# Calculating Maximum Gain

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#### Mr.Simplicity

##### Newbie level 2
For a square-wave with 100 microseconds period requiring total harmonic distortion of less than or equal to 10%, what will be the maximum gain?

Please do not just give the final answer. I want to understand the question and the steps involved in carrying out such a calculation?

Thank you

#### crutschow

##### Advanced Member level 5
What do you mean that the harmonic distortion must be less than 10%? A square-wave has much more than 10% distortion.

And what does that have to do with gain? :???:

#### LvW

##### Advanced Member level 5
For a square-wave with 100 microseconds period requiring total harmonic distortion of less than or equal to 10%, what will be the maximum gain?

Please do not just give the final answer. I want to understand the question and the steps involved in carrying out such a calculation?

Thank you

So you want to understand your question? We too!

#### Mr.Simplicity

##### Newbie level 2
So you want to understand your question? We too!

I am taking a sensors and instrumentation course this term at school. This question was from a series of three questions. I will post all the questions below so that you have a better understanding, though I do not think they are interrelated. I am quiet confused and did not mean to confuse more people. I understand and know how to solve the first two questions but the third question just blew my mind.

1. For a sine wave with 14V(pk) amplitude, what is the large signal bandwidth?
2. for a triangular wave with 14V(pk) amplitude, what is the large signal bandwidth?
3. For a square-wave with 100 microseconds period requiring total harmonic distortion of less than or equal to 10%, what will be the maximum gain?

Thanks

#### crutschow

##### Advanced Member level 5
I can understand your confusion. The third question makes no sense to me as stated. It requires more information before an answer can be supplied. I don't understand what 10% harmonic distortion has to do with amplifying a square-wave, and I don't understand what gain has to do with anything, since no signal levels are stated.

#### Junus2012

##### Advanced Member level 4
Hello

the harmonic distortion is a large signal behavioural of the operational amplifier. when the signal exceeding the maximum allowable slew rate it will experience the non linear distortion

among all of the three signal the easiest one is the square wave. the maximum limit with no harmonic distortion is
maximum output frequency = pulse amplitude / 2.(S.R+linear settling time) or maximum output pulse = frequency.(S.R+linear settling time)
the frequency is 1/signal time
but I believe that even through this condition the output signal still will have a certain harmonic distortion because the signal is going under the large signal condition where the amplifier is not fully linear
but me too I am interest to know how to solve this mathematically for a certain percent

I am taking a sensors and instrumentation course this term at school. This question was from a series of three questions. I will post all the questions below so that you have a better understanding, though I do not think they are interrelated. I am quiet confused and did not mean to confuse more people. I understand and know how to solve the first two questions but the third question just blew my mind.

1. For a sine wave with 14V(pk) amplitude, what is the large signal bandwidth?
2. for a triangular wave with 14V(pk) amplitude, what is the large signal bandwidth?
3. For a square-wave with 100 microseconds period requiring total harmonic distortion of less than or equal to 10%, what will be the maximum gain?

Thanks

#### LvW

##### Advanced Member level 5
I am taking a sensors and instrumentation course this term at school. This question was from a series of three questions. I will post all the questions below so that you have a better understanding, though I do not think they are interrelated. I am quiet confused and did not mean to confuse more people. I understand and know how to solve the first two questions but the third question just blew my mind.

1. For a sine wave with 14V(pk) amplitude, what is the large signal bandwidth?
2. for a triangular wave with 14V(pk) amplitude, what is the large signal bandwidth?
3. For a square-wave with 100 microseconds period requiring total harmonic distortion of less than or equal to 10%, what will be the maximum gain?
Thanks

I supose, you forgot the main part of the questions: All signals are applied to an opamp - and the questions are related to the OUTPUT signal. Is this correct?
Only in this case, the questions make sense. However, in order to answer the questions we need to know the opamp parameters. Otherwise the first two questions cannot be answered.

#### Junus2012

##### Advanced Member level 4
yes, it seem to be like an output of an operational amplifier

I supose, you forgot the main part of the questions: All signals are applied to an opamp - and the questions are related to the OUTPUT signal. Is this correct?
Only in this case, the questions make sense. However, in order to answer the questions we need to know the opamp parameters. Otherwise the first two questions cannot be answered.

#### LvW

##### Advanced Member level 5
yes, it seem to be like an output of an operational amplifier

Dont you have a clear description of the task?
Questions cannot be answered without knowing opamp parameters.

#### Junus2012

##### Advanced Member level 4
it is not me, Mr.Simplicity who posted that

Dont you have a clear description of the task?
Questions cannot be answered without knowing opamp parameters.

#### LvW

##### Advanced Member level 5
it is not me, Mr.Simplicity who posted that

Oh - sorry. Please forgive me.

#### Junus2012

##### Advanced Member level 4
it is ok LvW, no problem at all ..... it was so cool hahahaha

Oh - sorry. Please forgive me.

#### FvM

##### Super Moderator
Staff member
All signals are applied to an opamp - and the questions are related to the OUTPUT signal.
That should be assumed. Nevertheless THD of a square wave is a completely meaningless specification, I think. Or do you have an idea how to define it?

I'm not aware of a commonly used THD definition applicable to square waves.

#### LvW

##### Advanced Member level 5
That should be assumed. Nevertheless THD of a square wave is a completely meaningless specification, I think. Or do you have an idea how to define it?
I'm not aware of a commonly used THD definition applicable to square waves.

Perhaps 10% rise time - referred to the period - of the output square wave? Perhaps Mr.Simplicity can provide us with some additional information?

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