I have a very simple question to ask. Say my required Gain-bandwidth product is 1kHz * 1 = 1k, what is the minimum gain-bandwidth product of the op amp in order to assume an infinite gain?
In the book "sensors and signal conditioning", they gave an example of an application that had a GBW of 30 Khz. It mentioned that a opamp GBW of 5 Mhz was large enough to assume infinite gain. 5 Mhz/30khz=167 times. Is there a rule of thumb would help in figuring if a given opamp is suitable for my application in terms of GBW?
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.
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 !
10 or even less might be good in some cases. I imagine that 1000 would be good enough all the time.
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.
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!
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.
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.
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?
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.
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?
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