Opamp Gain Bandwith Product in the real world?

[ashcat_lt]

Trying to get my head around GBP for nerdy reasons.  I've come across things that seem to imply that it can be considered pretty much as a static lowpass with the cutoff set by the gain setting resistors.  Basically, if you know how to figure the gain of the opamp, you can figure the cutoff.  Cool.

But all of those examples are simple opamp gain stages involving resistors.  Real world gain stages in the things we do almost always have capacitors involved.  The "closed loop gain" is different at different frequencies.  The actual resistance in the feedback loop is actually the parallel of the Rf and whatever Cf looks like at a given frequency.  Likewise, Rg islike an open circuit at very low frequencies.  In fact, most of the popular opamp pedals have no place in the spectrum where the actually reach the gain predicted by the resistors alone.  And holy crap don't get me started on diodes...

So, like, WTF?  Is it actually true that this cutoff just floats around all the time?  Is the a simple way to determine that cutoff or do I really just have to figure out the equivalent resistance of all those different parts at every given time?  Does anybody care or ever bother?  If I try to model this just as a static filter based on the resistors will I be far enough off to hear it?

[PRR]

> do I really just have to figure out the equivalent resistance of all those different parts at every given time?

That's what the electrons do.

Mostly you design the accompanying parts so it hardly matters.

For DC amplifiers, you really only care about the high end of the audio band.

If the external parts promise a gain of 1,000, and the opamp is GBW 1MHz, it will fall-off from 1,000 by 1KHz. But promise a gain of 10, you're good to far past the audio band.

[ElectricDruid]

Is there a simple way to determine that cutoff or do I really just have to figure out the equivalent resistance of all those different parts at every given time?

No, you don't. If you're bothered about it, you should consider the worse-case scenario; what's the maximum gain the circuit could produce. This is usually pretty obvious from what's commonly known as a "DC to daylight" analysis. What does the gain look like at DC? (All the caps are open circuits) What does the gain look like at infinity? (All the caps are shorts). The bit in the middle that we care about will be somewhere between those two cases. One of them will be the worst case. Divide your GBW by that gain and see what you get. If it's reasonably above the audio range, you're comfortable.

Does anybody care or ever bother?

I never do. For most modern op-amps for audio stuff, you've got GBW to spare unless you're doing something extreme. I'd only really consider it if I was using some older op-amp for a specific circuit or effect. Some distortions (RAT for example) use slow op-amps and don't sound the same with modern faster ones.

If I try to model this just as a static filter based on the resistors will I be far enough off to hear it?

No, you'll be fine.

[Rob Strand]

I never do. For most modern op-amps for audio stuff, you've got GBW to spare unless you're doing something extreme. I

For simple stuff you pretty much ignore it *unless* you know it will be a problem.

Like if you build an AC reference the tiny roll-off can affect the accuracy.   When you get to this level of concern you also need to account for the common-mode gain.    Common-mode gain is another thing that affects the response but it is rarely accounted for.

Gain-bandwidth does screw-up the response of some filters.   If you look-up pre-distortion you should find how this is handled.

Then there was a widely quoted paper which got a 3rd order response by using the opamp's gain bandwidth as one of the poles.  So you use the opamp's roll-off to your advantage. (Can't remember the paper.)

[ashcat_lt]

That's what the electrons do.

Yeah and I guess I have to do it for other reasons anyway.  It does matter in some pedals.  The RAT has quite a lot of gain when cranked up, and even with a faster chip you can hear the effect of the GBP.  When I made my plugin "model" I found the cutoff had to quite low in order for it to reasonably match the hardware and other plugins.

That actually is most of why I'm asking.  Trying to make software simulations of things that sound like guitar pedals.  I'm not necessarily real worried about getting it exactly perfectly like the real thing as long as it sounds good, but if there's an easy way to get closer, I'd like to try.

I kind of get lost in the chicken and egg nature of some of these things.  Like the conduction of the diodes must depend somewhat on the action of the filters, but those filters' cutoffs depend on the conduction of the diodes.  Not to mention that the output of the whole thing (in a TS type circuit) depends on the output...

Thanks to everybody for your thoughts.

[Mark Hammer]

Think of GBP like this:  some folks can run really fast for very short distances, but not nearly so fast as the distance increases, while other folks can keep up a pretty fast pace for much longer distances.  Most op-amps can produce gobs of gain at low frequencies, but as the frequency increases, they can only produce lesser amounts, decreasing as the frequency to be amplified increases.

We tend to forget that what we commonly think of as "producing" gain in op-amps is really varying amounts of reducing gain from the open-loop maximum.  I like to describe it as putting the brakes on.  The more negative feedback is provided  from the output back to the input, the less gain is permitted from the absolute maximum.  That's why use of higher-value feedback resistances results in more amplification: less negative feedback to detract from the open-loop maximum ("open-loop" being the largest feedback resistance possible - infinity).

BGP can be used productively.  A local guy brought over his  Timmy pedal one evening a few years back, because he had heard somewhere that using an LM1458 sounded better than the stock chip.  I installed a socket and we tested out at least a half dozen different types of dual op-amps that evening, and by gum the 1458 really did sound best to both of us.  Why?  Because it's limitation with respect to BGP result in less top end at higher gain settings, and a warmer resulting sound.  I just finished boxing up a pair of Madbean Aristocrat (King of Tone clone) pedals the other day.  I used 1458s for one of them and 4580s for the other, and the 1458s sounded much nicer to me.  Less harsh.  Again, likely because of its limitations with respect to BGP, in comparison to the "higher quality" chips.

Lower BGP is not "magic".  Its role depends on what the circuit is intended to do.  If I was making a mic preamp, I sure as heck wouldn't use a 1458.  BUt if I'm making something whose goal is to generate more harmonic content, I want to rein in the upper harmonics and promote lower-order harmonics.  IN that context, the BGP properties of something like the 1458 are a virtue rather than a limitation, and come in handy, even at the cost of maybe a bit of noise.