How Does a Non-Inverting Amplifier Work? Gain and Offset Example (30mV to 3.3V)

A non-inverting amplifier is one of the most common op-amp circuits used to boost a signal's voltage without flipping its polarity — meaning the output waveform stays perfectly in phase with the input. In this article, we'll break down how it works, derive the gain formula, and walk through a real simulation in LTspice where a 30mV signal is amplified to 3.3V with a 1.65V DC offset added on top.

What Is a Non-Inverting Amplifier?

In a non-inverting amplifier, the input signal is applied directly to the op-amp's non-inverting (+) terminal, while a voltage divider made of two resistors (R1 and R2) feeds a portion of the output back into the inverting (-) terminal. This creates negative feedback, which stabilizes the gain and keeps the output in phase with the input.

This circuit adds one more part. A second pair of resistors (R3 and R4) brings a fixed reference voltage into the same non-inverting terminal as the signal. That reference is what lets the output sit on a new DC center instead of staying at 0V.

The Gain Formula

The closed-loop gain of this non-inverting amplifier is given by:

Av = 1 + R1 / R2

Where:

• R1 is the feedback resistor (connected between the output and the inverting input)
• R2 is the resistor connected between the inverting input and ground

This formula only holds if R3/R4 is set to the same ratio as R1/R2.

Worked Example: 30mV In, 3.3V Out

Using the LTspice circuit above, R1 = 54kΩ and R2 = 1kΩ. Plugging these into the formula:

Av = 1 + 54k / 1k = 55

The input source is a 30mV peak sine wave at 50Hz with no DC offset — SINE(0 30m 50). Since the gain is 55, the output swing becomes:

Vout swing = Av × Vin = 55 × 30mV = 1.65V peak

The reference voltage V4 = 1.65V sets where that swing sits, giving the full equation:

Vout = 1.65V + 55 × Vin

The op-amp is powered from a ±10V dual supply (V1 = +10V, V2 = -10V), which gives enough headroom so the 3.3V peak output never clips against the rails.

Why There's a DC Offset This Time

In the plain non-inverting amplifier, R2 connects straight to ground and the output stays centered at 0V. Here, R4 connects to a 1.65V reference instead of ground, and R3 matches R1. That reference voltage passes through the same gain as the signal, so it appears at the output as a steady 1.65V center. Change V4 and the output's center moves with it, the gain stays at 55 the whole time.

Key Takeaways

• Non-inverting amplifiers keep the output in phase with the input.
• Gain here is R1/R2, with no plus one, because the non-inverting terminal carries a mix of Vin and Vref rather than Vin alone.
• R3 and R4 add a DC offset without changing the gain, as long as R3/R4 matches R1/R2.
• A dual supply (±10V here) gives the output room to swing between 0V and 3.3V without clipping.