inverting op amp

Many sites have explanation about op-amps, most of them gives you ready equations that fit only for a specific case.

I will explain you where these equations come from and how you can solve other circuits even if any resistor changed to a capacitor or diode or anything else.

Symbol:

V_CC – positive rail of power supply (usually >0V)
V_EE – Negative rail of power supply (usually <=0)
note: – sometimes V_CC and V_EE don’t appear on circuits, just noticed that op-amp connected to +/- 12V (for example)
V_out – out put voltage of op-amp (output voltage can be in range of V_CC<V_out<V_EE)
V_- - negative input of op-amp
V₊ - positive input of op-amp

Property of op-amp

1. Input impedance, of positive input (V+) and negative input (V-), are very big. We can assume that it is infinite.
2. Output impedance of op-amp is very low, we can assume it as 0Ohm.

Negative op-amp feedback (Inverting Amplifier)

At negative op-amp feedback, op-amp will do anything to make V₊=V_-  - this sentence will solve you all problems.

Let assume that current flow according to red arrow.

According to property 1 that I mentioned above, I1 must be equal to I2 – no current is flow into op-amp inputs.

As I told before, op-amp will do everything it can to make V₊=V_- (when I say " will do everything it can" I mean that V_out will be changed this way to make V₊=V_-)

Now I guess you are asking yourself "How is it helping me to solve a circuit with a capacitor or a diode?", am I right?

It is the exactly the same solution way, all what is changeing is the connection between current and voltage. For example, let take a capacitor.

Now, for an example, I will assume that the current flow to an opposite direction.

As I mentioned above V₊=V_- on negative feedbacks, in this case V₊=V_-=0V

 

For constant V_in voltage wel will get the following equation:

The output voltage will look like this:

The slope of the graph is

If V_in is an alternative voltage then the output voltage can be calculated this way:

 

Now if you want to put a diode somewhere, all you need to do is to use diode current voltage equation that is:

non-inverting op-amp

The different between inverting amplifier and non-inverting amplifier is where you supply the input signal.

If you supply the signal to negative input (V-), like we did before it will be inverting amplifier and the output will be inverted to the input.

The graph below shows input voltage ( Vin - the bule line) and output voltage (Vout - the red line)

Do you remember that Vout= -Vin * R1/R2 for inverting op-amp?

So in this case Vin=2Vptp and Vout=-20Vptp so A=R1/R2=10.

A=Vout/Vin=-20/2=-10

Now let see how we create an eqution for non inverting amplifier.

noninverting opamp looks this way:

As I already mentioned before, I1=I2 in vegative feedback:

Also V+=V- in this case V+=V-=Vin so

Now let figure Vout:

The graph below shows input voltage ( Vin - the bule line) and output voltage (Vout - the red line)

In this case R1/R2=9