# Rise Time and Slew Rate Doubts

#### Saturn Globetrotter

Joined May 3, 2019
18
Hi,

Well, compare the slope of the ramp (slew) to the slope of a sine wave at the zero crossing as that is the maximum slope for a sine wave.
Then, deduce what the op amp would have to be able to do in order to reproduce the sine wave near that point on the sine wave.

This might be one of those things that you have to be told or you have to have read up on it already. Some things in electronics are not exactly obvious unless you really think about it for extended periods of time.
The slope of the slew is steeper than the slope of the sine wave at zero.
OK, here is the part I lack of. "What the op amp would have to be able to do in order to reproduce the sine wave near that point on the sine wave?"
Any guidance here? Sorry I couldn't answer that question as I am unsure. Any help would be appreciated.

#### Saturn Globetrotter

Joined May 3, 2019
18
What is V?

Are you saying that the amplitude of the input signal and the gain of the amplifier play no part?
V is amplitude of voltage, which is calculated from 0 of y axis to the peak voltage.
Or 2 pi f A (sorry for that)
As of the gain, I was not told to use it based on the exercises I did. Do you mind telling me how gain affects slew rate and what are the formulae which has f, A and K to calculate slew rate.

Here are the formulae I know for slew rate
1. (Change in Voltage)/(Change in Time)
2. 2 pi f A
That is all I know

#### Saturn Globetrotter

Joined May 3, 2019
18
input signal and the gain would somehow and in some way play a role in determining the required minimum slew rate
The input signal plays a role in determining the shape of the slew rate where we can calculate the minimum slew rate. I will quote my lecturer here. A sinusoidal input signal will produce an a little curvy slew rate, while a triangular input signal will produce a less curvy slew rate, sometimes a triangular slew rate and the rectangular input signal will produce a slew rate which is almost rectangular, meaning there is a (usually) straight slanting slope.
I wasn't told to use gain, but after all your help, I guess I need some guidance how gain affects minimum slew rate. Any help here? Thanks

#### MrAl

Joined Jun 17, 2014
6,810
Does this give a hint as to where I might have been going?

Question:

My response:

Let me be more specific since apparently I wasn't sufficiently clear. The question asked what the minimum slew rate of an amplifier with a certain gain needs to be in order to avoid distorting the output given an input signal that is a pure sine wave with a certain frequency and a certain amplitude.

The offered answer does not include anything about the shape of the input signal or the gain of the amplifier, so I asked whether they were saying that those factors play no part in the answer. Where I was going was trying to drop a hint that perhaps they DO play a part. I guess I mistakenly thought that that was pretty obvious.

I never claimed that an amplifier's slew rate is affected by the gain or the input voltage, but I most definitely was implying that the minimum slew rate that an amplifier needs to have IS impacted by the gain and the input signal and that, therefore, an answer to that question that does not involve them is most likely not correct.

Here's my (apparently highly flawed) line of reasoning -- the minimum slew rate that an amplifier has to have is determined by the maximum rate at which the output has to change in order to produce the desired output signal. Then, it seemed to me at least, that the desired output signal was somehow related to the input signal and the gain of the amplifier. Thus it seemed reasonable, to me at least, that the input signal and the gain would somehow and in some way play a role in determining the required minimum slew rate.

Since apparently I am completely mistaken in this belief, I will bow out and leave it to you to explain why the nature of the input signal and the gain of the amplifier don't matter when determining what an amplifier's minimum slew rate needs to be.
Hi,

Well to me that is kind of like writing a letter for a declaration of war only to have the receiver ask, "yeah but how did it get here, snail mail or carrier pigeon".

In other words, in this problems usually we look at the output as a point of origin in the quest and go from there.
In other words, if the output is 1v peak then we might choose one op amp, but if the output is 2v peak then another part number op amp. Yes it is true that the output is due to the input and gain, but it's a more or less side issue when it comes to slew rate.

Let me state this in a different manner using two different comparative examples...
The input is 0.1v peak and the gain is 10 so the output is 1v peak, so we need op amp OP0001, but if the input is 0.1v peak and the gain is 20 then the output is 2v peak so we need op amp OP0002.
V.S.
If the output is 1v peak we need OP0001, but if the output is 2v peak then we need OP0002.

The input is 0.2v peak and the gain is 5 so the output is 1v peak so we need OP0001, but if the input is 0.5v peak and the gain is 4 then we need OP0002.
V.S.
If the output is 1v peak we need OP0001, but if the output is 2v peak then we need OP0002.

See how both of these two examples rendered into only knowing what the output was to make the decision which is the main learning point. There are an infinite number of examples that always render into just knowing the output voltage in order to make the decision, so it makes sense to start there when learning about slew rate and sine wave replication.

#### MrAl

Joined Jun 17, 2014
6,810
The input signal plays a role in determining the shape of the slew rate where we can calculate the minimum slew rate. I will quote my lecturer here. A sinusoidal input signal will produce an a little curvy slew rate, while a triangular input signal will produce a less curvy slew rate, sometimes a triangular slew rate and the rectangular input signal will produce a slew rate which is almost rectangular, meaning there is a (usually) straight slanting slope.
I wasn't told to use gain, but after all your help, I guess I need some guidance how gain affects minimum slew rate. Any help here? Thanks
Hi,

The assumption is always a sine (or cosine) input.

#### MrAl

Joined Jun 17, 2014
6,810
The slope of the slew is steeper than the slope of the sine wave at zero.
OK, here is the part I lack of. "What the op amp would have to be able to do in order to reproduce the sine wave near that point on the sine wave?"
Any guidance here? Sorry I couldn't answer that question as I am unsure. Any help would be appreciated.

Hi,

Well if the sine wave has a certain slope near zero and it is the maximum for the entire wave, then wouldnt the op amp have to be able to follow that slope in order to prevent distortion of the sine wave?
So lets say the slope of the sine at the zero crossing is 0.1v per microsecond. What would the minimum slew rate have to be?

#### crutschow

Joined Mar 14, 2008
23,783
Do you mind telling me how gain affects slew rate and what are the formulae which has f, A and K to calculate slew rate.
It doesn't affect how fast the op amp can slew.
But gain does affect the output voltage for a given input voltage, and that affects the required op amp slew rate.

Do you know how the slew rate of a sinewave is determined?
Slew rate is dv/dt which is the differential of the signal, so you just take the derivative of a sinewave (Vsin 2πft) and evaluate that at time=zero, where the slope is the greatest.
That will give you the formula you posted.

Last edited:

#### Saturn Globetrotter

Joined May 3, 2019
18
Hi,

Well to me that is kind of like writing a letter for a declaration of war only to have the receiver ask, "yeah but how did it get here, snail mail or carrier pigeon".

In other words, in this problems usually we look at the output as a point of origin in the quest and go from there.
In other words, if the output is 1v peak then we might choose one op amp, but if the output is 2v peak then another part number op amp. Yes it is true that the output is due to the input and gain, but it's a more or less side issue when it comes to slew rate.

Let me state this in a different manner using two different comparative examples...
The input is 0.1v peak and the gain is 10 so the output is 1v peak, so we need op amp OP0001, but if the input is 0.1v peak and the gain is 20 then the output is 2v peak so we need op amp OP0002.
V.S.
If the output is 1v peak we need OP0001, but if the output is 2v peak then we need OP0002.

The input is 0.2v peak and the gain is 5 so the output is 1v peak so we need OP0001, but if the input is 0.5v peak and the gain is 4 then we need OP0002.
V.S.
If the output is 1v peak we need OP0001, but if the output is 2v peak then we need OP0002.

See how both of these two examples rendered into only knowing what the output was to make the decision which is the main learning point. There are an infinite number of examples that always render into just knowing the output voltage in order to make the decision, so it makes sense to start there when learning about slew rate and sine wave replication.
So what I should learn from your reply is to know about the output to learn about slew rates and sine wave replication?

#### Saturn Globetrotter

Joined May 3, 2019
18
Hi,

The assumption is always a sine (or cosine) input.
Man, I learn something new, all the while I was asked to use rectangular waveform including the assumptions. Even in Multisim Simulations, I was asked to use rectangular waveform

#### Saturn Globetrotter

Joined May 3, 2019
18
Hi,

Well if the sine wave has a certain slope near zero and it is the maximum for the entire wave, then wouldnt the op amp have to be able to follow that slope in order to prevent distortion of the sine wave?
So lets say the slope of the sine at the zero crossing is 0.1v per microsecond. What would the minimum slew rate have to be?
Yes, the op amp have to follow that slope to prevent any distortion.
Minimum slew rate
= 0.1/1 micro
= 100kV/µs

#### Saturn Globetrotter

Joined May 3, 2019
18
It doesn't affect how fast the op amp can slew.
But gain does affect the output voltage for a given input voltage, and that affects the required op amp slew rate.

Do you know how the slew rate of a sinewave is determined?
Slew rate is dv/dt which is the differential of the signal, so you just take the derivative of a sinewave (Vsin 2πft) and evaluate that at time=zero, where the slope is the greatest.
That will give you the formula you posted.
Alright, thanks for the information.

#### MrAl

Joined Jun 17, 2014
6,810
Man, I learn something new, all the while I was asked to use rectangular waveform including the assumptions. Even in Multisim Simulations, I was asked to use rectangular waveform
Hi,

A rectangular wave input can be used to *see* the slew rate, but to determine what slew rate is *required* the assumption is that the input is a sine wave and the output slew rate determined with the rectangular wave has to be able to follow that sine wave at each point in time.

#### MrAl

Joined Jun 17, 2014
6,810
Yes, the op amp have to follow that slope to prevent any distortion.
Minimum slew rate
= 0.1/1 micro
= 100kV/µs
I think you meant 100kV per second right?
I usually quote in volts per microsecond because the data sheets usually use that but there's no reason why that might not change for any manufacturer.

#### Saturn Globetrotter

Joined May 3, 2019
18
I think you meant 100kV per second right?
I usually quote in volts per microsecond because the data sheets usually use that but there's no reason why that might not change for any manufacturer.
Ah, yes, 100kV per second. I'm sorry.

#### Saturn Globetrotter

Joined May 3, 2019
18
Hi,

A rectangular wave input can be used to *see* the slew rate, but to determine what slew rate is *required* the assumption is that the input is a sine wave and the output slew rate determined with the rectangular wave has to be able to follow that sine wave at each point in time.
Ah, this is very clear and easy for me to understand, thanks a lot.

#### MrAl

Joined Jun 17, 2014
6,810
Ah, this is very clear and easy for me to understand, thanks a lot.
Ah, yes, 100kV per second. I'm sorry.
Hi,

No problem just wanted to make sure we were all on the same page.

#### Saturn Globetrotter

Joined May 3, 2019
18
Hi,

No problem just wanted to make sure we were all on the same page.
Alright, sure. By the way, do all users who commented on my thread get notified whenever someone comments on my thread? Or must they click on my thread to see updates?

#### MrAl

Joined Jun 17, 2014
6,810
Alright, sure. By the way, do all users who commented on my thread get notified whenever someone comments on my thread? Or must they click on my thread to see updates?
Hi,

I think whoever has been 'watching' this thread gets notified, and i think when someone replies they automatically get notified unless they turn that off for this thread. Most people dont turn it off though so everyone who replied will probably see the notification that someone has replied to the thread.

#### bogosort

Joined Sep 24, 2011
428
Man, I learn something new, all the while I was asked to use rectangular waveform including the assumptions. Even in Multisim Simulations, I was asked to use rectangular waveform
Consider a theoretically ideal rectangular waveform. Its transitions in amplitude have infinite slope requiring an amplifier with infinite slew rate to reproduce, otherwise the output will be slew-rate limited and the waveform will be distorted. Of course, we can't make amplifiers with infinite slew rate, but this is ok, as there is no such thing as a perfectly rectangular waveform -- any physically-producible waveform will necessarily have finite slope. From Fourier theory, we know that such signals can be represented as a sum of sinusoids of increasing frequency. Importantly, sharper transitions correspond to higher-frequency sinusoids; in other words, the closer a signal gets to vertical slope, the higher the frequencies of the corresponding sinusoids. (If you haven't studied signals and systems yet, this may not be familiar to you, but it will be.)

Now, consider a generic sinusoidal input of amplitude A in volts and frequency f in Hz: x(t) = A sin(2πft). Taking the derivative of x(t) gives us a function x'(t) = 2πfA cos(2πft), which tells us the slope of x(t) at every point t. As cosine reaches a maximum value of 1 at = 0, we see that the maximum possible slope of x(t) occurs when t = 0, at which point the slope of x(t) is equal to 2πfA volts per second. If we amplify x(t) with a gain factor of k, then the max slope of the output is equal to 2πfkA volts per second.

Clearly, increasing the gain of the amplifier, or the amplitude and/or frequency of the input, will cause a proportional increase in the maximum slope of the output. Thus, to determine the minimum slew rate an amplifier must have to avoid slew-related distortion, it is sufficient to compare the amplifier's slew rate with the maximum slope of a sine wave at the highest frequency and amplitude necessary for your application.

For example, suppose you know that your output will never exceed 10 V peak amplitude, and that your circuit is band-limited to a maximum frequency of 20 kHz, then selecting an amplifier with a slew rate greater than 2π * 20e3 * 10 / 1e6 ≈ 1.26 V / μs will prevent slew-related distortion.

I imagine that your instructor uses rectangular waveforms for input because they come equipped, so to speak, with the highest frequencies that your simulation can handle. Anything other than an ideal amplifier will produce a slew-distorted output, and by swapping various amplifier models of different speeds you can readily see the extent of the distortion.