Why an op-amp's gain and bandwidth are locked in an inverse tradeoff — and can't be maximized at the same time from a single stage.
A standard, uncompensated single-pole-dominant op-amp has a fixed specification called the gain-bandwidth product (GBW, or GBWP) — the frequency at which its open-loop gain rolls off to unity (1, or 0 dB). This single number is a genuine constant for a given op-amp model. For that specific part, the product of whatever closed-loopgain you configure it for — set entirely by external feedback resistors — and the resulting closed-loop bandwidth over which that gain stays flat, is approximately equal to that fixed GBW. Configure the circuit for more gain, and the usable bandwidth shrinks to match. Configure it for less gain, and the bandwidth opens back up. It isn't a coincidence and it isn't adjustable independently — it's a direct consequence of how the op-amp's internal compensation shapes its open-loop response.
A dominant-pole-compensated op-amp's open-loop gain falls at a fixed −20 dB/decade slope, from a very high DC gain down to unity gain at the GBW frequency. Because that slope is fixed, gain and frequency trade off along it at a constant rate — which is exactly what makes the open-loop curve's magnitude times its frequency, at any point along that −20 dB/decade line, equal to the same constant: the GBW. Draw a horizontal line at whatever closed-loop gain your feedback network sets, and the point where it crosses the open-loop curve is your closed-loop −3 dB bandwidth — automatically, with no extra calculation needed beyond gain × bandwidth ≈ GBW.
Because GBW is fixed for a given op-amp, an engineer wanting both high gain and wide bandwidth from a single stage of that part is asking for something its GBW spec simply can't deliver. There are exactly two real ways out: pick a fundamentally different, higher-GBW op-amp, or split the total required gain across multiple cascaded stages. Each stage individually carries less gain, so each stage's own gain line crosses the open-loop curve much further to the right — retaining far more bandwidth per stage — while the total gain across the stages still multiplies to reach the original target. This is also exactly why a design that specifies a required gain withoutchecking whether the resulting GBW-limited bandwidth is adequate for the actual signal frequencies involved is a common, real mistake: an op-amp chosen purely on its DC gain spec can have "enough gain" on paper and still roll off well before the frequencies the circuit actually needs to amplify.
A dominant-pole-compensated op-amp is deliberately designed so its open-loop gain falls at exactly one pole's worth of rolloff — a steady −20 dB/decade — all the way out to unity gain. Along a −20 dB/decade line, halving the frequency doubles the gain and doubling the frequency halves it, which means gain times frequency stays constant at every point on that line — and that constant is, by definition, the frequency where the line reaches unity gain: the GBW. A closed-loop gain configuration is just a horizontal line drawn at whatever gain your feedback resistors set; wherever it crosses the open-loop curve is where the loop gain runs out and the closed-loop response starts to roll off, which is exactly the closed-loop bandwidth. Since that crossing always lands somewhere on the same fixed −20 dB/decade line, gain × bandwidth is pinned to the GBW no matter which gain you choose.
False, for a standard, dominant-pole-compensated op-amp. Gain and bandwidth aren't separately adjustable knobs on the same part — they're locked together by a genuinely fixed gain-bandwidth product constant. Configure a higherclosed-loop gain, and the usable bandwidth necessarily drops in proportion, for that same op-amp. This isn't a flaw in a specific bad design — it's how a single-pole-dominant amplifier fundamentally behaves. Getting both high gain and wide bandwidth at once takes one of exactly two moves: selecting a different, higher-GBW op-amp, or splitting the required gain across multiple cascaded stages — not simply dialing a single stage up to a higher gain and expecting the bandwidth to hold steady.
Explains why a standard, single-pole-dominant op-amp's closed-loop gain and closed-loop bandwidth trade off against each other in an inverse, locked relationship — because their product is approximately fixed at the op-amp's gain-bandwidth product (GBW) — and why getting both high gain and wide bandwidth from the same amplifying task requires either a higher-GBW part or splitting the gain across multiple cascaded stages.
Datasheets list gain and bandwidth as separate rows, which makes them look like independently tunable parameters — pick whatever gain you need, then separately check whatever bandwidth you need, as if the two don't interact. For a standard dominant-pole-compensated op-amp they aren't independent at all: they're two readings taken from the same fixed open-loop rolloff curve. Once you fix where on that curve your closed-loop gain sits, the corresponding bandwidth is already determined — it's the frequency where that gain line crosses the open-loop response, not a separately adjustable spec.
A dominant-pole op-amp's open-loop gain falls at a fixed −20 dB/decade slope from a high DC gain down to unity gain at the GBW frequency. Because gain in linear terms is inversely proportional to frequency along a −20 dB/decade line, the product of gain and frequency is constant everywhere on that line, equal to the frequency-axis (unity-gain) intercept — the GBW. Closing the loop with resistive feedback sets a flat closed-loop gain equal to whatever the feedback ratio dictates; that closed-loop response tracks the flat gain line until it reaches the open-loop curve, at which point loop gain runs out and the response rolls off. That crossing point is the closed-loop −3 dB bandwidth, so for any closed-loop gain A configured on that op-amp, A × BW ≈ GBW.
This tradeoff is why a design that only checks whether an op-amp has 'enough gain' at DC, without checking GBW against the actual gain-times-frequency the application needs, is a common real-world mistake — the circuit can look correct on paper and still roll off well below the signal frequencies it's meant to amplify. The two real fixes are choosing a fundamentally higher-GBW op-amp, or distributing the required total gain across multiple cascaded stages, each carrying less gain individually and therefore retaining more bandwidth, with the stage gains multiplying to reach the same overall target.
For a standard single-pole-dominant op-amp, closed-loop gain × closed-loop bandwidth ≈ GBW, the op-amp's fixed gain-bandwidth product. This approximation holds well when the closed-loop gain is set by resistive feedback and the response is dominated by the op-amp's own single pole — it's the basis for quickly estimating usable bandwidth at any configured gain without a full loop-gain analysis.
No. GBW is an intrinsic property of the op-amp itself, set by its internal compensation capacitance and transconductance — it doesn't depend on the external feedback network at all. Changing feedback resistors changes the closed-loop gain, which in turn changes the resulting bandwidth, but the GBW constant those two multiply to stays the same.
Two: select a different op-amp with a fundamentally higher GBW spec, or split the total required gain across multiple cascaded amplifier stages using the same op-amp. Each stage in a cascade carries only part of the total gain, so each stage's own closed-loop bandwidth stays much higher, while the individual stage gains multiply together to reach the full required total gain.
Because bandwidth is set by where a stage's own gain line crosses that stage's own open-loop curve — a lower per-stage gain crosses much further out along the curve, at a much higher frequency. Cascading two such stages does narrow the overall bandwidth somewhat versus either stage alone (each stage's rolloff stacks with the other's), but the combined bandwidth of two lower-gain stages is still dramatically higher than a single stage carrying the full gain by itself.
For a simple single-pole-dominant op-amp, yes — GBW is numerically the same as the frequency at which the open-loop gain crosses 0 dB (unity), and datasheets often list it under either name, or as ft. The two labels describe the identical point on the open-loop Bode plot.
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