Operational Amplifier (Op-Amp)

The single most useful building block in analog electronics. An op-amp amplifies the difference between its two inputs with enormous gain — and with a couple of resistors you turn it into an amplifier, buffer, adder, subtractor, filter or comparator. Learn the symbol, the 741 pinout, the two golden rules, and every core circuit with its gain formula.

Complete Learning Path — Operational Amplifier

From the symbol and 741 pinout, to the golden rules and open/closed loop, then the inverting, non-inverting, buffer, summing, difference and comparator circuits

What is an Operational Amplifier?

An operational amplifier (op-amp) is a high-gain voltage amplifier with a differential input — an inverting (−) input and a non-inverting (+) input — and a single output. It amplifies the difference between the two inputs by a very large factor.

On its own that gain is too large to be useful, but add a couple of resistors as feedback and the op-amp becomes a precise, predictable circuit block. It is the heart of nearly all analog signal processing.

Operational amplifier schematic symbol with inverting minus and non-inverting plus inputs, an output, and V plus and V minus power supply pins
The op-amp symbol: it outputs Vout = A × (V+ − V−), where A is the huge open-loop gain.
2 in, 1 out
Differential input
A ≈ 10⁵
Open-loop gain
+ and −
Non-inv / inverting
±15 V
Typical supply
Why “operational”?

The name comes from early analog computers, where op-amps performed mathematical operations — adding, subtracting, integrating and differentiating voltages. Those same circuits are still everywhere today.

The 741 Pinout

The classic 741 comes in an 8-pin DIP. Knowing its pins is the first step to wiring any op-amp circuit.

741 operational amplifier 8-pin DIP pinout: pin 2 inverting input, pin 3 non-inverting, pin 6 output, pin 7 V plus, pin 4 V minus
Pin 2 = inverting input, Pin 3 = non-inverting, Pin 6 = output, Pins 7 / 4 = supply (V+ / V−).
Don't forget the supply

Every op-amp needs its power pins (7 and 4 on a 741) connected — they are often left out of textbook circuit drawings for clarity, but the chip won't work without them.

The Ideal Op-Amp & the Golden Rules

To design quickly, we assume an ideal op-amp. Real parts like the 741 come close enough that the two golden rules make analysis almost trivial.

Ideal op-amp characteristics: infinite open-loop gain, infinite input impedance, zero output impedance, infinite bandwidth, plus the two golden rules
Ideal characteristics and the two golden rules that hold whenever negative feedback is present.

No input current

Infinite input impedance means no current flows into either input pin.

Virtual short

With feedback, the op-amp drives its output so V+ = V−. If + is grounded, − becomes a virtual ground.

Open-Loop vs Closed-Loop

The single biggest idea in op-amp circuits: negative feedback tames the huge open-loop gain into a precise, useful one.

Open-loop op-amp has enormous gain and acts as a comparator, while closed-loop feedback sets a precise stable gain
Open-loop: gain ≈ 100,000+, output slams to a rail (a comparator). Closed-loop: feedback sets an exact gain.

Almost every useful op-amp circuit uses negative feedback (feedback to the inverting input). It sacrifices raw gain for accuracy, stability and predictable behaviour set entirely by external resistors.

Inverting Amplifier

Input through Rin to the inverting pin, feedback through Rf, non-inverting pin grounded. The output is an amplified, inverted copy of the input.

Inverting op-amp amplifier with input resistor Rin and feedback resistor Rf, gain equals minus Rf over Rin
The inverting amplifier — the inverting input is a virtual ground.
Vout = − (Rf / Rin) × Vin
Example: Rf = 100 kΩ, Rin = 10 kΩ → gain = −10 (output is 10× and inverted). Try the op-amp gain calculator.

Non-Inverting Amplifier

Signal into the non-inverting pin; the Rf–Rin divider feeds the inverting pin. The output keeps the same polarity and the gain is always ≥ 1.

Non-inverting op-amp amplifier, gain equals one plus Rf over Rin
The non-inverting amplifier — high input impedance, same-polarity output.
Vout = (1 + Rf / Rin) × Vin
Example: Rf = 100 kΩ, Rin = 10 kΩ → gain = +11.

Voltage Follower (Buffer)

Tie the output straight back to the inverting input: gain becomes exactly 1. Useless for amplifying — but perfect for buffering.

Op-amp voltage follower or unity gain buffer with the output connected to the inverting input
The voltage follower: gain = 1, huge input impedance, tiny output impedance.

Because it draws almost no current from the source yet can drive a heavier load, a buffer lets a weak signal (a sensor, a divider) drive the next stage without being “loaded down” — the same isolation role a regulator plays for power.

Summing Amplifier (Adder)

Several inputs, each through its own resistor into the virtual-ground node, add together at the output — an analog adder.

Summing op-amp amplifier adding three weighted input voltages V1 V2 V3 through resistors R1 R2 R3
Each input is scaled by Rf/R and the results are summed (and inverted).
Vout = − Rf × ( V1/R1 + V2/R2 + V3/R3 )
With all resistors equal: Vout = −(V1 + V2 + V3). The basis of audio mixers and DACs.

Difference Amplifier (Subtractor)

Amplifies the difference between two inputs while rejecting whatever is common to both — the core of instrumentation amplifiers.

Difference op-amp amplifier or subtractor amplifying V2 minus V1
The difference amplifier subtracts one input from the other.
Vout = (Rf / R) × (V2 − V1)
(with matched resistors, Rg = Rf). Great for reading small signals riding on noise.

Comparator

Run an op-amp open-loop and it compares its two inputs, swinging the output hard to one rail or the other — a 1-bit decision.

Op-amp comparator comparing an input to a reference, output swings rail to rail
Comparator: output = +Vsat when Vin > Vref, else −Vsat.
Tip: use a real comparator for speed

General-purpose op-amps work as comparators but are slow. For fast level detection use a dedicated comparator IC (e.g. LM393), and add hysteresis to avoid chattering on noisy signals.

Applications

From a single chip to entire signal chains — op-amps are everywhere in analog design.

Applications of op-amps: amplifiers, buffers, active filters, comparators, math blocks and instrumentation
A few of the countless jobs op-amps do.
Amplification

Boost small sensor or audio signals precisely.

Buffering

Isolate stages so they don't load each other.

Active filters

Low-, high- and band-pass without bulky inductors.

Comparison

Threshold and level detection.

Analog math

Add, subtract, integrate, differentiate.

Instrumentation

Precise measurement front-ends.

Key Terms — Glossary

TermMeaning
Op-ampHigh-gain differential voltage amplifier; the core analog building block.
Inverting input (−)Increasing its voltage drives the output down.
Non-inverting input (+)Increasing its voltage drives the output up.
Open-loop gain (A)The op-amp's raw gain with no feedback (very large).
Closed-loop gainThe gain set by external feedback resistors.
Virtual shortWith feedback, the two inputs sit at the same voltage.
Virtual groundThe inverting input at ~0 V when the + input is grounded.
Feedback resistor (Rf)Sets the gain together with Rin.
Slew rateHow fast the output can change (V/µs).
CMRRCommon-mode rejection ratio — how well it ignores signals common to both inputs.

Frequently Asked Questions

Quick, expert answers to the questions people ask most about op-amps.

What is an operational amplifier (op-amp)?

A high-gain voltage amplifier with two inputs (inverting and non-inverting) and one output. It amplifies the difference between its inputs, and with external feedback resistors it performs precise analog functions — amplifying, buffering, adding, subtracting, filtering and comparing.

What are the two golden rules of an op-amp?

With negative feedback: (1) no current flows into either input (infinite input impedance), and (2) the op-amp keeps both inputs at the same voltage (a virtual short). These two rules let you analyse almost any op-amp circuit quickly.

What is the gain of an inverting and non-inverting amplifier?

Inverting: gain = −Rf/Rin (inverts the signal). Non-inverting: gain = 1 + Rf/Rin (same polarity, always ≥ 1).

What is a voltage follower or buffer?

An op-amp with its output tied back to the inverting input, giving a gain of exactly 1. Its very high input impedance and very low output impedance let it buffer a weak source and drive a heavier load without loading the source.

What is a virtual short / virtual ground?

With negative feedback the output moves to keep both inputs at the same voltage (virtual short). If the + input is grounded, the − input sits at nearly 0 V too — a virtual ground.

What is the pinout of a 741 op-amp?

On an 8-pin DIP 741: pin 2 = inverting input, pin 3 = non-inverting, pin 6 = output, pin 7 = V+, pin 4 = V−, pins 1 & 5 = offset null, pin 8 = NC.

What is the difference between open-loop and closed-loop?

Open-loop (no feedback) uses the huge raw gain, so the output slams to a rail — that's how a comparator works. Closed-loop (with feedback) trades that gain for a precise, stable gain set by external resistors.

What are op-amps used for?

Amplifying small signals, buffering, active filtering, comparing voltages, and analog math (add, subtract, integrate, differentiate). They are the fundamental building block of analog signal processing and instrumentation.

Conclusion & Key Takeaways

Master the two golden rules and a handful of resistor patterns, and you can design most analog signal circuits with a single op-amp.

Amplifies difference

Vout = A(V+−V−).

Golden rules

No input current; virtual short.

Inverting

−Rf/Rin.

Non-inverting

1 + Rf/Rin.

Buffer

Gain 1, isolates stages.

Comparator

Open-loop, rail-to-rail.

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