Electrical
Operational Amplifier
High-gain differential amplifier — universal analog building block
An operational amplifier (op-amp) is a high-gain differential voltage amplifier with two inputs (inverting and non-inverting) and one output. Ideal model: infinite gain, infinite input impedance, zero output impedance, infinite bandwidth. Real op-amps approximate this. With negative feedback, op-amps implement amplification, integration, differentiation, filtering, summing, comparators, and active filters. The 741 (1968) popularized the part. Modern op-amps reach gigahertz bandwidth and sub-microvolt offset.
- InputsInverting (-) and non-inverting (+)
- Open-loop gain100,000 to 1,000,000+ (110 to 120 dB)
- Input impedanceMegaohms (BJT) to teraohms (FET)
- Golden rulesV+ = V-, no input current (with feedback)
- Famous part741 (1968), TL081, OPA series
- ApplicationsAmplifiers, filters, integrators, comparators
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Why op-amps matter
- Signal conditioning. Amplify weak sensor outputs.
- Active filters. Low-pass, high-pass, band-pass with cutoff control.
- Integrators and differentiators. Analog computation building blocks.
- Buffers. Isolate stages without loading.
- Comparators. Threshold detection (with or without dedicated comparator parts).
- Audio. Preamps, mixers, equalizers.
- Instrumentation. Precision DAQ front-ends and bridges.
Common misconceptions
- Output range is rail-to-rail. Most op-amps need headroom; rail-to-rail is a specific feature.
- Single supply is special. Same op-amp; just biasing constraints differ.
- Infinite bandwidth. Gain rolls off; GBW limits useful range.
- Zero offset. Real op-amps have offset voltage requiring nulling for precision.
- Drives any load. Output current and voltage capability are finite.
- Stability is automatic. Capacitive loads or wrong feedback compensation cause oscillation.
Frequently asked questions
What is an op-amp?
A high-gain differential voltage amplifier. The output equals the gain (typically 10^5 to 10^6) times the difference between non-inverting (+) and inverting (-) input voltages. Designed to be combined with negative feedback so that overall circuit behavior depends on external resistors and capacitors, not on the op-amp's internal characteristics. The workhorse of analog electronics.
What are the golden rules?
With negative feedback applied: (1) The two input voltages are equal. The op-amp adjusts output to make them so. (2) No current flows into either input (input impedance is essentially infinite). These two rules let you analyze most op-amp circuits in seconds. They derive from the ideal model and remain accurate within the op-amp's specifications.
How does an inverting amplifier work?
Input signal connects through R1 to the inverting input; feedback resistor Rf goes from output back to inverting input; non-inverting input grounded. By the golden rules, inverting input is at virtual ground (0 V). Current through R1 equals input voltage divided by R1 and must flow through Rf, so output equals minus Rf/R1 times input. Gain = -Rf/R1.
How does a non-inverting amplifier work?
Input goes directly to non-inverting input; feedback divider from output through Rf and R1 (R1 to ground, Rf from output to junction). Inverting input voltage equals output times R1/(R1+Rf) by divider. Golden rule forces this to equal input voltage. Solving, output equals input times (1 + Rf/R1). Gain is always positive and at least 1.
What is GBW?
Gain-bandwidth product. Open-loop gain rolls off at 6 dB per octave above a low corner frequency. The product of gain and frequency at any point in this rolloff is constant — the GBW. A 1 MHz GBW op-amp set for gain of 100 has 10 kHz closed-loop bandwidth. Slew rate (volts per microsecond) limits large-signal response separately.
What real-world deviations matter?
Several. Input offset voltage (a few microvolts to millivolts) causes output to deviate from ideal at zero input. Input bias current causes voltage drops across source impedances. Common-mode rejection ratio limits how well it ignores inputs that move together. Slew rate limits speed for large signals. Power-supply rejection limits noise from supplies. Each is specified in datasheets.
What are common op-amp circuits?
Inverting amplifier. Non-inverting amplifier. Voltage follower (unity-gain buffer). Summing amplifier (multiple inputs). Difference amplifier (instrumentation front end). Integrator (capacitor in feedback). Differentiator (capacitor at input). Active filters (Sallen-Key, multiple-feedback). Comparator (no feedback). Schmitt trigger (positive feedback for hysteresis). Each emerges from feedback configuration.