sound too.

All in all, my conclusion is that it was an interesting experiment with disappointing results.

[JohnH]

Fobits - great work +1 to you. Theres nothing like really trying something. I find that simulations are good for getting your head around a problem, but they dont tell you how it will sound. I guess I'm not planning to add a bass cut on a guitar either - bass controls on an amp seem like a credible alternative to that!

What does come out though, is again, the huge effect of cables and input impedances, even with those relatively short cables tha you used. You had 16' in the circuit, which is less than the very common length of 20', and yet it was sucking some of the tone away. So I'll wave my flag again in favour of buffers!

John