Understanding Op-Amp Circuit Analysis: Nodal Analysis vs. Basic Formulas

[ichabodgrant]

Hi. I have moved on to the next question. There is something I am confused.

The question wants us to express R_f in terms of R such that v_o = -15v_i.
After doing the last task, I think I understand the flow of solving it. But here still exists a problem.

My attempts and question are listed in the pic.

 

[NascentOxygen]

Why do you say voltage at C = voltage at D? It doesn't.

The signal at C is an amplifed non-inverted version of v_i.

 

[ichabodgrant]

Sorry.. I want to say V at E = V at D
a typo

 

[NascentOxygen]

Analysis of the second amplifier stage hinges on this relationship:
current from A to D + current from C to D = -(current from F to D)

 

[ichabodgrant]

So are node D and E having same potential?

 

[NascentOxygen]

So are node D and E having same potential?

Yes. You have two labels on the one node. Be consistent, choose one label to save getting confused.

 

[LvW]

Of course, you can start again at "Adam and Eve" (current-voltage relationships, KVL and KCL) - or you can make use of gain formulas which were derived from all this basic stuff:
* Non-inverting gain (1+RA/RB)
* Inverting gain (-RA/RB),
* Two inputs: Superposition theorem.

Following this approach, you immediately can write down the final formula with no calculations at all.
(If you have two resistors in series - connected to a voltage source - and if the voltage across the grounded resistor is to be found. Do you start with voltagew-current relations or do you start with the voltage divider rule?)

 

[ichabodgrant]

I think I was taught the superposition theorem...
I just simply get confused at the line joining node D and E...
As no current flow through these two nodes (or just 1 node as their potentials are the same), so current from C to D means from C to E?

 

[LvW]

Yes - of course. D and E form one single (common) node.

OK - you know the superposition rule. Do you also know the mentioned gain formulas? (I have used both formulas in an answer to your first post).
If not, I recommend to derive it by yourself for (a) a simple non-inv. amplifier and (b) for a simple inverting amplifier (both for ideal opamps).
Then - for future calculations (like this one) - you always can make use of these formuulas without the necessity to start always again at zero (KVL, KCL).

 

[ichabodgrant]

I know all these...
the non-inverting and inverting op-amp... I simply can't distinguish them easily...so I prefer deriving the equations every time...

 

[NascentOxygen]

I know all these...
the non-inverting and inverting op-amp... I simply can't distinguish them easily...so I prefer deriving the equations every time...

That is to be encouraged, so that you can accommodate arrangements which do not neatly fall within those memorized.

 

[donpacino]

That is to be encouraged, so that you can accommodate arrangements which do not neatly fall within those memorized.

In addition the inverting stage does not fall under a typical inverting stage (Av=Rf/Rin)

 

[LvW]

In addition the inverting stage does not fall under a typical inverting stage (Av=Rf/Rin)

It is an inverting stage with two inputs. Indeed, one of the classical opamp applications.

 

[donpacino]

It is an inverting stage with two inputs. Indeed, one of the classical opamp applications.

you said it right there. two inputs. The system must be evaluated as such.

in general taking shortcuts is all well and good but it leads to confusion if you do not understand the underlying concepts. if you try to use them when you reach harder problems, where they are no longer valid. a much better way to do this problem for understanding is nodal analysis. 2 equations and very quick to do

 

[donpacino]

Hi. I have moved on to the next question. There is something I am confused.

The question wants us to express R_f in terms of R such that v_o = -15v_i.
After doing the last task, I think I understand the flow of solving it. But here still exists a problem.

My attempts and question are listed in the pic.

I just saw part of your attempt that was not answered. op amps can supply and recive power. The current will come from the op amp output. When you are dealing with ideal components, you can almost think of the op amp output as an ideal dependent voltage source.

 

[psparky]

So are node D and E having same potential?

The voltage at D and E are the same...0 volts. D and E are same node and since V+=V-...which is grounded, voltage must be zero.

I give a small warning about using the basic inverted and non inverted basic formulas when you are learning op amps.

The reasons are this...the op amps your teacher gives you on the test are never simple enough to actually use these. Also, if your amp isn't exactly set up just right, these formulas don't work. (-RF/RA) and (1 + RF/RA).

Stick with nodal analysis on op amps and you will NEVER go wrong.
Once you get used to nodal analysis, you can see that you can easily derive the basic formulas.

That being said...learn the nodal first, then lean back on the basic formulas.
If I were teaching a course on this, I would insist on this method for your success.