Operational Amplifiers: Ideal Characteristics Simple Notes

An operational amplifier, or op-amp, is a high-gain differential amplifier in a small chip with two inputs and one output. It amplifies only the difference between its inverting (−) and non-inverting (+) inputs. The classic 741, introduced in 1968, remains the standard teaching example.

The raw open-loop gain is enormous, around one hundred thousand. Engineers wrap feedback components around the chip, and the feedback network, not the chip itself, sets the precise behaviour. That is why one cheap component can become an amplifier, filter, oscillator, or comparator just by changing a few resistors.

Key Concepts

• Differential input: the op-amp responds to (V+ − V−) and ignores voltages common to both inputs.
• Open-loop gain (AOL): raw gain with no feedback, typically 105 (100 dB) at DC, falling with frequency.
• Input impedance: how much the inputs load the source; about 2 MΩ for bipolar op-amps, 1012 Ω or more for FET-input types.
• Output impedance: ideally zero, so the output voltage does not sag under load.
• CMRR: ability to reject signals common to both inputs, such as mains hum; typically 70–120 dB.
• Slew rate: maximum rate of output change, in V/µs; the 741 manages only 0.5 V/µs, limiting high-frequency performance.
• Input offset voltage: the small input difference needed to force zero output; ideally zero, a few millivolts in practice.
• Virtual short: with negative feedback the huge gain forces both inputs to nearly equal voltage, as if shorted, though no current flows between them.

Formulas

• Basic equation: Vout = AOL × (V+ − V−). Feedback shrinks the difference to microvolts.
• CMRR: CMRR(dB) = 20 × log10(Ad / Acm).
• Gain-bandwidth product: gain × bandwidth is roughly constant; a 1 MHz GBW op-amp gives gain 10 only up to 100 kHz.

Worked Example

A non-inverting amplifier uses R1 = 10 kΩ, Rf = 90 kΩ, input 0.5 V DC. Find the output.

1. Gain: Av = 1 + Rf/R1 = 1 + 9 = 10. Vout = 10 × 0.5 = 5 V.
2. Virtual-short check: feedback returns 5 × 10/100 = 0.5 V to the inverting input, matching the non-inverting input.
3. The 5 V output sits comfortably inside ±12 V supplies, so no saturation.

Common Misconceptions

• The output can reach any voltage the gain demands. It saturates about 1–2 V inside the supply rails; asking for more just clips.
• Inputs draw no current. Ideally yes, but real bias currents (nanoamps bipolar, femtoamps FET) cause errors with megohm sources.
• Infinite gain means infinite output. Negative feedback tames the gain in every linear circuit; open-loop the op-amp is just a comparator slamming rail to rail.

Real-World Applications

• Audio mixers and preamplifiers use op-amps for clean, predictable gain.
• Instrumentation amplifiers measure tiny sensor signals in ECG monitors and weigh scales.
• Active filters for crossovers and anti-aliasing are built with op-amps, resistors, and capacitors.
• Comparators detect thresholds in battery chargers, thermostats, and over-voltage protection.

To recap: an ideal op-amp has infinite gain, infinite input impedance, zero output impedance, infinite CMRR, and zero offset. Real chips fall short in measurable ways, but negative feedback hides most flaws, which is why this humble chip appears in almost every analog circuit.