What Is an Op-Amp (Operational Amplifier)?

Detailed Explanation

The operational amplifier is the most versatile analog building block in electronics. Its behaviour is almost entirely determined by external components — resistors, capacitors — which define the feedback network, not by internal gain (which is deliberately made so high that it plays almost no role in closed-loop behaviour). Understanding the op-amp starts with the ideal model.

The Ideal Op-Amp Model

An ideal op-amp has three defining properties:

1. Infinite open-loop gain (A_OL = ∞): The output is A_OL × (V+ − V−). If A_OL is infinite, any nonzero differential input voltage produces infinite output — which means, in a closed-loop circuit, the feedback continuously drives the differential input toward zero.

2. Infinite input impedance: No current flows into or out of either input terminal.

3. Zero output impedance: The output can drive any load without the output voltage changing.

Real op-amps deviate from the ideal in ways that matter at high frequencies and precision levels, but the ideal model is sufficient for understanding most circuit configurations.

The Virtual Short (Closed-Loop Operation)

When negative feedback is applied — connecting the output back to the inverting input (−) through a feedback network — the op-amp's high gain enforces an important result: the inverting input voltage equals the non-inverting input voltage. This is the virtual short.

It is called "virtual" because there is no physical short between the two input pins, and no current flows between them (infinite input impedance). But in steady state, the feedback causes the op-amp to drive its output to whatever voltage is required to make V+ = V−.

Example: a unity-gain buffer (voltage follower) connects the output directly to the inverting input. The op-amp drives its output until V− equals V+, which means Vout equals Vin. The buffer presents infinite input impedance to the source and zero output impedance to the load — a near-perfect impedance isolator.

Key Parameters of Real Op-Amps

Input offset voltage (Vos): The small differential voltage that the op-amp intrinsically "sees" even when both inputs are at the same potential. Typical Vos: 0.1–5 mV for BJT op-amps; 0.5–10 mV for CMOS op-amps; under 100 µV for precision types (e.g. OPA2188, MAX44264). In a closed-loop circuit, Vos is amplified by the closed-loop gain and appears as a DC error at the output.

Input bias current (Ib): The small current that flows into each input due to transistor base or gate current. BJT op-amps: 10 nA to 1 µA. CMOS op-amps: 1 pA to 1 nA. Bias current flowing through the feedback resistors creates a voltage error. Minimise this by using lower-value feedback resistors (under 100 kΩ for BJT types) and by making the source resistances at both inputs equal.

Gain-bandwidth product (GBW): The frequency at which the open-loop gain falls to 1 (0 dB). For a single-pole op-amp: bandwidth × closed-loop gain = GBW (constant). A 1 MHz GBW op-amp set to closed-loop gain 100 has a signal bandwidth of 10 kHz. A 10 MHz GBW device at the same gain gives 100 kHz. Common values: LM358 = 1 MHz; MCP6001 = 1 MHz; OPA2134 = 8 MHz; TL072 = 3 MHz.

Slew rate (SR): The maximum rate of change of the output voltage, in V/µs. The output cannot change faster than the slew rate, regardless of feedback. The LM358 slews at 0.5 V/µs; the TL072 at 13 V/µs; the OPA2134 at 20 V/µs. For a full-scale output swing at a given frequency, the required slew rate is SR = 2π × f × Vpeak. A 10 kHz, 5V pk-pk sine wave requires SR ≥ 2π × 10,000 × 2.5 = 0.157 V/µs — achievable by most op-amps.

Common-mode rejection ratio (CMRR): How well the op-amp rejects signals common to both inputs. High CMRR is needed for differential measurement (thermocouple amplifiers, instrumentation amplifiers). Typical CMRR: 80–100 dB at DC, falling with frequency.

Single-Supply Operation

Many embedded systems run from 3.3V or 5V with no negative rail. Op-amps specified for single-supply operation (rail-to-rail input/output, RRIO) can amplify signals that swing between GND and Vcc without clipping prematurely.

Key considerations for single-supply circuits:

• DC bias: An AC signal centred at 0V cannot be amplified without clipping on the negative swing. Add a bias resistor network to set the non-inverting input to mid-supply (Vcc/2), allowing the output to swing symmetrically around that point.
• Output swing: Even rail-to-rail op-amps have a few millivolts of headroom at each rail. Do not attempt to drive the output to exactly 0V or exactly Vcc.
• Common-mode input range: Verify the op-amp's input common-mode range includes the signal voltages you intend to apply. Some non-RRIO single-supply op-amps cannot accept inputs near the supply or ground rail.

Common Applications

Voltage buffer (unity gain follower): Connects output to inverting input directly. Provides high-impedance input and low-impedance output — used to isolate a voltage reference, ADC input, or sensor from a loading load.

Inverting and non-inverting amplifiers: Set closed-loop gain using two resistors. See what are inverting and non-inverting op-amp amplifier configurations? for the full treatment.

Difference amplifier: Amplifies the voltage difference between two input nodes while rejecting common-mode voltage — the principle behind instrumentation amplifiers for thermocouple and Wheatstone bridge measurement.

Comparator (with caution): An op-amp can function as a comparator (output switches between rails based on which input is higher), but purpose-built comparators are faster and have open-drain outputs suited to threshold detection. See what is a comparator? for the comparison.

Integrator and differentiator: Replacing the feedback or input resistor with a capacitor creates a time-integrating or time-differentiating circuit — foundational in control systems and analogue signal processing.

Active filter: Combining resistors, capacitors, and the op-amp as an amplifier produces low-pass, high-pass, bandpass, and notch filters with defined frequency response — far more predictable than passive RC filters and with the ability to provide gain rather than only attenuation. See how to design an active filter with an op-amp for Sallen-Key and MFB topology design.

For analog circuit design, signal conditioning, and ADC front-end circuits for embedded products, Zeus Design's engineering team covers schematic design through to layout — contact Zeus Design to discuss your product's analog requirements.

Design Considerations

• Match source impedance at both inputs: To minimise the output error from input bias current, the Thevenin source resistance seen by each input should be equal. For an inverting amplifier with Rf and Rin, place a resistor of value Rf ∥ Rin at the non-inverting input to ground. This ensures both inputs see the same impedance and the bias currents produce equal and opposite offset voltages that cancel.
• Stability with capacitive loads: Op-amps can oscillate when driving capacitive loads (long cables, capacitive sensors, ADC inputs). If a load capacitance greater than a few hundred pF is unavoidable, add a small series resistor (10–100 Ω) between the output and the load. This provides phase margin at the cost of a small reduction in output swing and bandwidth.
• Gain-bandwidth product limits audio applications: A 1 MHz GBW op-amp set to gain 10 has only 100 kHz bandwidth — adequate for audio (20 Hz–20 kHz) but only just. At gain 100, bandwidth falls to 10 kHz, which is too low for full audio bandwidth. Use a higher-GBW op-amp or reduce the closed-loop gain, using multiple stages if necessary.
• Decoupling near the op-amp power pins: Op-amps need low-impedance supply decoupling just like digital ICs. Place 100 nF ceramic capacitors directly at each supply pin. A 10 µF bulk capacitor per supply rail should also be present somewhere on the board. Lack of decoupling causes oscillation and unexpected gain peaking, especially at high frequencies.

Common Mistakes

• Leaving the output floating (no feedback): An op-amp with no feedback path saturates to one supply rail and does nothing useful in analog circuits. Always close the loop (or use a purpose-built comparator if switching behaviour is needed).
• Overloading the output: Op-amp outputs are not high-current drivers. Typical output current capability is 10–40 mA short-circuit. Driving a 100 Ω load from a 3.3V supply draws 33 mA — at the limits of most general-purpose op-amps. Add a transistor emitter follower or a dedicated buffer stage for high-current loads.
• Ignoring input common-mode range on single-supply designs: A single-supply op-amp with an input common-mode range specified as V− to V+ − 1.5V cannot accept signals within 1.5V of the positive supply. Applying a signal near Vcc to such an op-amp causes output phase reversal or latch-up. Always check the input common-mode range specification, not just the supply voltage range.
• Using high-value feedback resistors with BJT-input op-amps: High-value resistors (1 MΩ and above) make the op-amp more sensitive to input bias current, EMI pickup, and thermal noise. For general-purpose BJT op-amps, keep feedback resistors under 100 kΩ; for CMOS op-amps with their lower bias current, higher values are acceptable.