An **inverting amplifier** is an operational amplifier circuit which produces amplified output that is 180° out of phase to the applied input. Inverting amplifier is also known as **inverting operational amplifier** or **inverting op-amp**.

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## Inverting operational amplifier

Figure 1 shows the basic inverting operational amplifier. The input signal V_{i} is applied to the inverting terminal through the R_{1} resistor. The non-inverting terminal of the op-amp is grounded.

### Analysis

**Case-1: When op-amp is ideal i.e. open-loop gain is infinite.**

The analysis of the inverting amplifier circuit is shown in figure 2. Since the op-amp is ideal and negative feedback is present, the voltage of the inverting terminal (V_{−}) is equal to the voltage of the non-inverting terminal (V_{+} = 0), according to the **virtual ground concept**.

V_{− }= V_{+} = 0 Volt

The currents entering both terminals of the op-amp are zero since the op-amp is ideal.

(1)

(2)

Apply KCL at node **P**

(3)

From equations (1), (2) and (3), we have

The closed-loop voltage gain A_{v} is given by

From voltage gain A_{v}, we can see that the output is 180° out of phase with the input.

**Case-2: When op-amp has a finite open-loop gain, A _{OL} (Practical case)**

The analysis of the inverting amplifier circuit is shown in figure 3. Since the op-amp has a finite open-loop gain, Hence the voltage of the inverting terminal (V_{−}) is not equal to the voltage of the non-inverting terminal (V_{+} = 0) i.e.

V_{− }≠ V_{+}

Assuming that the currents entering both terminals of the op-amp are zero.

(4)

(5)

Apply KCL at node **P**

(6)

From equations (4), (5) and (6), we have

(7)

As we know that,

(8)

From equations (7) and (8), we have

The closed-loop voltage gain A_{v} is given by

Therefore

From voltage gain A_{v}, we can see that the output is 180° out of phase with the input.