Op-Amp Non-Inverting Amplifier Calculator
Op-Amp Non-Inverting Amplifier Calculator
Gain 1 + Rf/R1, gain in decibels, output voltage and rail clipping for a non-inverting op-amp stage — plus the two speed limits that catch beginners out: closed-loop bandwidth and full-power bandwidth.
Non-inverting amplifier
R1 = 1 kΩ, Rf = 10 kΩ, Vin = 100 mV, 5 V single supply, an LM358B (GBW 1.2 MHz, SR 0.5 V/µs), 1.5 V peak out
Non-inverting amplifier and its speed limits
- R1
- from the inverting input to ground
- Rf
- from the inverting input to the output; 0 gives a follower
- GBW
- the op-amp’s gain–bandwidth product: gain × bandwidth is a constant, so gain is bought with speed
- SR
- slew rate, the fastest the output can change, in volts per microsecond
- V̂
- the amplitude (not peak-to-peak) of the output sine you need
Worked example
R1 = 1 kΩ, Rf = 10 kΩ, Vin = 100 mV, 5 V single supply, an LM358B (GBW 1.2 MHz, SR 0.5 V/µs), 1.5 V peak out
Gain = 1 + Rf ÷ R1 = 1 + 10 kΩ ÷ 1 kΩ = 11
In decibels: 20 × log10(11) = 20.83 dB
Vout = 11 × 100 mV = 1.1 V, inside the 0.10 V to 3.60 V an LM358B can reach on a 5 V rail
Closed-loop bandwidth = 1.2 MHz ÷ 11 = 109.1 kHz
Full-power bandwidth = 0.5 V/µs ÷ (2π × 1.5 V) = 500,000 ÷ 9.4248 = 53.05 kHz — the lower of the two, so that is the real ceiling
What gain costs you in bandwidth
| Closed-loop gain | In decibels | LM358B (GBW 1.2 MHz) | TLV9062 (GBW 10 MHz) |
|---|---|---|---|
| 1 | 0.00 dB | 1.2 MHz | 10 MHz |
| 2 | 6.02 dB | 600 kHz | 5 MHz |
| 10 | 20.00 dB | 120 kHz | 1 MHz |
| 100 | 40.00 dB | 12 kHz | 100 kHz |
| 1,000 | 60.00 dB | 1.2 kHz | 10 kHz |
How the non-inverting amplifier works
The signal goes straight to the + input and the feedback network — Rf from the output to the − input, R1 from the − input to ground — is a voltage divider calculator working in reverse. The op-amp drives its output to whatever voltage makes the divider’s tap equal the input, and that voltage is Vin × (1 + Rf ÷ R1). Because the source only has to drive the op-amp’s + input, which draws almost nothing, the stage does not load it: input impedance is hundreds of megohms for a CMOS part, against a bare Rin for the inverting amplifier calculator. The trade is that the gain can never go below 1 — with Rf = 0 you get a voltage follower, and a follower is still useful, because turning a high-impedance signal into a low-impedance one is half of analogue design.
The two speed limits. This is where beginners get bitten, and neither limit appears in the gain equation. The first is gain–bandwidth product: an op-amp’s open-loop gain falls at 20 dB per decade, so the product of closed-loop gain and closed-loop bandwidth is roughly constant. An LM358B’s 1.2 MHz GBW at a gain of 11 leaves 109.1 kHz of bandwidth; ask for a gain of 101 and you are down to 11.88 kHz, which will not pass audio. The second is slew rate, and it depends on amplitude rather than gain: the fastest a sine of amplitude V̂ changes is 2πfV̂, so the largest undistorted frequency is SR ÷ (2πV̂). At 0.5 V/µs and 1.5 V peak that is 53.05 kHz. Whichever is lower is your real ceiling — here the slew rate, which is the usual case for large outputs. Exceed the first and the gain quietly falls; exceed the second and a sine comes out as a triangle.
Choosing resistors. The ratio sets the gain, the absolute values set the noise, the loading on the output and the effect of bias current. A few kilohms is the usual compromise: low enough that the op-amp’s input bias current and stray capacitance do not matter, high enough that the output is not wasting current driving its own feedback network. Design mode picks the nearest E24 or E96 value to (gain − 1) × R1 and tells you the gain you actually get. As on the inverting page, a bipolar op-amp is happiest when both inputs see the same resistance — put R1 ∥ Rf (909.1 Ω here) in series with the + input if the source resistance is low.
Single supply. Unlike the inverting stage, a non-inverting amplifier works directly from one rail for signals that are already positive, provided the op-amp’s input range includes ground and the output can get close enough to the rails. That is exactly what the LM358 family was designed for. For an AC signal you still need to bias the + input to mid-rail and couple the input through a capacitor, and then R1 needs a capacitor in series with it so the stage has unity gain at DC. The corner of that high-pass is set by R1 and its capacitor — the RC filter calculator does that arithmetic.
Frequently asked questions
What is the gain of a non-inverting amplifier?
1 + Rf ÷ R1. With Rf = 10 kΩ and R1 = 1 kΩ the gain is 11, not 10 — the extra 1 is the signal arriving at the + input, which is passed straight through. In decibels that is 20.83 dB.
Can a non-inverting amplifier have a gain below 1?
No. 1 + Rf ÷ R1 is at least 1 for any positive resistors, and Rf = 0 gives exactly 1 — a voltage follower. To attenuate, put a divider in front of it, or use an inverting stage with Rf smaller than Rin.
How do I calculate the bandwidth of an op-amp circuit?
Divide the op-amp’s gain–bandwidth product by your closed-loop gain. An LM358B at 1.2 MHz and a gain of 11 gives 109.1 kHz. Then check the slew rate separately: the biggest undistorted sine is SR ÷ (2π × amplitude). The lower of the two figures wins.
What is the difference between inverting and non-inverting amplifiers?
The inverting stage gives −Rf/Rin, can attenuate, and has an input impedance of just Rin. The non-inverting stage gives 1 + Rf/R1, cannot go below 1, and presents the op-amp’s own enormous input impedance, so it does not load the source.
Why does my amplifier output look like a triangle instead of a sine?
Slew-rate limiting. The output is being asked to change faster than the op-amp can drive it, so each half-cycle becomes a straight ramp. Work out SR ÷ (2π × amplitude): if your frequency is above that, reduce the amplitude or use a faster part.
Related calculators
References
- Horowitz P, Hill W. The Art of Electronics, 3rd ed. Cambridge University Press, 2015. §4.2.1 the inverting amplifier, §4.2.2 the noninverting amplifier, §4.4 a detailed look at op-amp behaviour — gain–bandwidth product, slew rate and the departures from the ideal op-amp.
- Texas Instruments. LM358B, LM2904B industry-standard dual operational amplifiers, datasheet SLOS068AB. Gain–bandwidth product 1.2 MHz typical, slew rate 0.5 V/µs typical, supply 3–36 V; the output reaches to within about 100–150 mV of V− but stops 1.35–1.42 V short of V+ at 50 µA.
- Texas Instruments. TLV906xS 10-MHz, RRIO, CMOS operational amplifiers for cost-sensitive systems, datasheet SBOS839N. Gain–bandwidth product 10 MHz typical, slew rate 6.5 V/µs typical, supply 1.8–5.5 V, output within 20 mV of either rail into 10 kΩ.
- IEC 60063:2015. Preferred number series for resistors and capacitors (E6, E12, E24, E48, E96 and E192). International Electrotechnical Commission.