Inverting and Non-Inverting Op-Amp Circuits
The Operational Amplifier
An operational amplifier (op-amp) is an integrated circuit designed to amplify the difference between its two input voltages. It has an inverting input (marked “−”), a non-inverting input (marked “+”), and a single output. Without external components, its open-loop gain is enormous — typically hundreds of thousands — which makes it unstable for most applications. In practice, resistors are connected around the op-amp to form a negative feedback loop that sets a stable, predictable gain.
Two resistors define the gain in both configurations covered here: \(R_1\) (the input resistor, connected between the signal source and the op-amp input) and \(R_f\) (the feedback resistor, connected between the output and the inverting input). In practice designers usually keep both resistors in the kilohm range, so that the op-amp output and the signal source are not overloaded.
The Inverting Amplifier
In an inverting amplifier, the input signal is applied through \(R_1\) to the “−” input. The feedback resistor \(R_f\) connects from the output back to the same “−” input. The “+” input is connected to 0 V (ground).
Because the signal enters the inverting input, the output is 180° out of phase with the input — if the input goes positive, the output goes negative. The voltage gain is:
Inverting amplifier voltage gain:
$$G = -\frac{R_f}{R_1}$$
The negative sign indicates phase inversion. Only the magnitude \(|G| = R_f / R_1\) determines how much the voltage is multiplied.
The concept of a virtual earth helps explain why the formula works. Negative feedback forces the voltage at the inverting input to be essentially 0 V, even though that point is not connected directly to ground. This means that \(R_1\) and \(R_f\) share the same voltage reference at the inverting pin, and Kirchhoff’s current law gives the gain ratio.
An inverting amplifier uses \(R_1 = 10\) kΩ and \(R_f = 100\) kΩ. The input signal is a sine wave with a peak of 50 mV.
Step 1 — Calculate gain: \(G = -R_f / R_1 = -100 / 10 = -10\).
Step 2 — Calculate output peak: \(V_{OUT} = G \times V_{IN} = -10 \times 50\text{ mV} = -500\text{ mV}\).
The magnitude is 500 mV (0.5 V peak) and the output is inverted relative to the input. On a voltage–time graph, when the input sine wave is at its positive peak, the output is at its negative peak.
If you need to find \(R_f\) for a target gain: \(R_f = |G| \times R_1 = 10 \times 10 = 100\) kΩ. Always check that both resistors are ≥ 1 kΩ.
The Non-Inverting Amplifier
In a non-inverting amplifier, the input signal connects to the “+” input. The feedback network (\(R_f\) and \(R_1\)) connects from the output back to the “−” input, with \(R_1\) going from the inverting input to ground. The output is in phase with the input — positive input gives positive output.
Non-inverting amplifier voltage gain:
$$G = 1 + \frac{R_f}{R_1}$$
The “1 +” means the minimum gain is always greater than 1 (since \(R_f / R_1\) is positive). There is no phase inversion.
The non-inverting configuration is one of the least well answered topics in recent exams. The key distinction from the inverting case is: the input goes to the “+” pin and the feedback still goes to the “−” pin via \(R_f\). If you draw the circuit, \(R_1\) sits between the “−” pin and ground, and \(R_f\) connects the output back to that same “−” pin.
Design a non-inverting amplifier with a gain of 11. Choose \(R_1 = 10\) kΩ.
Rearrange: \(R_f = (G - 1) \times R_1 = (11 - 1) \times 10 = 100\) kΩ.
Check: \(G = 1 + R_f / R_1 = 1 + 100/10 = 1 + 10 = 11\). Correct. Both resistors are above 1 kΩ.
With \(V_{IN} = 100\) mV: \(V_{OUT} = 11 \times 0.1 = 1.1\) V. The output is in phase with the input (positive input gives positive output).
Comparing the Two Configurations
The table below summarises the key differences between the two op-amp circuits:
| Feature | Inverting | Non-inverting |
|---|---|---|
| Input connects to | − pin (via R1) | + pin |
| Gain formula | \(-R_f / R_1\) | \(1 + R_f / R_1\) |
| Phase shift | 180° inversion | No inversion |
| Minimum gain | Can be <1 | Always ≥1 |
In both circuits, the output cannot exceed the supply rail voltage. Always check for clipping when the calculated output is close to the supply voltage.