Rolloff?

[Bounty Hunter]

Could someone please define "rolloff" as relates to electronic circuits (in simple language)?  Thanks-

[bluesdevil]

You mean like a treble "rolloff" circuit? That would be a low pass filter made with a variable resistor (linear pot) with capacitor to ground. Look in the "Simple Mods" section of this site for a diagram.

[Mark Hammer]

So, your favourite six foot fullback is running down the field and seemingly on his way to a touchdown.  Except for one thing.  He has two guys who are also six feet and 220lbs hanging onto the waist of his pants.  He's able to run a bit with them hanging on and dragging behind him, but as he runs (drags, actually) further and further, he is clearly slowing down, and the strain of dragging 440lbs is showing more and more.  The first 5 yards with the extra weight was a bit slower but after 15 yards its VERY slow trudging.

So, were the two defending players a "brick wall"?  Not exactly.  There were, however, able to slow things down enough that after a certain point, very little progress was made by the fullback.

Filters are like that.  They often do not provide virtual "brick walls" against anything higher or lower than a certain frequency ranging passing (although there actually ARE complex filters referred to as "brick walls").  Rather, they provide an increasingly more difficult point for higher or lower frequency content to pass through.  Because it is not a sharp dropoff we call it a roll off.  Typically, the "corner frequency", where the rolloff starts to become noticeable, is 6db down/below the zone where there is still a flat frequency response.

So, if I had a 100k resistor and a 220pf capacitor in the feedback loop of an op-amp, this would provide a high-end "rolloff" starting at around 1/[2*pi*R*C] = 1/[2*3.14*.1meg*.00022uf] = 7.2khz.  Content at 7.2khz would be 6db below content lower in frequency than that.  Content at 14.4khz would be down 6db below that, and content at 28.8khz, 6db below that.  You can see that this "rolloff" is not a super-steep phenomenon.

Conversely, if I had an inverting op-amp with a .1uf cap and 100k resistor on the input, the low end would "roll off" around 16hz.  Content at 8hz would be 6db below that, and content at 4hz, an additional 6db lower.

If one were to have a filter with two cascaded sections, they would produce a steeper rolloff at 12db/octave.  This would be true if it was a highpass or lowpass filter.

A great many tone controls on distortion units are simple lowpass filters that provide the standard 6db/octave rolloff.  Unfortunately, this means that a lot of the objectionable "fizz" is not really cut enough to make for a warm tone.  For instance, with a rolloff at 2khz, content at 8khz is still only 18db lower than content at 2khz.  Less noticeable, for sure, but still in evidence and audible.  That's one of the reasons I've tried to remind people whenever possible of the virtues of 2-pole or other complex filters.  They help tofurther reduce the higher objectionable content.

Make sense?

[Bounty Hunter]

Make sense?

Yes! Thanks again.

[Ortiz]

Great explanation!

[gaussmarkov]

[edits in green] i hope it's ok to piggyback a question onto this thread:  not only the corner frequency, but the whole profile of the high-pass filter that mark describes above depends only on the product RC of the resistor value R times the capacitor value  C.  from what i have learned so far, the gain g depends on frequency f according to the equation

g = 2 pi f R C /sqrt(1 + (2 pi f R C)²).

so that means many resistor-capacitor pairs create the same filter as far as frequency versus gain is concerned, right?  we just have to keep R times C constant.  as i understand it, phase depends only on RC, too.  but we rarely talk about the effect of a filter on phase.  so that leaves current.  my searches say that current amplitude is described by the equation

I = V / sqrt(R² + (2 pi f C)^-2).

for a given voltage V, which depends on both R and C and not just RC.  this shows the current varies with frequency, too.

ok.  if i have not made any mistakes and you are still with me, my questions are: 

• are the choices of R and C governed by choosing a level for current? 
• can anyone give an example of how that choice is made?

thanks in advance for advice about this.  if i have highjacked this thread inappropriately, please lemme know....

[niftydog]

Basically what you have to keep in mind is the parallel impedances. The filter by itself behaves as you would expect, but chuck a 1k impedance in parallel with it and it starts to do some funny things. I don't think either of use necessarily want to go deep into mesh and nodal analysis just to understand what's going on, suffice to say that getting the right impedance is where it's at and not so much selecting for a required current.

[gaussmarkov]

Basically what you have to keep in mind is the parallel impedances. The filter by itself behaves as you would expect, but chuck a 1k impedance in parallel with it and it starts to do some funny things. I don't think either of use necessarily want to go deep into mesh and nodal analysis just to understand what's going on, suffice to say that getting the right impedance is where it's at and not so much selecting for a required current.

i've never even heard of "mesh and nodal analysis."    thanks, nifty!  i guess i'll try to learn more about impedance.