I would think that slew rate places a "limit" on the slope of the change that the output is expected to produce. So it does not depend on the input amplitude. If a step is applied to a first order network, the output changes and this change is limited in time by the amplifier characteristics. If the amplifier has a 10khz bandwidth, the output should change to 63% of the input step in one time constant, i.e is 15.9uS. If the slew rate permits this, then such an amplitude is allowable. if the slew rate is say .5V/uS, and we have an output change of 10V, then it will require 6.3*/.5= 12.6uS to reach 6.3V. One can even give a step of 15.9/1.26=12.62V and expect that slew rate does not place a limitation for the change. However if slew rate is .05V/uS, then even a step of more than 1.262V will get limited in the change by slew rate. A step of 1V is ok and a step of 2V is not. One has to consider the slew rate as the "LIMIT" on the change expected. A sinusoid has a max rate of change at 0 and will rise to 1.57 times the peak in quarter period. A 10khz sine, 10v peak will require a slope of at least 15.7V/25uS. or .628V/uS. So with a limited slew rate of .5V/uS, the sinusoid will tend to become triangular. If the amplitude is reduced to 7.96V peak, the slew rate will not "LIMIT" the rate of change of output.

.

V. s, V has it exactly right. Ultimately, it's a question of how

the capacitance(s) needed to stabilize the HF response (in

a particular closed-loop gain configuration) are charged up

and down when a very large error occurs at the input of an

operational amplifier; and in most simple designs, the peak

available current is determined by the tail bias used in the

input (gm) stage. Since this, in turn, will usually determine 

the closed-loop bandwidth in a generic op amp, using the

so-called dominant pole HF compensation method, there

is a fixed relationship slew-rate and unity-gain bandwidth.

For example, a modern voltage-feedback op amp design,

similar to Analog Devices ADA4857, can provide a small-

signal bandwidth of 1GHz and a slew-rate of over 3kV/us.

.

But it is not necessary for an amplifier to ever experience

slew-rate behaviour, even when its output waveform is -

at worst-case - a full-scale square-wave. A well-crafted 

current-feedback amplifier avoids the problem by using

the output voltage itself as the source of the necessary

charging/discharging current, This being proportional to

the instantaneous output voltage, the response to large-

signal inputs remains linear under all conditions. An old

design of mine, the AD844, has stood the test of time in

this regard. However, to realize the full potential of the

current-feedback amplifier requires considerable finesse

in the design of the IC and in the choice of package, as

well as in the PC board layout. It's borderline microwave

technik.

.

As often arises in these comments, there is inevitably a

major gap between what may be explained in a didactic

situation, and contemporary design of integrated circuits

of every flavour. There is only a handful of designers in

the world who are operating right at the cutting-edge of 

ultra-wideband IC amplifier design. And no textbook is

going to reveal their secrets.

'

The Lone Arranger

For my opinion, it is important to mention again the role of FEEDBACK in this context (as outlined so clearly by B. Gilbert); and if I remember well - the slew rate is measured/defined for 100% negative feedback only, is it not?

Please remember:  Electrical and electronic circuits are nonlinear !

https://en.wikipedia.org/wiki/Slew_rate

.

Lutz:

.

You write --

.

> ..the slew rate is measured/defined for 100% negative feedback

> only, is it not?

.

No, in fact the slew rate is an aspect of open-loop behavior, since

during these episodes the input stage - conventionally a simple gm

cell - is in severe overdrive, and the feedback process for whatever

closed-loop gain condition is suspended. In measuring slew-rate, it

makes no difference whether there is any feedback at all. 

.

There are a couple of notes to add to this tune.

.

First, the historical, and super-simple, gm cell - consisting of a pair

of BJTs biased by the tail-current I - when used in conjunction with

an integrator/gain stage with local feedback through a capacitor C

(usually followed by a simple unity-gain buffer) will exhibit an open-

loop crossover (unity-gain, zero-dB) radian frequency of w = gm/C.

Note the gmis just I/VK(where VK = kT/q); accordingly, w = I/VKC.

.

Now, the maximum rate of change that can occur in the capacitor is

determined simply by the peak current +/-I, that can be delivered by

the gmstage, and this rate is thus +/- I/C. 

.

So both the slew-rate and the unity-gain bandwidth are proportional

to the current I and inversely proportional to the HF compensation-

capacitor, C. 

.

If we wish to define a ratio of the slew rate to the (radian) frequency

we find that ratio simply is the voltage VK, A quick check shows this

to be dimensionally correct, surprising as it may seem. It also shows 

that the simple form of op amp, presumed above, cannot break free

of this linkage. We should also note a basic dilemma: we can either

make the unity-gain frequency stable over temperature, by using a

tail current I that is PTAT - Proportional to Absolute Temperature - 

so as to stabilize the gmover temperature, but which will make the

slew rate PTAT;  or, one can use a temperature-stable tail current

so as to stabilize the slew-rate over temperature, but which makes

the unity-gain frequency decline linearly with temperature.

.

There are good solutions to these conflicting effects. They  should

be included in any analog IC design course (or textbook). 

.

The Lone Arranger

Hi all

More complex solution see for example in

https://www.researchgate.net/publication/279512571_Slew_Rate_and_Step_Response_of_the_Noninverting_Structure_with_an_Operational_Amplifier

Josef

Conference Paper Slew Rate and Step Response of the Noninverting Structure wi...

.

Josef:

.

Your math is elegant and probably correct - as far as

the mathematics are concerned - though I don't have

time to follow your argumentation.

.

Alas,a REAL circuit knows nothing about maths,

and it will operate strictly according to its "knowledge"

of the physics. And this is where your analysis proves

less useful, since the models you start from are much

too simple. I could show, given the time, that even the

most rudimentary op amp exhibits many mischievous

deviations from the sort of model you show.

.

This is not to criticize your fluency in mathematics, but

the only meaningful analysis of settling time in a REAL

circuit needs to take into account many subtleties that

are not readily addressed by algebraic manipulations.

.

T h e r e   i s   n o   v i r t u e   i n   c a l c u l a t i on .

.

That being the case, there is no reason why a skilled

analog design should ever be disdainful of simulation,

as not only the QUICKEST path to gaining numerous

useful - and often unexpected - insights, but because

it is also the MOST ACCURATE, by far, in predicting

the behaviour of one's first silicon out of the ovens. At

Analog Devices today, even very large circuits (using

multi-millions of transistors and thousand of analog

elements in the mix) to be ready for sampling at "first

light".

.

I'm assuming one has accurate device models for the

elements and very reliable CHARACTERIZATION of

actual devices - a labour-intensive, task demanding a

level of knowledge and patience; which, unfortunately,

is rarely available. In such circumstances, reliance on

simulation is a fool's errand.

.

The Lone Arranger

Yes Barrie,

your comment is certainly correct. But my methods are certainly good and helpful to first estimate.

Josef

Regarding slew rate and negative feedback:

Barrie, thank you for clarification.

I agree that my short comment was probably a bit misleading.

Of course, the slew rate is a property of the opamp unit alone (overdrive of the first stage) - however, in this context, I think we cannot forget negative feedback. The question is: How to measure the slew rate of the opamp?

Answer: Of course with a suitable voltage step at the differential input, but it is very important that the initial DC operating point was within the amplifiers linear region.

More than that, it is common practice to use not a single step but a periodic squarewave for such measurements (stable oscilloscope display) - and we require that between two successive voltage jumps the first stage is NOT overdriven (because of recovery times) but has time enough to return to linear operation.

And that is the case for negative feedback. And the only condition is: The amplitude of the test signal must (a) be large enough to overdrive the first stage (for a short time slot) and (b) small enough not to drive the output stage of the amplifier with feedback into saturation.

(That was the background and motivation of my former remark/comment about slew rate and feedback).

.

Lutz:

.

The peak slew rate is a property of every amplifier whether

it uses global feedback or not.

.

Let's take a leaf out of the microwave designer's notebook for

a minute or two. An RF low-noise amplifier might, erroneously,

be studied using small-signal excitation (that actually means

signals of zero magnitude; but "small" has stuck); and in the

1 - 100 GHz range, the designer may need to rely on the use

of S-parameter models, which are inherently linear in nature,

and only useful in small-signal (zero magnitude) studies.

.

This is so because the LNA designer need to concentrate

on achieving the lowest possible noise in the process that is

to be used, often for the lowest possible power consumption.

With this mind-set, they'e not inclined to study the response

of their circuit under pulse excitation. After all -- "This is not 

a pulse amplifier". But the circuit does not know what it must

do, in order to satisfy its destined application. Indeed, these

sly little silvery sylphs may happily go into oscillation when

pulsed to some value other than the nice, solid steady-state 

solution of an AC analysis, whether performed using lots of

pencils plotting arcane math transformations (and abundant

erasers, too), or by the marvels of modern circuit simulators.

Circuits are shaped by their signals -- which we might, if

poetically inclined, view as their life-blood.

.

Every circuit leads a Jekyll and Hyde existence: its persona

seems to be one thing, when it's analyzed through a tedious

succession of algebraic equations, or even studied through

simulation, fed a diet of wimpy signals having zero amplitude;

but it can only truly come to life, and really get excited, when

transformed by a hearty shove with mercurial speed. 

.

Back to the point. These (open loop) LNAs suffer from slew-

rate limitations: as indeed every amplifier must. Slew rate

has little (or more likely, nothing) to do with the use of global

negative feedback, and it is certainly not limited to op amps.

.

Open-loop audio amplifiers touted for their excellence "due

to the absence of any feedback at all !" will, even if they are

well designed, have to experience the pangs of slew-limited

behavior at some point; but fortunately well above the rated

maximum output power. They must. Every amplifier must.

.

So what does our RF designer do, instead of (actually, as

well as, we certainly hope) the use of pulse testing?  Well,

the situations that are of more interest, and most studied,

in designing LNAs  - typically for use in mobile phones, or 

in the base stations, in microwave point-to-point links, etc.

- are (a) the response to two carriers of equal but various

magnitudes, universally defined in power terms, rather

than as voltages or currents; and (b) the overall response

when a low-power carrier (that might be you calling, and

you may only present picowatts at your recipeint's phone)

occurs at  the same time as a blocker (someone close to

the person you are calling, who's also making a new call)

perhaps at a local power of milliwatts; that is 60 dB, or as

we ordinary people say, a million times higher than your

pitiable picowatt signal.

.

I digressed in this note to put you - as much as possible -

into the mind-set of the RF designer who constantly sees

signals in power terms. This is perhaps justifiable, even

though the mischievous primordial circuit knows only how

it's affected by the voltages buzzing on its branches and

the currents nudging into its nodes. When the rates of

change in these currents exceed a certain critical value,

the voltages change as fast as the capacitances of the

active elements (and any additional capacitance) at the

associated nodes allow each to be charged or discharged.

.

In the presence of a blocker, the LNA in any phone

will inevitably lapse into slew-rate-limited slumber. 

.

But the RF designer - not thinking much about voltages

and currents - has a different, and generally justifiable,

way of characterizing large-signal behavior, which is by

means of such labels as P1dB, IIP3 and several others.

Indirectly, these are measures of limits in the internal

magnitude of voltages and currents and the onset of

slew-rate-limited behavior. The infernal circuit knows

all about these, but it promises to get better with a little

more tweaking of its cardiovascular system.

.

Finally, on this sunny 26oC afternoon, I'll leave you with

a teaser. To set the scene, let me mention that, ADICE

(our Analog Devices Integrated Circuit Emulator) has a

feature which I suggested would be of widespread use:

the ability to automatically hop out of each fully-settled

time-step in a transient analysis, and temporarily enter 

into the simulator's noise analysis routine with all the

eigenvalues "frozen" at that particular, fleeting instant.

The noise-spectral densities (NSD) for each frequency

in the analysis are written into a file NSD(t,f). Then the

resourceful emulator returns to the trme-stepping mode

and continues with the transient analysis, accumulating

information about the circuit's noise until completed at

the final time-step.

.

This suggestion was met with rather more than raised

eyebrows; actually - widespread disagreement on the

part of our CAD team. What would be the dimensions

of the NSD vector? (That's usually a good question to

ask, when working in any nonlinear domain). I said "It

doesn't matter in this case.." (gulp) "..it's only intended

as a way to see how evil noise arises in a wide-awake

circuit". I needed to fight those raised eyebrows to get

them to write the needed code to make this happen.

"You''ll appreciate its value in the long run", I said.

'

Eventually, they relented. I named this function "TNT"

(Transient Noise Test). As expected, it has proven its

value many times over.

.

Okay, now you are looking at the output noise of, let's

say, a classical op amp, connected for operation as a

simple voltage follower, using ADICE as your Window

of Insights. You're letting TNT run during a study of this

circuit when driven in and out of slew-limiting, using a

noise-free square-wave excitation, of amplitude large

enough to push the circuit into these nether regions. 

'

Then you notice that the NSD over the frequencies of

interest is very much higher during the slewing interval.

That seems backwards. Surely all of an op amp's noise

is generated at its input. During slewing the amplifier is

briefly blind to what is happening up front. But TNT, in

all its proven wisdom, shows that the noise increases -

and by a large measure - while the amplifier is slewing.

.

Why?

.

The Lone Arranger

"Why?"

The  "slewing"  is  non-linear , 

ie, not under linear 'calculated' control.    

Yes Glen, slew rate is given by the nonlinear behaviour of the circuit.

But it is "a structural nonlinearity" here - which is given by a design of amplifiers (its internal structure) - for greater signals there are limitations "of available currents" - thus slew rate exists.

Nonlinearity of individual transistors is not the main cause.

Josef,

I think I see what you mean.  

For my example, It is a matter of the Physics. 

As Barrie pointed out, this is a deep subject. 

Quote: "The peak slew rate is a property of every amplifier whether it uses global feedback or not."

To Barrie G.:

Thank you very much for your long and detailed contribution which was addressed to me. It will take some extra time to read and to process all the information. However, I must confess that my answer (which was the cause of your reply) was restricted to operational amplifiers (very large open-loop gain) only. And, in particular, I was discussing slew rate MEASUREMENTS (applying negative feedback) only.

Dear Barrie,

Thank you very much for your comments above. Modeling of the real world is an art. Some times we set-up models which do not "cooperate". We should verify results obtained from the models by means of measurements (observations) of the real world. Our equipment for observations has limitations. Our ability to understand our environment is limited.

concerning: "--- Surely all of an op amp's noise is generated at its input. ---"

Question: How about the noise generated inside the op amp ?

All the best

ERIK

P.S. Please be careful with TNT. It might explode ;-)

https://en.wikipedia.org/wiki/Trinitrotoluene

Trinitrotoluene (TNT), or more specifically 2,4,6-trinitrotoluene, is a chemical compound

with the formula C6H2(NO2)3CH3.

.

Josef:

You write ---

> Nonlinearity of individual transistors is not the main cause.  

.

.A fully linear system would, by definition, never exhibit any

slewing limitations. It is precisely the nonlinear behaviour of

a circuit that causes slewing.  In the case of an op amp, this

is invariably the nonlinearity of the input gm stage; and In the

case of a simple BJT input pair, this nonlinearity is that of the

tanh function, which limits the peak output current (available

to charge the "HF compensation" capacitor) to the supplied

tail current, +/-I, almost fully reaching this value for an input

voltage of +/-4kT/q, that is, about +/-100mVP. The trailing

"P" is a convention I use to remind us that this voltage is

Proportional To Absolute Temperature. (The abbreviation

was first introduced in a JSSC paper I wrote in 1976).

'

There many ways by which this limitation can be overcome.

When I have a little spare time I will add some to this thread.

.

The Lone Arranger

.

Erik:

'

You have the right answer to the teaser I proposed.

The noise of most op-amps when pushed into slew

rate limitations is that of all the stages following the

point at which this limitation occurs. When operating

in this condition, the presumed low-noise input stage

is unable to exert control over the loop, and the post-

slewing circuitry may get nasty.

.

This is hard to demonstrate at the bench, but it might

be possible by crafty measurement techniques.  For

example, make the op amp's input voltage at a such

a level as to exactly cause the output to always be

operating in slew limitations at a minimum necessary

frequency. The output will be a triangular wave for a

nicely designed circuit, or perhaps a sawtooth wave

for one having some inherent imbalance - in which

case, the mean level of the output may quickly drift

up or down toward one or the other supply voltages.

.

Now apply this output to a high-performance spectrum

analyser, and ignore the fundamental peak of the tri-

wave frequency and its trail of harmonics, but look at

the noise floor higher up in frequency. Compare that

to the op amp having its noninverting input shorted to

a quiet ground, with the inverting input connected to

the output, to implement a simple voltage-follower.

.

It will be apparent that this modulation of the output

noise spectrum will be quite different when operating

the amplifier at high gains. In such cases, the blinding

of the input during slewing will, in general, cause the

output noise to decrease, of course.

'

It's all good healthy fun, however you cut it.

'

The Lone Arranger

'

FELLOW TRAVELERS:

'

THIS THREAD IS NOW VERY LONG,  AND WHILE THE SUBJECT

IS FAR FROM FULLY EXHAUSTED, I PROPOSE A FRESH START

UNDER THE HEADING OF A NEW "QUESTION" -- WHICH I WILL

NOW PROPOSE.....

'

The Lonely Arranger

Barrie Yes, I fully agree with your description. The current limit is just what I have called "structural nonlinearity".

I know the essence of Structures "with current on demand". Their slew rate is indeed great - but there's a catch - is a function of the input voltage. It may happen that for small input voltage is a classic OPA faster than the CFA.

Josef

I'm leaving this thread.

Goodbye.

Barrie

So I am sorry, Barrie. Your comments are always interesting. Josef

Josef: See the new question I have launched.

V.s.V Mani

You are developing a solution to the problem.

Barrie has started another Question Thread 

into which your Solutions Thinking may be valuable. 

I appreciated reading your calculated Slew-Rate approach 

and the verbal way this is fed-back to the Vinput amplifier stage. 

Now, I need to envision a comparator "Window" stage,

which peaks-over-time ( as described in your equations ) , 

giving an over-the-thresh-hold voltage

used to neutralize some of the gain of the Vinput amplifier. 

In this thinking, the designer could embed

a control stage against Slew-Rate over-drive of specific chips. 

the apprentice Glen

I thank all readers and wish a happy new year.