# Finding the closed loop gain expression

Thread Starter

#### HugoBugo

Joined Oct 24, 2020
4

Hi! thanks in advance for the help.

I'm trying to solve this exercice for school but a really can't seem to get it right.
I get really confused when that VDD apperas and can't identify the feedback mesh

Here is what i think it is:

But then again i'm not sure if that vdd or that resistor is suppose to be there.

If anybody could give any help i whould be much appreciated.

#### RBR1317

Joined Nov 13, 2010
709
If U1 is an ideal op-amp, then its output resistance is zero. So how does R3 & RL affect vout?

#### ericgibbs

Joined Jan 29, 2010
17,987
hi HB,
Welcome to AAC.
If you have a LTSpice simulation asc file, please post it.
E

#### LvW

Joined Jun 13, 2013
1,669
Are you sure that the circuit looks like the one you have shown?

Thread Starter

#### HugoBugo

Joined Oct 24, 2020
4
hi HB,
Welcome to AAC.
If you have a LTSpice simulation asc file, please post it.
E
Hello! The LTSpice model is just so i could have a picture of the circuit in the exercice. The componets have no set values, it's a exercice made so i can analyse the circuit and obtain the expressions on its feedback, assymptotic Gain, Closed loop gain, impedances and Bode plots.

Thread Starter

#### HugoBugo

Joined Oct 24, 2020
4
Are you sure that the circuit looks like the one you have shown?
Hello! yes the exercice consists of the first circuit and asks to analytically analyse the circuit and calculate all the expressions for the feedback, gains, impedances and then using logorithmic scale make the bode plots for the circuit

Thread Starter

#### HugoBugo

Joined Oct 24, 2020
4
If U1 is an ideal op-amp, then its output resistance is zero. So how does R3 & RL affect vout?
in the third part of the exercice they say that input immpedanc
Hello! yes the exercice consists of the first circuit and asks to analytically analyse the circuit and calculate all the expressions for the feedback, gains, impedances and then using logorithmic scale make the bode plots for the circuit
Forget the part about the bode plots, it is not asked to do that.

#### MrAl

Joined Jun 17, 2014
10,593
View attachment 229615

Hi! thanks in advance for the help.

I'm trying to solve this exercice for school but a really can't seem to get it right.
I get really confused when that VDD apperas and can't identify the feedback mesh

Here is what i think it is:
View attachment 229617

But then again i'm not sure if that vdd or that resistor is suppose to be there.

If anybody could give any help i whould be much appreciated.

The exact answer depends on what other information you have about the op amp.
If you dont have any other information about it then you might assume that the op amp is the same as the ones you have used up to this point in your studies.

One of the most important is the op amp internal gain. If you are not ever given that though then i would think they want you to assume it has infinite internal gain because that is what a lot of these theoretical questions assume. That equates to zero output impedance which then means the two resistors on the output do not affect the output in any way. They also did not give the power supply values so this is probably a mostly theoretical question. So the feedback is just with the other components that are connected to the inverting input.
If you wanted to, you could calculate with some finite internal op amp gain too and compare results.
Another thing you could do is calculate the output with both resistors in the circuit symbolically and the internal op amp gain also symbolic, then see what happens to the output as you like the internal gain numerical value go from some lower value like 100 to some high value like 1000000 and then to infinity. The results will be interesting. This kind of exercise really shows you important features of these circuits.

The other question is do they want you to consider the current source as input or the equivalent voltage source on the input. Because the current source is shown i would think they want you to consider the current source as the output. This means you will get an expression like Vout=Iin*K where K is determined by the circuit component values.

[LATER]
A good way to determine if the two output resistors matter or not is to do a symbolic analysis of the entire circuit the way it stands in its entirety. You could use for example Nodal Analysis.
Now if either or both of the two resistors in question do not matter, they will cancel out of the equation(s). If they cancel out of the equation for Vout then they can not possibly contribute to the solution for Vout. This means you dont really have to know if they matter or not beforehand because a good analysis will reveal that information as you calculate Vout.
In simpler terms, if you end up with a function like this for the output voltage:
Vout=f(R1,R2,R3,R4,R5,R6)
then the output depends on all of those resistors, but if you end up with something like this:
Vout=f(R1,R2)
then the output only depends on R1 and R2 and the other resistors never change the output.
Now we do have to remember though that this is a theoretical problem. If it were a practical problem we would have to consider the loading effect on the output of the op amp and that would mean the two output resistors would definitely not cancel out. For example if the load resistors was 0.000001 Ohms it is highly unlikely that it will not pin the output to near ground which would be close to zero volts. In pure theory however, even that resistance may not change the output.

Last edited:
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