--- title: "Ideal op-amp properties; inverting gain" subject: "Basic Electronics Engineering" chapter: 4 key: "semester_2/basic_electronics_engineering:opamp-props-inverting-gain" source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/opamp-props-inverting-gain site: BCT Engineering --- # Ideal op-amp properties; inverting gain Basic Electronics Engineering · Chapter 4: The Operational Amplifier and Oscillator - Asked in: 2073 Bhadra, 2+4 marks - Video: [Operational Amplifiers - Inverting & Non Inverting Op-Amps](https://www.youtube.com/watch?v=idJEMYhrIfs) — The Organic Chemistry Tutor - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/opamp-props-inverting-gain - Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-4 ## Question Mention any four properties of an ideal OP amp. Derive the expression of voltage gain of an inverting amplifier using OP amp. ## Short answer Ideal op-amp: infinite open-loop gain, infinite input resistance, zero output resistance, infinite bandwidth. Inverting amplifier: Vin through R1 to inverting input, Rf feedback, non-inverting terminal grounded. Virtual ground gives V- = 0. Current: Vin/R1 = -Vo/Rf => Av = Vo/Vin = -Rf/R1. ## Answer #### Four properties of an ideal op-amp 1. Infinite open-loop voltage gain. 2. Infinite input resistance, so no current flows into the inputs. 3. Zero output resistance. 4. Infinite bandwidth, infinite CMRR and zero offset voltage. ```text +Vcc |\ | V- o-| \ | | >--o Vo V+ o-| / |/ | -Vcc ``` #### Voltage gain of an inverting amplifier ```text +-----[ Rf ]-----+ | | | |\ | Vin o--[ R1 ]-+-----|- \ | | >------+----o Vo +-----|+ / | |/ GND ``` The input Vin is applied through R1 to the inverting input; the feedback resistor Rf connects the output to the inverting input; the non-inverting input is grounded. **Derivation** (ideal op-amp) - Virtual short: V− = V+ = 0, so the inverting node is at virtual ground. - No current enters the op-amp, so the input current I1 = (Vin − 0)/R1 flows entirely through Rf. - KCL at the inverting node: (Vin − 0)/R1 = (0 − Vo)/Rf **Av = Vo/Vin = −Rf/R1** The minus sign shows that the output is 180° out of phase with the input. The input resistance equals R1. Example: R1 = 10 kΩ, Rf = 100 kΩ gives Av = −10. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is the inverting node at virtual ground in this circuit? A. The non-inverting input is grounded and V- = V+ = 0 B. The inverting input is connected to ground C. Rf is zero D. The op-amp is off Answer: A. Virtual short makes V- equal V+ = 0 even without a direct ground connection. (Key point: Virtual ground) 2. Why does the input current I1 flow entirely through Rf? A. No current enters the op-amp input (infinite Ri) B. The op-amp output is zero C. R1 is infinite D. Rf is zero Answer: A. Infinite input resistance means all of Vin/R1 must go through Rf. (Key point: Current path) 3. What is the voltage gain? A. Av = +Rf/R1 B. Av = -Rf/R1 C. Av = 1 + Rf/R1 D. Av = -R1/Rf Answer: B. KCL gives Vin/R1 = -Vo/Rf, so Av = -Rf/R1. (Key point: Gain) 4. For R1 = 10 kΩ and Rf = 100 kΩ, what are the gain and the input resistance? A. -10 and 10 kΩ B. +10 and 100 kΩ C. -10 and 100 kΩ D. -0.1 and 10 kΩ Answer: A. Av = -100/10 = -10, and the input resistance equals R1 = 10 kΩ. (Key point: Example) ## Close variants set in other exams - [Ideal op-amp properties; non-inverting gain](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-noninverting-gain) — Basic Electronics Engineering, chapter 4, asked 3× ## Related in Basic Electronics Engineering - [Voltage gain of non-inverting op-amp](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-noninverting-gain) — Basic Electronics Engineering, chapter 4, asked 2× - [Op-amp properties and summing amplifier](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-summer-v1-2v2-3v3) — Basic Electronics Engineering, chapter 4 - [Properties of ideal op-amp](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aideal-opamp-properties) — Basic Electronics Engineering, chapter 4, asked 2× - [Op-amp properties and integrator](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-integrator) — Basic Electronics Engineering, chapter 4 - [Op-amp properties; square wave generator](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-five-props-square-wave) — Basic Electronics Engineering, chapter 4 - [Op-amp properties and differentiator](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-differentiator) — Basic Electronics Engineering, chapter 4, asked 2× ## Related in other subjects - [Non-inverting op-amp voltage gain](https://www.bctengineer.com/question.md?key=semester_1%2Ffundamental_of_electrical_and_electronics_engineering%3Anon-inverting-amplifier-gain) — Fundamental of Electrical and Electronics Engineering, chapter 6 - [Input impedance of inverting op-amp](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ainverting-input-impedance) — Advanced Electronics, chapter 2 - [Output voltage of two op-amp IA](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Atwo-opamp-ia-output) — Advanced Electronics, chapter 4 - [Summing amplifier using op-amp](https://www.bctengineer.com/question.md?key=semester_1%2Ffundamental_of_electrical_and_electronics_engineering%3Asumming-amplifier-op-amp) — Fundamental of Electrical and Electronics Engineering, chapter 6