Can someone explain me why Vx is 0 regardless of Ix?

[AMSA84]

Here is the picture that worth more one thousand words.

Thank you in advance.

 

[D.A.(Tony)Stewart]

If Av=R2/1R1 and open loop gain, G = 1e6 and open loop output impedance, Ro of say 300 Ohms, the Zout will become Ro/G *Av at DC
Since G changes with frequency as GBW is constant, Zout will also rise with f.

Effectively if any Vo occurs it is because the device does not have enough current drive to oppose the applied current. When it saturates externally, THe gain is high enough to force Vin(-) to match Vin(+) until it current limits or overheats.

 

[LvW]

In short: Both statements (Vx=0 and Rout=0) are not correct. It is only a simplification - and this fact should be mentioned.

In the shown circuit the opamp has negative resistive feedback with the consequences as follows:

* The voltage Vx at the inverting input is very small (Vout/Aol) because the open-loop gain Aol of the opamp is very large (1E4...1E6).
Therefore, we introduce just a very small error by setting Vx=0 during calculations (µVolts in reality).

* Something similar happens with the output resistance. Without feedback the output resistance, normally, is app. 50..200 Ohms.
However, due to negative feedback this resistance will be drastically reduced (divided by the loop gain) to values which mostly are below 1 Ohm.
For this reason and taking other uncertainties into account (tolerances) it is common practice to assume Rout=0.

Recommendation: Read some papers/contribution about feedback theory. Negative feedback is the most important technique for amplification.

 

[AMSA84]

I want to thank you all the answers.

I forgot to say that this was to derive the output resistance.
If the input voltage is zero, why the Vx would be 0?

 

[FvM]

Set up an equation for OP input and output voltage, containing R1 and R2, OP open loop gain and DC output impedance as well as offset voltage and get Vx as function of Ix or in other words Rx.

 

[AMSA84]

Sorry but I didn't understood what you said.

 

[D.A.(Tony)Stewart]

DO you know any equations for Op Amp?

Frank was suggesting you prove it with simple Kirchoff loop equations..

I know that in general , open loop gain, G = 1e6 and open loop output impedance, Ro ~ 300 Ohms, and Av=R2/R1

The Zout is, Ro reduced by the ratio of open/closed loop gain.

Thus Vx= Ix* Zout ( as long Ix*Ro <Vsupply (saturation))

and of course since Vin(+)=0 if Vin(-)=0 the Vx=0