Op Amp Feedback Component Values

[JFace]

I've seen a wide range of values used in op amp feedback designs, and I was wondering what are the advantages and disadvantages of going towards the extremes of component values.

Example, if you have a 10k ohm potentiometer (wired as a rheostat) from the output pin to the negative pin of an op amp, this may be considered a low value compared to other pedal designs. Or say we go down to 1k, or even 100 ohms? What if we go in the other extreme, to 1M, 10M, or 1G ohm 

What are the implications of these feedback values, assuming we keep the path to reference and associated capacitors proportional each time we change a feedback potentiometer? For the purposes of discussion, let's assume the gain is variable from 1 to 101 in a non inverting op amp configuration (ex. 100k potentiometer, 1k from (-) pin to cap, cap is 10uF to ground).

[R.G.]

More than most repliers know or will take the time to reply.

Find a copy of "Applications of Operational Amplifiers: Third Generation Techniques" by Gerald Graeme, or "Audio IC Opamp Applications" by Jung, or "Opamps for Everyone" in the TI applications literature.

The shortest guide to this is to note that the opamp output forces a voltage at the output side of the feedback impedance (note the use of the term impedance) that minimizes the difference between the + and - input voltages. If the opamp is set up as a follower, with no input resistor on the - input, the resistor can be almost anything from a wire up to many megohms. In this case, the DC accuracy suffers if the equivalent resistance on the - input is different from that on the + input, because any bias currents come through those resistances, and cause a DC error if they're different. If you're doing AC amplifiers, blocking DC, the DC accuracy doesn't affect you at all.

But the thermal noise the feedback resistor produces does. Resistor thermal noise goes up with resistance. Want low noise? Use low resistances. Again, this will not matter if you're not doing much amplification after the stage in question, but if you're following it with a mega-gain distortion stage, it will.

For inverting stages, the thermal noise and equivalent input resistance of the combination input resistor and feedback resistor both matter.

In general, stay as low as you can, while not using such a low resistance that the opamp's current limits can't drive it well because of a low value input resistor in inverting mode.

See how the special cases creep in no matter how I try to minimize them down to quick quips?

[JFace]

If we are in non-inverting mode, then does impedance theoretically have no lower limit? Can I have a 100 ohm feedback potentiometer and a 1 ohm resistor from the (-) input to reference? I am wondering why pedal designers choose high value feedback pots (100k, 250k, 500k, 1M)  when they could easily use 10k or 1k to reduce noise. Perhaps an answer is that they have accessibility to the higher value components, and the noise figure is tolerable. The dc blocking capacitor would have to increase to maintain the low cutoff frequency, but that's no problem for a large value electrolytic.

[PRR]

> Can I have a 100 ohm feedback potentiometer and a 1 ohm resistor from the (-) input to reference?

Good technique (taking values to absurd extremes to see what happens).

The opamp has to *drive* that feedback network (as well as the actual load you originally wanted to drive).

At full-gain, your plan is a 101 Ohm load on the opamp.

At unity gain it is a 1 ohm load.

Most all-purpose opamps can drive 2,000 Ohms well, 1,000 or 500 Ohms OK, but strain and suck with lower loads.

Specifically: a jellybean opamp with a 1 Ohm load can deliver at-most around 30 milliVolts. A weak guitar level.

Also, for full bass that 1 Ohm leg will want a 10,000uFd capacitor to break the DC. Even with modern tiny parts, that could be the size of your thumb; huge by DIP standards.

So 100 Ohms and 1 Ohm is awful dang low for chip opamps.

There's no point in absurdly low resistances for low hiss. The opamp has internal equivalent resistances which generate hiss. Both sources add. We'd like our resistors' hiss to be lower than opamp resistance hiss. But stuff like '741 and TL072 hisses like a 2,000 Ohm resistor. We want to be below 2K. 1K is reasonably below.

> gain is variable from 1 to 101

At gain of 101 the opamp output has to drive 101K which is easy. The resistance noise of the network (referred to input) is under 1K (990 Ohms).

At gain of 1 the opamp output has to drive 1K. This is lower than spec-sheet rating but for guitar levels this works fine. Resistance noise is 1K. Total hiss is hardly higher than the opamp with an ideal (zero hiss) feedback network.

[Frank_NH]

Interesting topic.  Here's some relevant info from a chapter of an online reference on op amps (analog.com):

"It should also be noted that the gain is based on the ratio of the resistors, not their actual values. This means that the designer can choose just about any value he wishes within practical limits."

"If the values of the resistors are too low, a great deal of current would be required from the op amps output for operation. This causes excessive dissipation in the op amp itself, which has many disadvantages. The increased dissipation leads to self-heating of the chip, which could cause a change in the dc characteristics of the op amp itself. Also the heat generated by the dissipation could eventually cause the junction temperature to rise above the 150°C, the commonly accepted maximum limit for most semiconductors. The junction temperature is the temperature at the silicon chip itself. On the other end of the spectrum, if the resistor values are too high, there is an increase in noise and the susceptibility to parasitic capacitances, which could also limit bandwidth and possibly cause instability and oscillation."

So it sound like if you use lower resistors in the feedback network, your current consumption will increase, possibly leading to excessive chip heating, but also draining your battery faster (not an issue if you use a AC-DC power source).  So the resistances you see in most designs are likely a compromise between current consumption and noise.