Real Operational Amplifiers

Every circuit in this topic so far has leaned on the idealised op-amp: infinite open-loop gain, infinite input resistance, zero output resistance. Real devices only ever approximate this ideal, and one particular shortfall — a gain that fades away as frequency rises — turns out to place a hard, unavoidable limit on what any single real op-amp circuit can do.

How real op-amps fall short of the ideal

The ideal operational amplifier model — introduced earlier in this topic and used throughout the virtual-earth analysis of the inverting, non-inverting, summing, and difference amplifiers — assumes infinite open-loop gain, infinite input resistance, and zero output resistance. A real, physical op-amp only ever approximates each of these:

• Finite open-loop gain. Real open-loop gain is very large (often $10^5$ or more) but not truly infinite, so the virtual-earth assumption ($V_+ \approx V_-$) is an excellent approximation rather than an exact one.
• Finite input resistance. Real input resistance is very high — commonly quoted in megaohms — but not infinite, so a very small current does actually flow into the input terminals, unlike the zero-current assumption used throughout virtual-earth analysis.
• Non-zero output resistance. A real op-amp's output behaves like a source with some small internal resistance, so under load (when supplying current to whatever the output is connected to) the output voltage sags slightly below the ideal predicted value, rather than holding perfectly steady.
• Limited, frequency-dependent gain. The open-loop gain itself is not constant with frequency — it falls away as the signal frequency rises. This limitation matters enough, and is examined closely enough, to deserve its own detailed treatment below.

The frequency response curve

If a real op-amp's open-loop gain is measured and plotted against signal frequency (typically using a logarithmic frequency axis, since the range of frequencies of interest spans several orders of magnitude), a characteristic curve emerges: the gain stays roughly constant, and very large, over a range of low frequencies, but beyond a certain frequency it begins to fall away steadily as frequency increases further. Push the frequency high enough, and the open-loop gain drops to a small fraction of its low-frequency value — the op-amp simply cannot sustain its full amplifying ability at high frequencies.

This falling-off matters directly for the amplifier circuits built in this topic, because their closed-loop gain (set by the feedback resistor ratio, such as $-R_f/R_{in}$ or $1+R_f/R_1$) can only be achieved in practice while the op-amp's own open-loop gain remains large enough to sustain it. Once the open-loop gain has fallen close to the intended closed-loop gain, the circuit can no longer maintain that gain, and the amplifier's actual performance falls away too.

Gain × bandwidth = constant

For a given real op-amp, the relationship between the gain a circuit is built to provide and the range of frequencies (the bandwidth) over which it can sustain that gain is captured by a single, fixed figure — the gain-bandwidth product:

This constant is a fixed property of a particular op-amp device, usually quoted as a single specification figure (in hertz) by the manufacturer. It means that as feedback is used to reduce the closed-loop gain of a circuit built from that op-amp — exactly what happens when a smaller ratio of $R_f$ to $R_{in}$ (or $R_1$) is chosen — the usable bandwidth over which that lower gain can be maintained increases proportionally. Equally, demanding a higher gain from the same op-amp can only be achieved over a correspondingly narrower range of frequencies.

Bringing the topic together

Across this topic, the ideal op-amp model and the virtual-earth technique introduced earlier provided the foundation for analysing two basic gain-setting circuits — the inverting and non-inverting amplifiers — each suited to different practical circumstances depending on whether inversion, attenuation, or high input resistance was needed. The same virtual-earth technique then extended naturally to circuits combining or comparing multiple signals: the summing amplifier, with its audio-mixing and digital-to-analogue conversion applications, and the difference amplifier. Finally, this lesson has returned to the assumptions behind the whole ideal model, showing where real devices fall short — most significantly through the gain-bandwidth trade-off — and why that trade-off is an unavoidable practical constraint on any real circuit design, however carefully the feedback resistors are chosen.