Gain Bandwidth Product, Open vs Closed Loop Gain, and Feedback

Swarly88

Joined Nov 12, 2018
25
Greetings,

It feels like I am having difficulty discerning GBP when it comes to open and closed loops and feedback. The literature and videos I've found to try and understand this better don't really explain the differences (specifically) and it feels like its being used interchangeably (Obviously it's not; but as a student new to the material it feels that way). Here is my current understanding and PLEASE correct me where I am wrong (This is all in my own words):

In an open loop configuration, an "ideal" amplifier has an unbounded gain potential because there is nothing holding it in check without a feedback loop. A closed loop configuration attempts to curtail this with a resistor network, with a negative feedback driving any observable error to zero and a positive feedback amplifying that error. In term of gain bandwidth product, this is the linear relationship of the frequency response of an amplifier between the -3 dB break frequency, and the 0 dB cutoff frequency (or unity gain, where the input would match the output). It is along this slope that the decibel value along the y-axis of the bode plot and the frequency value along the x-axis would equal the cutoff frequency, no matter where along that line they are selected. In an open loop response, this GBP relationship would not exist because the bode plot would just be a straight line that goes on forever. In a closed loop response, the GBP does not appear until the -3 dB break, and would just be the open loop straight line until that point.

The biggest point of confusion is in those last two lines that I have underlined. I will read or watch one thing where they are talking about GBP with an open loop and another thing where they talk about GBP with a closed loop. At an additional request, this is more so just for my own understanding, but what practicality does an open loop offer? Is it just to see what an unrestricted performance that particular amplifier can provide?

Thank you in advance for any assistance. I always like to bounce my knowledge as I understand it with someone who does to see where any faults may lie.

MrChips

Joined Oct 2, 2009
30,988
Where did you get that crazy notion as underlined?

Here is the open-loop gain of an OPA365 50MHz opamp.

As you can see, the gain falls off to 1 at 50MHz.

Papabravo

Joined Feb 24, 2006
21,264
Open loop there is relatively little difference between an "ideal" amplifier and a "real" amplifier. In both cases the slope of the output characteristic is so close to vertical as to be indistinguishable from one another, as the differential input transitions fro 0- to 0 to 0+. The gain is large: on the order of 10^5 to 10^6. Also "ideal" amplifiers do not have infinitely large power supplies, so the output will limit as close to the supply rails as the circuit topology allows. An open loop amplifier is not really good for much and has relatively few applications, except as a comparator, and they have better parts for that application anyway.

In any closed loop application you can trade gain for bandwidth and vice versa. There is a bandwidth starting from DC and going up to, but not including, some maximum for which the available gain is ALWAYS greater than 1. At frequencies above that limit the gain is always less than 1.

The bode plot going on forever, and always starting at 0 dB, is part of the idealization that distorts your picture of reality, because an open loop amplifier is no amplifier at all. In fact for any small, symmetric, periodic signal, with an average value of zero, the output of your ideal amplifier will be a very close approximation to a bi-polar square wave. The gain in a real open loop amplifier will be large and constant until the output can no longer follow the input. Then it becomes meaningless to talk of an amplifier, because the output is no longer related to the input in any meaningful way.

Papabravo

Joined Feb 24, 2006
21,264
Where did you get that crazy notion as underlined?

Here is the open-loop gain of an OPA365 50MHz opamp.

View attachment 170064

As you can see, the gain falls off to 1 at 50MHz.
This is a real amplifier, not an ideal one.

MrChips

Joined Oct 2, 2009
30,988
This is a real amplifier, not an ideal one.
Oh sorry. I never had the good fortune to play with an ideal opamp.

Swarly88

Joined Nov 12, 2018
25
Where did you get that crazy notion as underlined?
You'd be amazed what an undergrad can come up with when exposed to new material, but I appreciate the correction. Junior year so far has pretty much been death by bode plot. But I digress.

Could you possibly elaborate on your post a bit? Say, would there be an "expected" difference between that and a closed loop response? My understanding there is what you lose in gain with a closed loop, you "gain" (achieve) an increase in bandwidth and stability?

Papabravo

Joined Feb 24, 2006
21,264
Oh sorry. I never had the good fortune to play with an ideal opamp.
Me neither, but we all know what the specs look like.

Swarly88

Joined Nov 12, 2018
25
Also "ideal" amplifiers do not have infinitely large power supplies, so the output will limit as close to the supply rails as the circuit topology allows.
Thank you for that! I could swear that an op amp was limited by its voltage supply.

And thank you for the rest of the response. Is it safe to assume that an "ideal" op amp is more of a theory or pipe dream in the electronics world? The fact that you phrased it as a "distortion of reality" makes me think I was taking its concept too literally.

Papabravo

Joined Feb 24, 2006
21,264
You'd be amazed what an undergrad can come up with when exposed to new material, but I appreciate the correction. Junior year so far has pretty much been death by bode plot. But I digress.

Could you possibly elaborate on your post a bit? Say, would there be an "expected" difference between that and a closed loop response? My understanding there is what you lose in gain with a closed loop, you "gain" (achieve) an increase in bandwidth and stability?
Sure. A gain of 120 dB would be nearly impossible in a closed loop environment, and a 3 dB point at 80 Hz. is not too useful. Putting that part in a closed loop configuration will lower the maximum gain at low frequencies and greatly extend the bandwidth to frequencies far above 80 Hz.

Swarly88

Joined Nov 12, 2018
25
That makes sense; makes the op amp more practical.

Was there anything else that was glaringly wrong in my original post?

crutschow

Joined Mar 14, 2008
34,715
Note that the gain-bandwidth relationship you are taking about usually refers to an op amp (ideal or otherwise) that has a single-pole -6db/octave (-20dB/decade) rolloff starting from a low frequency.
Thus it does have a gain-bandwidth even when it's open loop.
In an open loop response, this GBP relationship would not exist because the bode plot would just be a straight line that goes on forever. In a closed loop response, the GBP does not appear until the -3 dB break, and would just be the open loop straight line until that point.
So this statement is not accurate.
That the amplifier has a GBP when open-loop means the signal open-loop gain at a specific frequency is determined by the open-loop Bode plot.
Thus, for example, for the amp response in post #2 (and assuming that there is some DC feedback to stabilize the operating point), the signal gain at a frequency of 1kHz would be ≈95dB and the gain for a 100kHz signal would be ≈55dB.

Now if you close the loop with a gain of 55dB, then the amp will have a constant gain of 55dB up to 100kHz, where the gain would then start to rolloff at -6dB octave.

Make sense?

MrAl

Joined Jun 17, 2014
11,592
Hello,

If you are talking about a theoretical op amp with no frequency roll off (flat out to infinity) then you can start with a voltage controlled voltage source with any gain you think it should have.
For example, if you choose 100000 as the gain, then if you input 1uv you get 1v out, and that is at any frequency.
If you choose to use an op amp with some roll off, then you can use a voltage controlled current source with gain whatever you need and a resistor and capacitor to produce the roll off, adjusted to match whatever op amp you want to use.

These are both theoretical, but the first one is ideal and the second one takes a single step toward a practical op amp.
Note there are other things to consider too like input offset.

The open loop gain dictates what the closed loop error will be. With a gain of 100000 there will be little error, but with a gain of 10 or 100 you'll see more. That means that for a 1mv input (and resistors setting the gain) you dont get exactly 1v you might get 1.01v or maybe even 1.1v out or perhaps 0.99v or 0.90v all of which are in error to the target output of 1v.