Operational amplifier in: — AQA A-Level Physics

This topic covers the operational amplifier (op-amp) as a fundamental building block in analogue electronics. You will study its ideal properties, the effects of negative feedback, and how it is configured as inverting, non-inverting, summing, and differential amplifiers, as well as comparators. Understanding these circuits is essential for analysing sensor interfaces, audio amplifiers, and control systems.

In the wider AQA A-Level Physics course, op-amps link to potential dividers, sensors (such as thermistors and LDRs), and the processing of analogue signals. Mastery of op-amp circuits is crucial for tackling exam questions on gain, saturation, and the design of practical amplifier stages, and it provides a foundation for further study in electronics and engineering.

• →Ideal op-amp properties: infinite open-loop gain, infinite input impedance, zero output impedance, and infinite bandwidth.
• →Golden rules for negative feedback: no current flows into the input terminals, and the voltage at the inverting input equals the voltage at the non-inverting input (virtual earth if non-inverting input is grounded).
• →Inverting amplifier: gain = -Rf / Rin, input and output are in antiphase (180 degrees).
• →Non-inverting amplifier: gain = 1 + (Rf / R1), input and output are in phase.
• →Saturation: output voltage cannot exceed the supply rails; when saturated, the op-amp no longer follows the golden rules and the output clips at approximately ±Vsupply.

• Identifies the summing amplifier as an inverting op-amp configuration with several input resistors connected to the inverting input.
• States that the non-inverting input is connected to zero volts, so the inverting input is a virtual earth.
• Applies the ideal op-amp rule that negligible current enters the inverting input, so the sum of the input currents flows through the feedback resistor.
• Writes the current-balance equation in the form V₁/R₁ + V₂/R₂ + ... = −Vout/Rf, preserving the correct signs.
• Rearranges the equation to make the output voltage the subject, for example Vout = −Rf(V₁/R₁ + V₂/R₂ + ...).
• Explains that equal input resistors give an output proportional to the negative sum of the input voltages, scaled by Rf/Rin.
• Describes a practical use, such as mixing audio signals or combining sensor outputs, and notes that the output saturates if the required voltage exceeds the supply rails.
• Explains that changing an input resistor changes the weighting of that input, allowing weighted addition.

• 💡Label each input current with its direction towards the inverting node, then write one current-balance equation.
• 💡If the question gives equal input resistors, state that simplification explicitly before substituting values.
• 💡Keep the feedback resistor symbol distinct from the input resistors so the algebra is unambiguous.
• 💡Check the sign and the order of magnitude of your answer against the supply rails to see whether saturation is likely.
• 💡Always start by stating the two golden rules for an ideal op-amp with negative feedback: no input current and V- = V+. This demonstrates understanding and often earns method marks.
• 💡When calculating gain, write the formula explicitly with the correct signs and resistor labels. For inverting amplifiers, include the negative sign to show phase inversion.
• 💡For questions involving saturation, calculate the ideal output first, then compare it to the supply rails. If it exceeds them, state that the output saturates and give the saturated value (approximately ±Vsupply).

• Omitting the negative sign in the output expression; correct this by remembering that the inputs connect to the inverting terminal, so the output is inverted.
• Adding the input voltages directly without dividing by their resistances; correct this by using each input current, which is the input voltage divided by its own resistor.
• Assuming the virtual earth exists without negative feedback; correct this by checking that the feedback resistor connects the output to the inverting input.
• Mixing units, such as using kilo-ohms for some resistors and ohms for others; correct this by converting all resistances to the same unit before calculating.
• Students often think the op-amp amplifies the voltage difference by its open-loop gain even in negative feedback. Correction: In negative feedback, the output adjusts to make the input voltage difference nearly zero, and the gain is set by external resistors.
• Students sometimes believe that current flows into the op-amp inputs. Correction: For an ideal op-amp, input impedance is infinite, so no current flows into the inputs; all current flows through the feedback network.
• Students may forget that the output saturates when the required output exceeds the supply voltage. Correction: Always check that the calculated output is within the supply rails; if not, the output clips at the rail voltage and the golden rules no longer apply.

1. 1Day 1-2: Learn the ideal op-amp properties and the two golden rules. Practice identifying inverting, non-inverting, and comparator configurations from circuit diagrams.
2. 2Day 3-4: Derive the gain formulas for inverting and non-inverting amplifiers using Kirchhoff's laws and the golden rules. Memorise the formulas and understand the role of each resistor.
3. 3Day 5-6: Work through calculations for gain, output voltage, and saturation. Include examples with sensor inputs (e.g., thermistor in a potential divider) to see how op-amps process real signals.
4. 4Day 7-8: Attempt exam-style questions, focusing on multi-step problems that combine op-amps with potential dividers and saturation. Review mark schemes to identify common pitfalls.
5. 5Day 9-10: Create a summary sheet with key formulas, golden rules, and circuit diagrams. Test yourself with active recall and past paper questions under timed conditions.

• 📋Calculation of voltage gain and output voltage for inverting and non-inverting amplifiers: Write the correct formula, substitute values, and include units and sign.
• 📋Explanation of saturation and its effect on output: Calculate ideal output, compare to supply rails, and state the saturated output voltage.
• 📋Circuit analysis with sensor inputs: Combine potential divider equations with op-amp gain to find output voltage for a given physical quantity (e.g., temperature).
• 📋Design or selection of resistor values to achieve a required gain: Rearrange the gain formula and choose appropriate E-series resistor values, explaining your reasoning.