Inverting amplifier realized with op-amp is given in figure bellow.

Simulate op-amp inverting amplifier.

Input impedance is not very high, comparing to non-inverting amplifier. Actually, input impedance is equal to **R _{2}**, since input voltage source must provide current that is reverse proportional to

**R**.

_{2}Output voltage is in opposite phase with input voltage (phase shift is 180 degrees). Since voltage amplification of operational amplifier is very high, and negative feedback is applied, inputs in operational amplifier can be treated as **V _{+}**=

**V**, since V

_{–}_{+}is on the ground and V

_{–}is on the virtual ground.

Voltage gain can be calculated in two ways.

- By combining superposition theorem and node potential of input and output terminal.

Potential of inverting input can be calculated as voltage divider from output voltage:

added to potential of voltage divider from input voltage

Due to virtual ground:

Voltage gain is

- By equaling currents.

Since currents that flow from/to operational amplifier input can be neglected, current through **R _{2}** is equal to current through

**R**. Then, again

_{1}**V**=

_{+}**V**

_{–}

**=**0V, so

Final result for voltage gain is the same:

Go to op-amp inverting amplifier simulation.

**External links:**

Inverting Op-amp Amplifier on All about circuits

Inverting Op-amp Amplifier on electronics-tutorials

Inverting Op-amp Amplifier on Hyperphysics

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