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.
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.
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.
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.
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.
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.
Voltage Follower (Buffer)
Tie the output straight back to the inverting input: gain becomes exactly 1. Useless for amplifying — but perfect for buffering.
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.
Difference Amplifier (Subtractor)
Amplifies the difference between two inputs while rejecting whatever is common to both — the core of instrumentation amplifiers.
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.
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.
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
| Term | Meaning |
|---|---|
| Op-amp | High-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 gain | The gain set by external feedback resistors. |
| Virtual short | With feedback, the two inputs sit at the same voltage. |
| Virtual ground | The inverting input at ~0 V when the + input is grounded. |
| Feedback resistor (Rf) | Sets the gain together with Rin. |
| Slew rate | How fast the output can change (V/µs). |
| CMRR | Common-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.