The operational amplifier (op-amp) is the Swiss-army knife of analog electronics — amplifiers, filters, comparators, integrators, sensor interfaces and active rectifiers are all built from it. “Characteristics of an ideal op-amp”, “gain of inverting and non-inverting amplifiers”, “virtual ground” and “slew rate” are classic questions in BCS (EEE), PGCB, BPDB, BTCL, polytechnic and university exams. This post explains them with an animated inverting amplifier, formulas, solved problems and MCQs.
- An op-amp is a high-gain differential amplifier: Vout = AOL(V+ − V−).
- Ideal op-amp: infinite open-loop gain, infinite input impedance, zero output impedance, infinite bandwidth, infinite CMRR, zero offset.
- Golden rules (with negative feedback): (1) V+ = V− (virtual short), (2) no current flows into the inputs.
- Inverting amplifier: Av = −Rf/Rin. Non-inverting: Av = 1 + Rf/R1. Voltage follower: Av = 1.
- Output is limited by the supply (saturation) and by slew rate and gain–bandwidth product.
1. What Is an Op-Amp?
An operational amplifier is a direct-coupled, high-gain differential amplifier, usually an IC, with two inputs — inverting (−) and non-inverting (+) — and one output. It is normally powered from dual supplies (e.g. ±15 V). The name comes from its original use in analog computers to perform mathematical operations (add, subtract, integrate, differentiate). Internally it has a differential input stage, a high-gain intermediate stage and an output (push-pull) stage.
2. Ideal vs Practical (741) Characteristics
| Parameter | Ideal | Typical µA741 |
|---|---|---|
| Open-loop voltage gain AOL | ∞ | ≈ 2 × 10⁵ (106 dB) |
| Input impedance | ∞ | ≈ 2 MΩ |
| Output impedance | 0 | ≈ 75 Ω |
| Bandwidth | ∞ | Gain–bandwidth product ≈ 1 MHz |
| CMRR | ∞ | ≈ 90 dB |
| Slew rate | ∞ | ≈ 0.5 V/µs |
| Input offset voltage | 0 | ≈ 1–2 mV |
| Input bias current | 0 | ≈ 80 nA |
CMRR (common-mode rejection ratio) = Ad/Acm — how well the op-amp amplifies the difference while rejecting signals common to both inputs (e.g. noise).
3. Golden Rules and Virtual Ground
- No current flows into either input (infinite input impedance).
- With negative feedback, the output adjusts so that V+ = V− (because AOL is so large, the difference needed is tiny).
In an inverting amplifier the + input is grounded, so the − input is also at 0 V — a virtual ground: it is at ground potential but no current flows to ground through it.
4. Inverting Amplifier (Animation)
The input signal is applied through Rin to the − input; Rf feeds back from output to − input. Because the − input is a virtual ground, the current through Rin is Vin/Rin, and the same current flows through Rf:
Vout = −(Rf/Rin) Vin, input impedance = Rin
5. Other Basic Configurations
| Circuit | Output / function | Notes |
|---|---|---|
| Non-inverting amplifier | Vout = (1 + Rf/R1)Vin | Very high input impedance; in phase |
| Voltage follower (buffer) | Vout = Vin | Gain 1; isolates source from load |
| Summing (inverting adder) | Vout = −Rf(V1/R1 + V2/R2 + …) | Audio mixers, DACs |
| Difference amplifier | Vout = (Rf/R1)(V2 − V1) (matched resistors) | Basis of instrumentation amplifiers |
| Integrator | Vout = −(1/RC)∫Vin dt | Square wave → triangle; PI controllers |
| Differentiator | Vout = −RC dVin/dt | Edge detection (noise-sensitive) |
| Comparator | Output = +Vsat or −Vsat | Open-loop; zero-crossing detector |
| Schmitt trigger | Comparator with positive feedback (hysteresis) | Noise-immune switching |
6. Practical Limitations
- Output saturation: output cannot exceed about 1–2 V below each supply rail (rail-to-rail op-amps get closer).
- Slew rate (SR): maximum rate of change of output (V/µs). For a sine of peak Vp, the full-power bandwidth is fmax = SR/(2πVp).
- Gain–bandwidth product (GBW): closed-loop gain × bandwidth ≈ constant (≈ 1 MHz for 741).
- Offset voltage and bias currents cause DC errors; corrected by offset-null pins and bias-compensation resistors.
- Finite CMRR, noise and output current limits.
7. 741 Pin Diagram (8-pin DIP)
| Pin | Function | Pin | Function |
|---|---|---|---|
| 1 | Offset null | 5 | Offset null |
| 2 | Inverting input (−) | 6 | Output |
| 3 | Non-inverting input (+) | 7 | +VCC |
| 4 | −VEE | 8 | No connection |
8. Solved Problems
Problem 1. Inverting amplifier with Rin = 10 kΩ, Rf = 100 kΩ and Vin = 0.2 V. Av = −10 ⇒ Vout = −2 V.
Problem 2. Non-inverting amplifier with R1 = 10 kΩ, Rf = 90 kΩ. Av = 1 + 9 = 10.
Problem 3. Summing amplifier: Rf = 10 kΩ, R1 = R2 = 10 kΩ, V1 = 1 V, V2 = 2 V. Vout = −(1 + 2) = −3 V.
Problem 4. A 741 (SR = 0.5 V/µs) must output a 10 V-peak sine. Find the maximum frequency. fmax = 0.5 × 10⁶/(2π × 10) ≈ 7.96 kHz.
Problem 5. With GBW = 1 MHz, what is the bandwidth at a closed-loop gain of 100? BW ≈ 1 MHz/100 = 10 kHz.
9. Practice MCQs (click to see answer)
1. The input impedance of an ideal op-amp is: (a) Zero (b) Infinite (c) 1 kΩ (d) 75 Ω
2. Gain of an inverting amplifier is: (a) 1 + Rf/Rin (b) −Rf/Rin (c) Rin/Rf (d) 1
3. A voltage follower has a voltage gain of: (a) 0 (b) 1 (c) 10 (d) ∞
4. The inverting input of an inverting amplifier is at: (a) Supply voltage (b) Virtual ground (c) Output voltage (d) Floating
5. CMRR of an ideal op-amp is: (a) Zero (b) One (c) Infinite (d) 90 dB exactly
6. Slew rate is expressed in: (a) V/µs (b) dB (c) Hz (d) Ω
7. An integrator converts a square wave into a: (a) Sine wave (b) Triangular wave (c) Spike train (d) DC level
8. In IC 741, pin 6 is the: (a) Inverting input (b) Output (c) +VCC (d) Offset null
9. A Schmitt trigger uses: (a) Negative feedback (b) Positive feedback (c) No feedback (d) Only capacitors
10. Gain of a non-inverting amplifier with Rf = 47 kΩ and R1 = 4.7 kΩ is: (a) 10 (b) 11 (c) −10 (d) 0.1
10. বাংলায় দ্রুত রিভিশন
- অপ-অ্যাম্প: উচ্চ গেইনের ডিফারেনশিয়াল অ্যাম্প্লিফায়ার; দুটি ইনপুট (− ইনভার্টিং, + নন-ইনভার্টিং), একটি আউটপুট।
- আদর্শ অপ-অ্যাম্প: অসীম গেইন, অসীম ইনপুট ইম্পিড্যান্স, শূন্য আউটপুট ইম্পিড্যান্স, অসীম ব্যান্ডউইথ ও CMRR।
- সোনালি নিয়ম: ইনপুটে কারেন্ট যায় না; নেগেটিভ ফিডব্যাকে V₊ = V₋ (ভার্চুয়াল গ্রাউন্ড)।
- ইনভার্টিং গেইন = −Rf/Rin; নন-ইনভার্টিং গেইন = 1 + Rf/R₁; ভোল্টেজ ফলোয়ার = ১।
- সীমাবদ্ধতা: স্যাচুরেশন, স্লু রেট (fmax = SR/2πVp), গেইন-ব্যান্ডউইথ গুণফল (741-এ ≈ ১ MHz)।
- 741 পিন: ২ = (−), ৩ = (+), ৬ = আউটপুট, ৭ = +VCC, ৪ = −VEE।
Related Posts
- FET vs BJT: Key Differences
- Integrated Circuits: Advantages & Disadvantages
- What Is an Oscillator?
- Semiconductor Diode: Working & Characteristics
References: Ramakant A. Gayakwad, Op-Amps and Linear Integrated Circuits; Sedra & Smith, Microelectronic Circuits; Texas Instruments µA741 datasheet. Images and animations: original work by Totalecer.
Thank you for visiting my blog.