Deriving Equation Vin = Vout * R2/(R1+R2)

[Fys]

I have a bit difficulties deriving the equation V in =Vout * R2/(R1+R2)
Because I can't see a closed loop here
Can someone help with this

Thx

 

[stewartcs]

Read this page, it explains it in detail (near the middle of the page)...

http://en.wikipedia.org/wiki/Operational_amplifier

 

[berkeman]

I have a bit difficulties deriving the equation V in =Vout * R2/(R1+R2)
Because I can't see a closed loop here
Can someone help with this

Thx

It's more traditional to write it as Vout = Vin * (whatever)

The opamp has very high gain, so that if there is any difference in voltage between the + and - inputs, the output swings hard in that direction (if + > -, the output swings positive hard). So bringing the midpoint of R1 and R2 back to the - feedback input will cause the opamp to do whatever it can (sorry for the anthropomorphising) to make the voltage on its - input equal Vin. The output Vout will stabilize to whatever it takes across R1 + R2 to get Vin at the midpoint. Makes sense?

 

[ferncpi]

I have derived this in the attached file.

This is the negative feedback (feedback from output of the opamp to the inverting input of the opamp).
With negative feedback, voltage at inverting input (V-) = voltage at non-inverting input (V+). And the output voltage will be controlled by the V-.
Without the negative feedback, the amplifier is called "open loop" where the output voltage is Gain*different voltage between V+ and V-.