How tone control works

[Harry]

Could someone explain to me how a low-pass and high-pass filters work. I know both filters work with a capacitor and resistor but what are they actually doing.

[vanhansen]

I've been away for a little while but I think I can still explain this in real simple basic terms without diving in to the why's and how's of each.

High pass - allows high frequencies through, sends low frequencies to ground.

Low pass - allows low frequencies through, sends high frequencies to ground.

resistor in series with cap (to ground) = low pass filter
cap in series with resistor (to ground) = high pass filter

[aron]

Here's a highpass filter (AKA low cut)



The capacitor is in parallel with a resistor (in this case a pot)

[Mark Hammer]

Fundamentally, whenever we talk about a highpass or lowpass filter, we are talking about a network of components that provide an "easier" path for some frequencies than for others.  A lowpass filter can be said to provide an easier path for lower frequencies (although this is qualified, more in a moment) and a highpass provides an easier path for higher frequencies.  That's really all it is.  Where is provides an easier path to can play many different roles or have many different impacts.  As well, different filter slopes provide different degrees of advantage for different frequency ranges.  If we say a "steep" filter, we mean that whatever falls within the "passband" (the range of frequencies not facing any impediment) is at a much greater advantage, relative to content outside the passband.

The simplest and most common arrangement would be a one-pole lowpass filter - a resistor in series with the signal, and a capacitor to ground from the "far" end of that resistor.  This bleeds higher frequency content to ground with a slope of 6db/octave.  The slope commences at the "corner" or "turnover" frequency.  So, if the corner frequency is 1khz, content at 2khz (one octave up) is 6db lower, and content at 4khz is 6db below that, and so on.  A steeper (2-pole, 3-pole, etc) filter yields greater attenuation outside the passband.  The corner frequency is given by the formula F=1/(2*pi*R*C) where F is the corner frequency, R is in megohms, and C is in microfarads.

A highpass simply flips the components, with the resistor to ground and the cap in series.  Same formula applies.

There are other configurations too.  For instance, you will often see a cap and resistor in series going to the input of an op-amp.  Those two make a highpass filter, same formula again...usually.  You will often see a resistor and capacitor in the feedback loop of an op-amp.  *Those* two make a lowpass filter...same formula applies.

The RC series highpass and RC parallel lowpass have some interesting properties when it comes to op-amps.  When you increase the value of a resistor in the feedback loop of an op-amp, if there is a parallel cap the corner frequency goes down as the resistor value goes up.  If you look at a Distortion Plus or DOD 250, you will see that the gain is set by a pot going to ground through a cap.  That TOO makes a highpass filter, but in this instance as you turn up the gain, the LOW-end rolloff changes.

The example Aron provides is another application.  Here the resistor provides an impediment to ALL frequency content, but if you happen to have a membership card to the high frequency club, the maitre'd will lift the barrier and let you pass through the cap with little or no impediment.  Clearly, the advantage that "bypass" cap provides will depend on how much impediment if provided in the first place by the resistor.  If the resistor is a low value, then it will provide little impediment, and the bypass cap will provide little advantage.

On many amplifiers (and the amp simulators you may have seen at ROG and elsewhere), you will often see a volume pot with a cap straddling the input and wiper lugs.  Ignore the portion of the pot between input and wiper and it turns into a highpass filter (cap in series, resistor to ground), whose corner frequency is given by the usual formula.  Now add in the other part of the pot.  What you have is a combo volume control and highpass filter.  If the volume is turned down (input portion of pot has a much higher resistance than the part going to ground) then obviously the cap provides tremendous advantage to higher frequencies.  They just zip through.  As volume gets turned up (resistance to ground now much bigger than resistance leading to wiper), there is little advantage provided to anything but the highest frequencies.  Congratulations, you now understand bypass caps on Fender guitars, and bright switches on Fender amps.

There, that's enough for starters.  My fingers hurt and there's a football game on.

[niftydog]

the two simplest forms of filters are;

Code Select Expand

         ___
      o-|___|-o-o---o
                |
               ---
               ---
      Low pass  |
                |
               ===
               GND




          ||
        o-||-o--o---o
          ||    |
               .-.
               | |
               | |
     High pass '-'
                |
                |
               ===
               GND

Think of capacitors as being AC short circuits. That is, to an AC signal, a capacitor appears like a short circuit. Conversely, capacitors are a DC open circuit.

In reality, the amount of "short-circuitedness" depends on the value of the capacitor, the impedances associated with the signal and the frequency of the AC signal. Hence, we can use these propertys to create a filter by selecting the capacitance and resistance values.

Low pass filters have the capacitor to ground. This means that the higher the frequency, the more it tends to see the capacitor as a short circuit - hence the higher frequencys get shunted to ground. Vice versa, the lower the frequency (ie; the closer to DC it is) the more it sees the capacitor as an open circuit - hence the lower frequencys pass more or less unaffected.

High pass filters have the capacitor in series with the signal. Thus, higher frequencys pass unaffected - ie; as if the capacitor was a short circuit. Lower frequencys see the capacitor as an open circuit (or if you like, much more resistive than the high frequencys) and hence are blocked from passing.

The reason we have the resistor is so that we can fine tune the response of the filter. The formula for determining the -3dB point or the "corner frequency" is Æ'=1/[2pi x R x C].

for more, see the links under "Beginners Tutorials" in the FAQ section of this forum.

[Harry]

Ok, FIrst thanks for the responses, Mark you coulda seperated yours into chapters it was so long. One thing I still don't understand, and I hope none of you already explained it (some of the stuff was over my head).

What I'm failing to understand is what is exactly happening when (Let's just say in a Low-pass filter) the current enters the resistor and then passes the cap. I'll just state my theory and then maybe you can correct it.

The current enters the resistor and it's current is reduced. Then the capacitor is charged and discharged, and I'm just guessing slower than originally because of the reduced current, thus resulting in a lower frequency response. Which would change the tone.

Now if that's correct how would different valued caps affect the circuit?

[vanhansen]

Hopefully Mark's fingers have recovered.    That was a hefty answer, but a damn good one.  Thanks, Mark.  As always, you share incredible knowledge.

[Mark Hammer]

Thanks, Van.

The two forms that Niftydog shows are obviously "in the ballpark".  What I think is also important to know is when *other* configurations possess the properties of high and lowpass filters.  Aron shows one in the form of what got called a "tone control" in the old Univox Squarewave.  There, a pot and cap were in parallel.  When the pot was set high, low end had a hard time passing through, but high end zipped past the cap.  As the pot resistance was decreased, the cap provided less and less advantage for the high end, until at lowest resistance the full signal passed via the pot.  As tone control, then, this was a variable highpass filter, serving as a "bass-cut" control.

If you look at the thread on the Anderton compressor, I note another instance of a high pass filter being formed by an RC network that can help to improve the clarity of a compressor by adding a little bit of zip to upper content.  Again, the key thing is to be able to look at a schematic and realize "Hey, THOSE parts will trim back on high end, and/or THOSE ones will trim back on low end"; essentially to recognize high and lowpass filter functions even when they are not obvious or in their classic form.

RG Keen's excellent (and classic) "Technology of..." paper on the Ibanez Tube Screamer (available at geofex) does a great job of showing how creative use of high and lowpass filter functions, placed strategically in a circuit, can achieve a particular oucome.  Well worth reading, even if distortion is not your bag.

Finally, your thread has the header of "tone controls".  Although highpass and lowpass filters CAN be used as tone controls, not all tone controls are only treble cut, or bass cut.  Some controls provide boost and cut.  Admittedly, though, some of the more commonly found tone controls on things you will find here ARE either simple treble-cut/lowpass, simple bass-cut/highpass or combinations (e.g., the BIg Muff tone control).

[brett]

Hi.
Just throwing in 2c worth because being a dumby actually helps explain these things sometimes.

Here's my analogy:
Applying voltage to a circuit is like turning on the garden hose.  There's a pressure (=voltage).  You can always think of voltage as a pressure (because it is!).

Have a look at nifty's diagrams.  There's only three ways the water can go. One is out into the air (the hose bursts and all hell breaks loose.  In electrical terms, this happens at hundreds of volts or more and is recognised by sparks, burns, etc.).  OK, so let's assume that we're talking about low voltages.

The other two options are for the water/electricity to escape via the resistor or the capacitor.  Like water, current will ALWAYS take the LINE OF LEAST RESISTANCE.  Like the other learned gentlemen said, capacitors offer low resistance to alternating currents, while resistors offer the same resistance to AC and DC.  So current will flow through the two devices in proportion to their resistances.

Have I confused you yet?  Because here's the final catch that makes it all happen.  The resistance of a capacitor goes down when the frequency goes up, or when the capacitor is big.  Check out Nifty's diagrams again:
A) in a high-pass filter, high frequencies get a free ride straight through, and have a high-resistance path to the side.  For low frequencies, it's the opposite - MUCH harder to get through the cap than to run off to the side.
B) the low-pass filter just does the opposite.  It's dead easy for high frequencies to run off through the cap (usually to ground).

By the way, none of this changes the frequencies themselves, just the amount of different frequencies that get through.

Crikey.  That was supposed to be 2c worth.
cheers
Brett Robinson

[Harry]

thanks brett, you're speaking more on my level. never thought of a capacitor as a resistor dependent on the frequency going into. Well at least that'll give me something to think about as I try understand the great mystery behind electricity.

[niftydog]

don't worry about trying to analyse current flow just yet, just think about it in general terms.

When I said

the amount of "short-circuitedness" depends on the value of the capacitor, the impedances associated with the signal and the frequency of the AC signal.

what I was getting at was that a capacitor can be seen to change it's impedance (resistance) depending on the frequency of the signal... as you've now discovered. I guess that wasn't very clear was it!?  :?

[jmusser]

Mark, I'm lost on wht you're talking about as far as "slope" and "corner". Is this the area of the sine wave, where if you were on a roller coaster, you'd just start down hill? Also, I was wondering if the resistance to change in a capacitor is also known as "reactance". Most of this stuff makes more sense to me if I can see the effect on the wave form. So far, I have yet to hear anything as dramatic in the tone and texture control realm, as I have with the Whisker Biscuit. It's totally amazing!

[Mark Hammer]

Mark, I'm lost on wht you're talking about as far as "slope" and "corner". Is this the area of the sine wave, where if you were on a roller coaster, you'd just start down hill? Also, I was wondering if the resistance to change in a capacitor is also known as "reactance". Most of this stuff makes more sense to me if I can see the effect on the wave form. So far, I have yet to hear anything as dramatic in the tone and texture control realm, as I have with the Whisker Biscuit. It's totally amazing!

The "corner" frequency is that nominal frequency where the effect of the filter "begins".  If one is talking about a bandpass/resonant filter, we would say "center frequency".  Because highpass and lowpass only have an effect on *one* side of the spectrum, with an ostensibly flat response below/above that, we call it a "corner" frequency.  In baxandall type boost/cut tone controls of the "shelving" type, this can also be called a "turnover" frequency.

The slope is simply how "steep" a change is produced per octave.  "Shallower" filters still let in a fair amount of spectral content above/below the corner frequency becauased they only attenuate material outside the passband by 6db/octave.  That's why you can have a shallow lowpass filter, like the Rat tone control, that can have a VERY low corner frequency if rolled off fully, yet still be able to tell that it is a fuzz.

I wouldn't look for a specific effect on a waveform, if I were you because the filter only alters the audible spectrum.  It does NOT alter the balance between harmonics across all notes on an equal basis, so you could see a significant rounding off by a lowpass filter of higher notes on a scope while very low notes remain every bit as square as they started out.

The reason why the Whisker Biscuit and BMP have as robust a tonal change as they do is because they essentially pan between a lowpass and highpass filter.  Looking at the schem at http://www.runoffgroove.com/whisker.html  you can see a lowpass filter formed by the 33k/.033uf network at A and a highpass filter formed by the 33k/.0047uf network at B.  The lowpass filter has a corner frequency of 146hz, while the highpass has a corner frequency of 1026hz.  If you quadruple the one and chop by 75% the other, you end up with a 12db dip at 292hz and another at 205hz, so a general 6db scoop in the mid-200's zone, when the tone control is centred and the combined impact of the two filters is taken into account.  Rotate it one way and most of the low end is filtered out by the highpass filter.  Rotate it the other way and most of the mids and treble are filtered out by the lowpass filter.

Although personally, I find it a rather annoying control, many users and designers find it a ridiculously useful control largely because it produces such a robust tonal change with a single knob.  Consider replacing the 33k resistor on the A side with a 4k7 fixed resistor in series with a 50k pot wired as a variable resistor.  This will enable one to tune the lowpass filter, such that combinations of the basic tone control and low-tune pot will create a huge range of tones, including tones very similar to the Rat, and the mid-peak of the TS-9.  

At the low resistance range (4k7), the lowpass rolloff will be 1026hz, exactly the same as the highpass filter.  Roll the tone control over to the bass end and you'll get a nice vocal-sounding bluesy tone, with just a hint of squawk.  As the low-tune pot is increased, the lowpass side will roll off lower and lower until a lowest rolloff of 88hz.  Come to think of it, stick an 82k-100k fixed resistor in parallel with the tune pot, because 88hz is a bit too low.  The combination of 4k7 plus a 47k pot in parallel with 82k with get you a maximum resistance abut 34.5k, which will nail you a lowest corner frequency of 140hz.  Try it out and let me know what you think.

[jmusser]

Thanks Mark, for the in depth response. A lot of times what you talk about is not out of the realm of my comprehension, it's just that there are a few key terms that I'm not familiar with, and that gets me confused right off the bat. It's like having the grasp on how a carburetor works, but if the guy explaining the mixture screw calls it a "fuel restricter", you're just guessing. I appreciate your diligence in the explanations, and expect a lot of other people do too. I will try your suggested tone mods for the WB. I guess really the tone control on there you would either love or hate, because of it's broad spectrum. For me, I like having the choice, but others really have "their" sound, and wouldn't need it or want it. To me, it's just a cool thing to go from sweet and dark to gritty and nasty with the twist of one knob.