Op amp newbie

You might want to refer to book by Allen and Holberg. It gives step by step approach to design of opamps.

The actual gain of the circuit is:

G / (1 + GH)

Where: G is the gain of the op-amp H is the gain of the feedback section

If G is very large, the one in the denom doesn't matter much and can be ignored. If yoy do a little math, you will see that the overal gain ends up as 1/H in that case.

If G is not very large, we can work out what the G has to be to get the accuaracy we need. For most op-amp, you assume that the G has a phase shift of 90 degrees.

Take the case of the non-inverting unity gain amplifier working at 1kHz. In this case, the H is simply 1. Lets assume that we want the overal gain to be at least 0.99 for a 1% error.

Remember that the phase angle of result is not know until we calculate it. We use | X | to say ignoring the phase.

Remember that we said "assume G is at 90 degrees"

Square both sides:

sqrt(0.99^2 / (1 - 0.99^2)) = G

G = 7.018

Given this we check the data sheets to see that the op-amp we have selected has a gain of at least 7 at 1kHz.

A good rule of thumb is that an op-amp for a filter must have a GBP greater than:

GWP > 10 * Q^2 * Fc

The G/(1 +GH) still works here but for a filter, the H is complex value instead of siply being one.

The voltage gain of *all* op-amps rolls off rapidly from bizarrely large numbers at DC / LF towards one @ the gain-bandwidth product frequency.

No op-amp has *infinite* gain but it makes the basic sums easier to understand if you pretent they do. ;-)

Another poster appears to have given you the full and correct equations for calculating closed-loop gain.

As you'll see, the simplistic 'theoretical' gain such as the classis - Rf / Rin for a simple inverting stage is subject to a term that takes account of the open-loop gain of the op-amp ( or indeed any other amplifer section ) being finite.

In practice I would advise that the gain of the op-amp should be significantly greater than the closed-loop gain at any frequency that you desire some accuracy at.

For example. Many popular bi-fet op-amps used in audio have a GBW product of 4MHz.

The highest frequency normally considered relevant for audio is 20kHz. At this frequency such an op-amp has an open-loop gain of 200 or 46dB.

It would be inadvisable to expect to use such an op-amp for closed-loop gains greater than say 30dB in audio use. In practice I'd be likely not use it for > 20dB. Clearly the closed-loop gain also can't exceed the open-loop gain !

Graham

It depends somewhat on what you are doing.

The problem is that as you get closer and closer to the limit, then there will be less and less feedback available to linearize the circuit at higher frequencies and you will have more and more distortion. If the op-amp is followed by an aggressive low-pass filter, the distortion might be tolerable, since the filter will knock it down quite a bit.

--Mac

Filter ?

What filter ?

Graham

Graham, I said "if the op-amp is followed by an aggressive low-pass filter, the distortion might be tolerable since the filter will knock it down quite a bit."

I don't know why I'm quoting it; it is still visible above. ;-)

But anyway, does it make sense now? If not, I really don't know what to say!

--Mac

It sounded like an odd thing to do. Can't say I've ever seen such an arrangement. Have you ? The cost of a passive LP filter would be such that it would simply make sense to use a better op-amp I would have thought.

Graham

Yes. In a sampled IF system. IF bandwidth is 50 MHz.

Well, since it is a sampled IF system, a brickwall anti-aliasing filter is mandatory anyway. And finding op-amps which can drive 50 Ohms at 50 MHz with low distortion is not necessarily trivial.

--Mac

It may surprise you to hear that it can. Use of positive feedback makes that happen. And yes, there are real world practical circuits that use it.

NT

In practically all unity gain buffers it happens at the gain cross over frequency so it isn't even rare.

indeed, but even with nfb it can happen, as Ken explained.

reactions receivers are back in fashion, aka regenerative receivers.

pfb is also used when starting sine oscillators, with feedback dropping to 1 only once oscillation has built up. A whole lotta goods use oscillators.

NT

Maybe the OP should have said NFB. I rather think that's what he meant.

I don't think that's what the OP had in mind though. Can you give an example of one btw ?

Graham

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Indeed. Now also consider an nfb'ed opamp with a tight phase margin. At hf, closed loop gain can exceed 1 without instability, since there is phase shift along with that >1 gain. >1 gain only causes oscillation when your phase shift is zero: the further from zero that shift goes, the more gain can be tolerated before oscillation occurs.

Think about it: how much gain could be tolerated when phase shift is 90 deg? Would a closed loop gain of 1.1 be stable?

NT

open-loop

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Using op-amps ?

Indeed, I've used that myself. Gain > 3 for the Wein Bridge arrangement to ensure start-up. I don't see how a discussion of this is relevant to the OP's interest in GBW product vs practical gains though.

Graham

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Yes, as I pointed out elesewhere, almost all unity gain buffers peak at the gain cross over point for this reason.

open-loop

example of

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interest in

It isn't, but bigcat said that closed-loop gain can exceed the open-loop gain. I think the oscillator example is irrelevant to that, and I'm a little shaky on regenerative (q-multiplier) circuits - in a setting like that, don't the definitions of "open-loop gain" and "closed-loop gain" get a little foggy?

Thanks, Rich

open-loop

example of

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interest in

Why would they get foggy? More complex I guess, as there are 3 gain figures not 2. With regen a single valve stage can give you gains of

With opamps it gets more complex, but closed can still exceed open IIUC.

NT

open-loop

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ensure

interest in

Not to me but maybe I'm being very literal in my interpetation of their meaning ?

Graham