“`html Inverting Amplifier – Interactive Explanation

Inverting Amplifier

An inverting amplifier is an operational-amplifier circuit in which the input signal is applied to the inverting (−) input through a resistor. The output voltage is inverted relative to the input voltage.

1. Basic Circuit

Rf ┌──/\/\/\/───┐ │ │ │ │ Vin ───── Rin ─────●───────┐ │ │ │ │ │ (−) │ │ │\ │ │ │ \ ├──── Vout │ │ \ │ │ / │ (+) / │ │ / └───────┴ │ GND

2. The Main Idea

The non-inverting input is connected to ground:

V₊ = 0 V

Because negative feedback is used, the op-amp tries to make the two input voltages approximately equal:

V₋ ≈ V₊ ≈ 0 V

Virtual Ground: The inverting input is approximately 0 V even though it is not physically connected to ground.

3. Why Does the Output Become Negative?

Suppose the input voltage is positive:

V_in = +1 V

Since the inverting input is approximately 0 V, the input resistor has approximately 1 V across it. This produces a current:

I = V_in / R_in

The op-amp input draws almost no current. Therefore, essentially the same current must flow through the feedback resistor R_f.

The op-amp changes its output voltage so that the required feedback current can flow. The output therefore moves in the negative direction.

4. Voltage Gain

A_v = − R_f / R_in

Therefore:

V_out = − (R_f / R_in) × V_in

5. Worked Example

Given:

V_in = 1 V
R_in = 10 kΩ
R_f = 100 kΩ

Step 1: Calculate gain

A_v = −100 / 10 = −10

Step 2: Calculate output

V_out = −10 × 1 = −10 V

Therefore:

V_out = −10 V

6. Interactive Calculator

Change the values below to see how the inverting amplifier responds.

Input Voltage Vin (V)

Rin (kΩ)

Rf (kΩ)

Voltage Gain −10.00

Output Voltage −10.00 V

Calculation

1 Gain = −100 / 10 = −10

2 Output = −10 × 1 = −10 V

7. What Happens When the Input Changes?

For R_in = 10 kΩ and R_f = 100 kΩ:

If V_in = +1 V: V_out = −10 V

If V_in = +2 V: V_out = −20 V

If V_in = −1 V: V_out = +10 V

This is why it is called an inverting amplifier: the output has the opposite polarity to the input.

8. Three Rules to Remember

Rule 1: With negative feedback: V₊ ≈ V₋

Rule 2: Ideal op-amp input currents are approximately zero: I₊ ≈ I₋ ≈ 0

Rule 3: For an inverting amplifier:

V_out = −(R_f/R_in)V_in

Practical limitation: The calculated output cannot exceed the op-amp’s actual output voltage range. For example, an op-amp powered from ±12 V cannot normally produce an ideal calculated output of −20 V.

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