Finding closed loop gain in ideal op amp

In summary, the question is asking for the closed-loop gain of an ideal OP-Amp in negative feedback configuration with given resistor values. The feedback factor, β, can be found by using the voltage divider rule on the four resistors R3 to R6. The overall gain can then be calculated using H. Blacks formula, which is not in the course syllabus but can be found on Wikipedia. Alternatively, standard circuit analysis can be used to find the potentials at the op-amp inputs and solve for the gain. It is recommended to start with simpler problems and gain confidence in arithmetic before attempting more complex formulas.
  • #1
whatphysics
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Hello there, this isn't necessarily a homework question. I came across this qn during revision and didn't know how to solve it. Any help would be greatyly appreciated.

The answer is 0.97

1. Homework Statement

For the ideal OP-Amp in negative feedback configuration shown in Figure Q30, calculate the closed-loop gain, AVCL=VO/VS= ________. Assume R1=10 KΩ, R2=5 KΩ, R3=2 KΩ, R4=2 KΩ, R5=5 KΩ, R6=1 KΩ, RL=10 KΩ.

Homework Equations


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The Attempt at a Solution


Im unsure how to deal with the bottom bit, the resistors R3 to R6 which is connected to the inverting input. Do i try and find the Req for that bit and then treat it as Req is the feedback resistor? How would I proceed to attempt this question?

Thank you for all your help.
 

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  • #2
What you need is the feedback factor β which depends on R3...R6 only.
Forget RL because this is a load resistor only - and does not has any influence on gain (because the ideal opamp has zero output resistance - an ideal voltage source).
The feedback factor β is defined as the voltage ratio β=Vin-/Vout (Vin- is the voltage at the inverting input node).
The overall gain is according to H. Blacks formula:
G=α*Aol/(1+β*Aol)=α/[(1/Aol)+β].
For infinite open-loop gain Aol (ideal opamp) we have:
G=α/β.
(The feedforward factor is simply α=R2/(R1+R2)
 
  • #3
LvW said:
What you need is the feedback factor β which depends on R3...R6 only.
Forget RL because this is a load resistor only - and does not has any influence on gain (because the ideal opamp has zero output resistance - an ideal voltage source).
The feedback factor β is defined as the voltage ratio β=Vin-/Vout (Vin- is the voltage at the inverting input node).
The overall gain is according to H. Blacks formula:
G=α*Aol/(1+β*Aol)=α/[(1/Aol)+β].
For infinite open-loop gain Aol (ideal opamp) we have:
G=α/β.
(The feedforward factor is simply α=R2/(R1+R2)

H.Blacks formula and Feedforward factor arent in my course syllabus.
How do I find the feedback factor using R3 to R6? I am aware that Vo/Vs=1/β for non inverting input
 
  • #4
whatphysics said:
H.Blacks formula and Feedforward factor arent in my course syllabus.
How do I find the feedback factor using R3 to R6? I am aware that Vo/Vs=1/β for non inverting input
Yes - but the signal is applied not directly to the non-inv. input but through a diver with the factor α.
Blacks formula can be found using wikipedia.
The feedback factor contains 4 resistors only.
It shouldn`t be a problem for you to apply the voltage divider rule twice.
 
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  • #5
whatphysics said:
H.Blacks formula and Feedforward factor arent in my course syllabus.
You can also approach the problem using standard circuit analysis and the simplifying properties of the ideal op-amp (you should know what these are). Start by finding the potentials at the op-amp inputs in terms of Vs. Then consider what currents can flow and where in the feedback network.
 
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  • #6
Not knowing your level of expertise
remember what i told you in the EE thread?

Since they gave you values for all resistors it is just an arithmetic exercise to figure voltages at + and - inputs.
Set them equal and rearrange that equation to give Vo/Vs.

Opampforanime.jpg

A question well phrased is half answered.
"What's V@+input?" is easy, by inspection you know what it is.
Can you figure out Vintermediate and V@-input by plain old step by step simplifying that R3,4,5,6 string?

Feedback Factor and Black's formula become intuitive after you've worked a few hundred problems like this one .
I think you need to start out simpler. What before why.
When you've got confidence that your arithmetic works, you should use it to prove Black's formula.
Then you'll have confidence in that powerful tool, too.

That's how i learned, anyway.

Good luck in your studies.

old jim
 
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FAQ: Finding closed loop gain in ideal op amp

What is a closed loop gain in an ideal op amp?

In an ideal op amp, the closed loop gain is the ratio of the output voltage to the input voltage. It is also known as the voltage gain or amplification factor.

How is the closed loop gain calculated in an ideal op amp?

The closed loop gain in an ideal op amp is calculated by taking the ratio of the feedback resistance to the input resistance. This can be represented by the formula A = -Rf/Ri, where A is the closed loop gain, Rf is the feedback resistance, and Ri is the input resistance.

What is the significance of the closed loop gain in an ideal op amp circuit?

The closed loop gain determines the amplification of the input signal in an ideal op amp circuit. It also helps in stabilizing the output voltage and controlling the overall gain of the circuit.

Can the closed loop gain in an ideal op amp be greater than 1?

Yes, the closed loop gain in an ideal op amp can be greater than 1. This indicates that the output voltage is amplified compared to the input voltage. However, the actual gain of an ideal op amp is infinite and is limited by the power supply and other factors.

How does negative feedback affect the closed loop gain in an ideal op amp circuit?

Negative feedback reduces the closed loop gain in an ideal op amp circuit. This is because the feedback signal is in opposite phase with the input signal, resulting in a decrease in the overall gain of the circuit. However, negative feedback also helps in reducing distortion and improving stability in the circuit.

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