Op-Amp Gain Calculator
Closed-loop gain for every standard topology, plus the two ceilings that actually stop you: gain-bandwidth product and slew rate.
Gain is the easy part. Two other things stop you.
Gain-bandwidth product caps small signals. A 1 MHz op-amp set to a gain of 100 gives you 10 kHz, not 1 MHz. Gain and bandwidth trade one for one and you do not get to choose both — wanting more of each means a faster part, or splitting the gain across two stages.
Slew rate caps large ones, separately. A part can have ample bandwidth for a 20 kHz signal and still be unable to produce it at 10 V peak, because the output cannot physically move that fast. A µA741 at 0.5 V/µs runs out at about 8 kHz for a 10 V swing. That is why a 741 audio stage sounds fine quiet and turns into triangle waves loud, and why no amount of checking the bandwidth figure would have warned you.
- Bandwidth follows noise gain, not signal gain. An inverting stage at −1 has a noise gain of 2, so it has the bandwidth of a gain-of-2 non-inverting stage. The feedback network cannot tell which input the signal arrived at.
- A non-inverting stage cannot attenuate. Gain is 1 + Rf/Rg, which is above 1 for every possible pair of resistors. To go below unity you need a divider first, or the inverting topology.
- The inverting input is a virtual earth. That makes the input resistor the entire load your source sees — so lowering it for more gain also loads the source harder. The non-inverting topology has no such tension, which is usually why you pick it.
- Differential rejection is set by resistor matching. With 1% resistors you get about 46 dB of common-mode rejection however good the op-amp is. That limit is exactly why instrumentation amplifiers are sold as single parts with laser-trimmed networks.
How to use
- Pick the topology — inverting, non-inverting, buffer or differential.
- Enter the two resistors in any notation: 10k, 4k7, 100k.
- Choose a real op-amp and set the output swing and signal frequency.
- Read the gain, and then check which of the two ceilings binds first.
Frequently asked questions
Why does my amplifier lose gain at high frequency?
Because gain and bandwidth trade one for one. An op-amp is specified by a gain-bandwidth product, so a part with 1 MHz set to a gain of 100 gives you 10 kHz and nothing you do to the resistors changes that. Wanting more of both means a faster part, or splitting the gain across two stages — two stages of 10 from a 1 MHz part gives 100 kHz overall instead of 10.
What is slew rate and how is it different?
Slew rate is how fast the output voltage can physically move, in volts per microsecond, and it limits large signals independently of bandwidth. A circuit can have ample bandwidth for a 20 kHz signal and still fail to produce it at 10 V peak. The frequency where that starts is called full-power bandwidth, and for a 741 at 0.5 V per microsecond it is about 8 kHz — which is why a 741 audio stage sounds fine quiet and turns into triangle waves loud.
What is noise gain and why does it set the bandwidth?
Noise gain is the gain the feedback network applies to anything at the non-inverting input, and it is 1 + Rf/Rin regardless of which input your signal went into. So an inverting stage at a signal gain of minus one has a noise gain of two, and therefore the bandwidth of a gain-of-two stage. The feedback loop simply cannot tell where the signal arrived.
Can a non-inverting amplifier have a gain below 1?
No. The gain is 1 + Rf/Rg, and since both resistors are positive that expression is above one for every possible pair. Setting Rf to zero gives exactly one, which is a buffer. If you need attenuation, put a divider in front of the stage or use the inverting topology, which can take any gain you like above zero.
Which topology should I choose?
The non-inverting one when the source is weak or high impedance, because the signal goes straight to an op-amp pin and sees essentially infinite impedance. The inverting one when you need attenuation, a summing junction, or a phase flip, accepting that the input resistor becomes the whole load your source sees. The buffer when you want no gain at all, just an impedance change.
Why is my differential amplifier rejecting common mode so badly?
Almost certainly resistor matching rather than the op-amp. Common-mode rejection in a discrete difference amplifier is set by how well the two resistor pairs track each other, and with 1 percent parts the ceiling is about 46 decibels however good the amplifier is. That single limit is why instrumentation amplifiers are sold as monolithic parts with laser-trimmed networks inside.
Does a bigger feedback resistor cause problems?
Above about a megohm, yes. It generates real thermal noise, it works against the op-amp input bias current to produce a DC offset, and the few picofarads of stray capacitance across it start rolling off the high end on their own. If you need very high gain, two moderate stages beat one stage with an enormous feedback resistor.
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