Operational amplifier configurations revision notes

Overview\n\nOperational amplifiers (op‑amps) are the workhorses of analog electronics. In the AQA A Level Physics specification they are introduced as ideal devices with infinite open‑loop gain, infinite input impedance and zero output impedance. The revision notes below focus on the three most common linear configurations – inverting, non‑inverting and summing – and then discuss how real op‑amps deviate from the ideal model.\n\n## Inverting Amplifier\n\n- The classic inverting amplifier uses a single feedback resistor R2 and an input resistor R1.\n- The input signal is applied to the inverting (-) input through R1 while the non‑inverting (+) input is grounded.\n- The voltage gain is given by Vout = - (R2 / R1) Vin.\n- The negative sign indicates a 180° phase shift – the output is inverted.\n- The magnitude of the gain is determined solely by the resistor ratio.\n- The input impedance is approximately equal to R1, which is usually chosen to be high to minimise loading.\n- The output can swing only between the supply rails; the maximum usable output is typically ±(Vsupply – 1.5 V).\n\n## Non‑Inverting Amplifier\n\n- In a non‑inverting amplifier the input signal is applied to the (+) input.\n- The feedback network consists of R1 from the output to the (-) input and R2 from the (-) input to ground.\n- The voltage gain is Vout = (1 + R2 / R1) Vin.\n- There is no phase inversion – the output follows the input.\n- The input impedance is very high, essentially the op‑amp input impedance, because the (+) input draws negligible current.\n- The output swing is again limited by the supply rails, but the usable range is slightly larger because the output is not forced to cross zero.\n\n## Summing Amplifier\n\n- A summing amplifier is a special case of the inverting amplifier where multiple input signals are fed through individual resistors R1, R2, … to the inverting input.\n- The output is the negative weighted sum of the inputs: Vout = - (Rf / R1) V1 - (Rf / R2) V2 …\n- If all input resistors are equal (R) and the feedback resistor is Rf, the expression simplifies to Vout = - (Rf / R) (V1 + V2 + …).\n- The summing node is at virtual ground (≈0 V) because the op‑amp forces the inverting input to follow the non‑inverting input.\n- The input impedance of each branch is R, so the total input impedance is R / n for n identical branches.\n- Summing amplifiers are widely used in audio mixers, signal conditioning and analog computing.\n\n## Real Operational Amplifiers\n\n- Real op‑amps have finite open‑loop gain (typically 10^5 to 10^6), which means the virtual‑ground assumption is only approximate.\n- Bandwidth is limited; the gain‑bandwidth product is constant, so higher closed‑loop gain reduces the usable frequency range.\n- Slew rate limits the maximum rate of change of the output voltage (V/s). For a sinusoidal input, the maximum frequency is fmax = (slew rate) / (2π Vpp).\n- Output saturation occurs when the output reaches the supply rails; the op‑amp cannot drive beyond this limit.\n- Input bias currents and offset voltages introduce small errors, especially in high‑impedance circuits.\n- Power supply rejection ratio (PSRR) describes how well the op‑amp rejects variations in the supply voltage.\n\n## Key Equations\n\n- Inverting gain: Vout = - (R2 / R1) Vin\n- Non‑inverting gain: Vout = (1 + R2 / R1) Vin\n- Summing output: Vout = - (Rf / R1) V1 - (Rf / R2) V2 …\n- Gain‑bandwidth product: f × |A| = constant\n- Slew‑rate limit: fmax = (slew rate) / (2π Vpp)\n\n## Example Problem\n\nProblem: A 10 Vpp sinusoidal signal is applied to a non‑inverting amplifier with R1 = 1 kΩ and R2 = 9 kΩ. The op‑amp has a slew rate of 0.5 V/µs. What is the maximum frequency that can be amplified without distortion?\n\nSolution:\n- Gain = 1 + R2/R1 = 1 + 9 = 10\n- Vpp at output = 10 × 10 Vpp = 100 Vpp\n- fmax = (slew rate) / (2π Vpp) = 0.5 V/µs ÷ (2π × 100 V) = 0.5 × 10^6 V/s ÷ (628 V) ≈ 796 Hz\n- Therefore the amplifier can handle frequencies up to about 800 Hz before slew‑rate distortion occurs.\n\n## Design Considerations\n\n- Choose R1 and R2 to set the desired gain while keeping the input impedance high.\n- For audio applications, keep the gain‑bandwidth product well above the highest audio frequency (≈20 kHz).\n- Use a rail‑to‑rail op‑amp if the output must swing close to the supply rails.\n- Add compensation capacitors if the circuit is prone to oscillation at high frequencies.\n- When summing many signals, ensure that the input resistors are matched to avoid bias errors.\n\n## Common Pitfalls\n\n- Forgetting the negative sign in the inverting gain.\n- Assuming the output can exceed the supply rails; always subtract a safety margin.\n- Using the same formula for both inverting and non‑inverting gain.\n- Ignoring the effect of input bias currents in high‑impedance designs.\n- Overlooking the bandwidth‑gain trade‑off when selecting resistor values.\n\n## Further Reading\n\n- AQA A Level Physics textbook – Chapter on Electronics.\n- Datasheets of popular op‑amps such as the LM741, TL081 and LM358.\n- Online simulation tools (e.g., Falstad, LTspice) for visualising op‑amp behaviour.\n- Practical guides on designing audio mixers and signal conditioning circuits.\n\nThese notes cover the core concepts required for the AQA A Level Physics specification and provide a solid foundation for tackling both calculation and conceptual questions on operational amplifiers.