Non-Inverting Amplifier
The inverting amplifier isn't the only way to build a controllable, closed-loop op-amp circuit — and its one real drawback, feeding the input signal through a resistor into the inverting input, matters more than it might first appear. The non-inverting amplifier fixes exactly that, at the cost of always amplifying rather than ever attenuating.
The standard non-inverting amplifier circuit
The non-inverting amplifier rearranges the same basic ingredients as the inverting amplifier — an op-amp, two resistors, and negative feedback — into a different layout:
- The input signal, $V_{in}$, is applied directly to the non-inverting input ($V_+$) of the op-amp — not through a resistor.
- A resistor $R_1$ connects the inverting input ($V_-$) to ground.
- A feedback resistor $R_f$ connects the inverting input to the output.
- $R_1$ and $R_f$ together form a potential-divider feedback network, feeding a fraction of $V_{out}$ back to $V_-$.
Notice the key structural difference from the inverting amplifier straight away: here the input drives the non-inverting input directly, while the feedback network sets the voltage at the inverting input.
The gain formula
For this configuration, the voltage gain is:
The full derivation of this result is not required — you only need to be able to apply the formula correctly. That said, the qualitative reasoning behind it follows the same virtual-earth-style logic used for the inverting amplifier, and it's worth having some intuition for where it comes from:
- Since no current flows into the non-inverting input (infinite input resistance), there is no voltage drop before it — so $V_+ = V_{in}$ exactly.
- Because the op-amp forces $V_- \approx V_+$ (the same near-zero input-difference argument as before), the inverting input also sits at essentially $V_{in}$.
- $R_1$ and $R_f$ form a potential divider between $V_{out}$ and ground, with $V_-$ sitting at the tap point between them — so $V_-$ is a known fraction of $V_{out}$, namely $V_- = V_{out}\dfrac{R_1}{R_1+R_f}$.
- Setting this equal to $V_{in}$ and rearranging leads to the $1 + R_f/R_1$ result — but again, reproducing this derivation is not something you're required to do; applying the formula is what matters.
When to choose the non-inverting configuration
Given two working amplifier circuits, the choice between them comes down to two practical differences:
- Gain range. Since $R_f/R_1 \geq 0$ for any real resistor values, the non-inverting gain $1 + R_f/R_1$ is always at least 1 — this configuration can amplify but can never attenuate a signal. The inverting amplifier, by contrast, can easily be built with a gain magnitude less than 1 (simply by making $R_f$ smaller than $R_{in}$), so it's the natural choice whenever some deliberate attenuation, as well as amplification, is needed.
- Input resistance — usually the decisive factor. In the non-inverting configuration, the signal drives the op-amp's own non-inverting input directly, which has a very high (ideally infinite) input resistance. In the inverting configuration, the signal instead drives the circuit through the input resistor $R_{in}$, so the source "sees" an input resistance of only around $R_{in}$ itself — much lower. Whenever the signal source has a high output resistance of its own, or would be disturbed ("loaded down", drawing away significant current and dropping its own output voltage) by a low input resistance, the non-inverting amplifier is the better choice. This matters a great deal when amplifying the small output of a sensitive sensor, for example, where drawing much current from the sensor itself would corrupt the very signal being measured.
| Property | Inverting amplifier | Non-inverting amplifier |
|---|---|---|
| Gain formula | $-R_f/R_{in}$ | $1 + R_f/R_1$ |
| Phase / sign | Inverted (180° shift) | In phase (no inversion) |
| Gain range | Can attenuate or amplify | Always $\geq 1$; amplifies only |
| Input resistance seen by source | Roughly $R_{in}$ (moderate) | Very high (op-amp's own input resistance) |
| Best suited to | General gain-setting, inversion, or attenuation | High-resistance or easily-loaded sources |
Choose the non-inverting amplifier whenever preserving the source signal's own characteristics — not drawing significant current from it, not loading it down — matters more than needing phase inversion or the ability to attenuate. If the source can comfortably supply some current without its own voltage being disturbed, the inverting amplifier remains the simpler, equally valid default.
Key takeaways
- In the non-inverting amplifier, $V_{in}$ is applied directly to the non-inverting input, while $R_1$ (to ground) and $R_f$ (to output) form a potential-divider feedback network at the inverting input.
- The gain is $\dfrac{V_{out}}{V_{in}} = 1 + \dfrac{R_f}{R_1}$ — the derivation is not required, only correct application of the formula.
- Qualitatively, $V_+ = V_{in}$ (no input current), $V_- \approx V_+$ (op-amp feedback), and $V_-$ sits at the potential-divider tap point between $R_1$ and $R_f$.
- The output is in phase with the input — there is no 180° inversion, unlike the inverting amplifier.
- Gain is always $\geq 1$, so this configuration can amplify but never attenuate a signal.
- Input resistance seen by the source is very high, since the signal drives the op-amp's non-inverting input directly rather than through a resistor.
- Choose the non-inverting amplifier when the source has high output resistance or must not be loaded down, such as when amplifying a sensitive sensor's output.
- Choose the inverting amplifier when inversion or sub-unity gain (attenuation) is required, or when loading the source isn't a concern.