The ideal operational amplifier (A-level only) — AQA A-Level Physics

This topic introduces the operational amplifier (op-amp) as an ideal component, focusing on its theoretical properties: infinite open-loop gain, infinite input impedance, zero output impedance, infinite bandwidth, and infinite common-mode rejection ratio. Students learn how these assumptions simplify circuit analysis, particularly for the inverting amplifier and comparator circuits, which are key applications in the AQA A-Level specification.

Understanding the ideal op-amp is essential for analysing more complex analogue circuits and provides a foundation for topics such as feedback, oscillators, and active filters. It also reinforces core physics principles like potential dividers, Kirchhoff's laws, and signal amplification, bridging the gap between theoretical physics and practical electronics.

• →Ideal op-amp properties: infinite open-loop voltage gain, infinite input impedance, zero output impedance, infinite bandwidth, and infinite common-mode rejection ratio (CMRR).
• →Virtual earth principle: when negative feedback is applied, the voltage difference between the inverting and non-inverting inputs is zero, so the inverting input sits at 0 V if the non-inverting input is grounded.
• →Inverting amplifier gain: A = -Rf / Rin, where Rf is the feedback resistor and Rin is the input resistor; the negative sign indicates 180 degree phase inversion.
• →Comparator circuit: an op-amp without feedback, used to compare two input voltages; the output saturates to the positive or negative supply rail depending on which input is larger.
• →Saturation: in an ideal op-amp, the output voltage cannot exceed the supply voltages; in reality, it is slightly less than the supply rails.

• Identify the inverting input, non-inverting input, output, and the positive and negative power supply connections on an op-amp symbol.
• State that the output voltage is proportional to the potential difference between the two inputs, with the proportionality constant being the open-loop gain.
• Explain that infinite open-loop gain means any finite output is produced by a vanishingly small input potential difference, so the inputs are at almost the same potential when negative feedback is used.
• Explain that infinite input resistance means no current flows into either input terminal, so the op-amp draws no input current.
• Describe the role of the power supply connections in setting the maximum positive and negative output voltages available from the op-amp.
• States that an operational amplifier is a differential amplifier with very high open-loop voltage gain, usually supplied as an integrated circuit.
• Explains that treating it as a building block means using standard configurations such as inverting, non-inverting, comparator and summing circuits.
• Applies the ideal op-amp assumptions: infinite open-loop gain, infinite input impedance, zero output impedance and infinite bandwidth.
• Uses the virtual earth or virtual short idea for a negative-feedback circuit, so the inverting input is at approximately the same potential as the non-inverting input.
• States that negligible current flows into either input, so current through the input resistor equals current through the feedback resistor.
• Derives or uses gain relationships from resistor ratios, for example the inverting amplifier gain is the negative ratio of feedback resistance to input resistance.
• Explains that negative feedback stabilises gain and reduces distortion, making the block predictable in a larger system.
• Describes how op-amp blocks can be cascaded or combined, for example a summing amplifier feeding a filter or comparator.

• 💡Label the op-amp symbol clearly with the inverting input, non-inverting input, output, and supply rails when drawing or annotating a diagram.
• 💡Use the ideal assumptions of infinite open-loop gain and infinite input resistance when analysing circuits with negative feedback.
• 💡Remember that the power supply connections determine the saturation limits, so quote them when discussing output voltage limits.
• 💡Sketch the op-amp block with its two inputs and one output, then label the feedback path before doing any algebra.
• 💡When deriving a gain, write the virtual-earth condition and the current-balance equation as separate lines so the examiner can follow your reasoning.
• 💡Check whether the circuit has negative feedback; if it does not, do not use the virtual short rule.
• 💡Give final gains as dimensionless ratios or in decibels only if the question asks for decibels, and keep resistor values in the same unit throughout.
• 💡Always state the ideal op-amp assumptions when asked to explain circuit behaviour; marks are awarded for correct terminology such as 'infinite input impedance' and 'virtual earth'.
• 💡In calculations, show the formula, substitute values with units, and include the negative sign for inverting amplifiers. Round final answers to an appropriate number of significant figures (usually 2 or 3).
• 💡For comparator questions, remember to state that the output saturates to the supply voltage (or slightly less) and that the op-amp is used without feedback.

• Assuming current flows into the op-amp inputs; with infinite input resistance the ideal input current is zero, so the correct statement is that no current enters the inputs.
• Confusing the inverting and non-inverting inputs; the inverting input is marked with a minus sign and reverses the sign of the output relative to that input.
• Believing the output can exceed the power supply rails; the output saturates at values set by the positive and negative supply voltages.
• Treating the op-amp as a device that creates energy rather than as an amplifier that needs a power supply; correct this by stating that the output cannot exceed the supply rails and that the op-amp shapes a signal using external components.
• Assuming the inputs are always at the same potential in every circuit; correct this by specifying that the virtual short applies only when negative feedback is present and the output is not saturated.
• Using the open-loop gain directly in a negative-feedback design; correct this by using the external resistor ratio, because negative feedback sets the closed-loop gain.
• Thinking that current flows into the input terminals in an ideal op-amp; correct this by applying the ideal assumption of infinite input impedance, so input current is negligible.
• Students often think the virtual earth means the inverting input is physically connected to earth. Correction: it is at 0 V due to negative feedback, but not directly connected to ground.
• Many believe that an ideal op-amp has zero gain. Correction: it has infinite open-loop gain, but negative feedback reduces the effective gain to a finite value set by external resistors.
• Students sometimes forget that the output of an inverting amplifier is inverted (180 degrees out of phase). Correction: the negative sign in the gain formula indicates this phase inversion.

1. 1Week 1: Learn the ideal op-amp properties and the virtual earth principle. Create flashcards for each assumption and test yourself daily.
2. 2Week 1: Practice deriving the inverting amplifier gain formula from first principles using Kirchhoff's laws and the virtual earth concept.
3. 3Week 2: Solve numerical problems on inverting amplifiers and comparators, including unit conversions and significant figures.
4. 4Week 2: Review past paper questions on op-amps, focusing on explanation questions and calculations. Mark your answers using the mark scheme.
5. 5Week 2: Summarise the differences between ideal and real op-amps, and list practical applications such as audio amplifiers and sensor circuits.

• 📋Calculation of output voltage for an inverting amplifier: use A = -Rf / Rin and Vout = A x Vin; watch units and negative sign.
• 📋Explanation of virtual earth and derivation of gain formula: describe the ideal assumptions and use Kirchhoff's laws to derive A = -Rf / Rin.
• 📋Comparator circuit analysis: determine output voltage based on input comparison; state saturation and supply rails.
• 📋Practical circuit design: select resistor values to achieve a given gain; rearrange A = -Rf / Rin and consider available resistor values.