Op-Amp Fundamentals

What is an Op-Amp?

An operational amplifier (op-amp) is a high-gain differential amplifier IC. It has two inputs — inverting (−) and non-inverting (+) — and one output. The output voltage is the difference between the inputs multiplied by the open-loop gain: V_out = A_OL × (V⁺ − V⁻). Since A_OL is extremely large (typically 100,000 to 1,000,000), even a tiny difference between the inputs produces a massive output swing.

The Ideal Op-Amp Model

• •Infinite open-loop gain (A_OL → ∞).
• •Infinite input impedance — the inputs draw zero current.
• •Zero output impedance — can drive any load without voltage drop.
• •Infinite bandwidth — gain is flat at all frequencies.
• •Zero offset voltage — when V⁺ = V⁻, output is exactly 0 V.

No real op-amp is truly ideal, but modern op-amps come remarkably close. The ideal model is used for initial circuit analysis; then you check whether the real device's imperfections matter for your application.

The Two Golden Rules (with Negative Feedback)

When an op-amp has negative feedback (output connected back to the inverting input through a resistor network), two powerful rules apply that make analysis easy:

• •Rule 1: The inputs draw no current (I⁺ = I⁻ = 0). Because input impedance is effectively infinite.
• •Rule 2: The op-amp adjusts its output so that V⁺ = V⁻ (virtual short). The voltage difference between the inputs is driven to zero by the feedback.

Power Supply: Dual and Single

• •Dual supply (e.g., ±15 V) — the classic setup. Output can swing both positive and negative. Common in audio and precision circuits.
• •Single supply (e.g., 0 to 5 V) — used in battery-powered and digital systems. Output can only swing between ground and V_CC. Often needs a 'virtual ground' at V_CC/2.
• •Rail-to-rail op-amps — output can swing very close to the supply rails. Important for single-supply designs with limited voltage headroom.

Op-Amp as a Comparator (Open Loop)

Without any feedback, the op-amp compares its two inputs. If V⁺ > V⁻, the output goes to the positive rail. If V⁺ < V⁻, the output goes to the negative rail. This makes a simple voltage comparator — useful for threshold detection (e.g., is the battery voltage below 3.3 V?).

Popular Op-Amp ICs

• •LM741 — the classic (1968). Dual supply, educational use. Slow and noisy by modern standards.
• •LM358 / LM324 — single-supply, dual/quad op-amp. Very common and cheap. Output doesn't swing to ground well.
• •MCP6002 — modern single-supply, rail-to-rail, low power. Great for 3.3 V / 5 V systems.
• •OPA2134 — high-quality audio op-amp. Low noise, wide bandwidth.
• •TL072 — JFET input, low noise e audio. Popular in guitar pedals and audio equipment.