Operational Amplifiers — Eduqas A-Level Design and Technology

Operational amplifiers (op-amps) are high-gain voltage amplifiers with differential inputs and a single-ended output. In A-Level Design and Technology, you will focus on the ideal op-amp model: infinite open-loop gain, infinite input impedance, zero output impedance, and infinite bandwidth. These properties allow op-amps to be configured with external feedback components to perform precise mathematical operations like amplification, summation, integration, and differentiation. Understanding op-amps is essential for designing analogue circuits in control systems, audio processing, and sensor interfacing.

The two most common configurations are the inverting and non-inverting amplifiers. In the inverting amplifier, the input signal is applied to the inverting input through a resistor, with feedback from the output to the inverting input. The voltage gain is determined by the ratio of feedback resistor to input resistor (Av = -Rf/Rin). The non-inverting amplifier applies the input to the non-inverting input, with feedback to the inverting input, giving a gain of Av = 1 + Rf/Rin. Both configurations rely on the concept of a virtual short circuit between the inputs, meaning the inverting input is at the same potential as the non-inverting input when negative feedback is applied.

Op-amps are a cornerstone of modern electronics, enabling the design of filters, comparators, oscillators, and regulators. In your WJEC A-Level, you will analyse and design circuits using op-amps, calculate gain and bandwidth, and consider practical limitations such as slew rate, input offset voltage, and output voltage swing. Mastery of op-amps will allow you to tackle complex system design problems and understand how analogue signals are processed before conversion to digital.

• →Ideal op-amp characteristics: infinite open-loop gain, infinite input impedance, zero output impedance, infinite bandwidth, and zero input offset voltage.
• →Virtual short circuit: when negative feedback is applied, the voltage at the inverting input equals the voltage at the non-inverting input (V- = V+).
• →Inverting amplifier gain: Av = -Rf/Rin, where Rf is feedback resistor and Rin is input resistor. The negative sign indicates phase inversion.
• →Non-inverting amplifier gain: Av = 1 + Rf/Rin. The output is in phase with the input.
• →Summing amplifier: an extension of the inverting amplifier that adds multiple input voltages weighted by resistor ratios: Vout = -Rf(V1/R1 + V2/R2 + ...).

• Award credit for correctly listing at least four ideal op-amp characteristics (e.g., infinite open-loop gain, infinite input impedance, zero output impedance, infinite bandwidth).
• Credit given for explaining virtual earth as a point held at 0 V due to negative feedback and high gain, not a direct connection to ground.
• Expect clear differentiation between ideal and real op-amp behaviour, with examples such as finite slew rate or input bias currents.
• Look for correct application of virtual earth in deriving gain formulas, e.g., Vout = -Rf/Rin for an inverting amplifier.

• 💡Always begin circuit analysis by assuming ideal op-amp conditions and then note any real-world constraints that may apply.
• 💡Use diagrams to illustrate virtual earth—label voltages clearly and show that the inverting input is held at 0 V by feedback.
• 💡Memorise the standard gain formulas but understand their derivations via virtual earth to handle variant circuits effectively.
• 💡Always start by labelling the inverting and non-inverting inputs and writing the virtual short condition: V- = V+. Then apply Kirchhoff's Current Law at the inverting input node to derive the gain equation.
• 💡When calculating gain, pay attention to resistor values and units. Use standard form (e.g., 10kΩ = 10 × 10³ Ω) and ensure your final answer includes the correct sign for inverting amplifiers.
• 💡For design questions, choose standard resistor values (E24 series) that give a gain close to the required value. Show your working and state any assumptions (e.g., ideal op-amp).

• Treating the virtual earth as a physical earth connection, leading to incorrect circuit analysis.
• Ignoring the requirement for negative feedback to create a virtual earth; applying the concept to open-loop configurations.
• Assuming ideal op-amp output can exceed supply rails or drive unlimited current.
• Mixing up inverting and non-inverting gain formulas due to misunderstanding of virtual earth placement.
• Misconception: The virtual short circuit means the inputs are physically shorted. Correction: The inputs are not connected; the feedback forces the inverting input to track the non-inverting input voltage, but no current flows into the op-amp inputs.
• Misconception: The gain of an inverting amplifier is always negative. Correction: The negative sign indicates a 180° phase shift, not a negative voltage. The magnitude of gain is |Rf/Rin|.
• Misconception: Op-amps can output any voltage. Correction: Real op-amps have output voltage limits (rail-to-rail or within 1-2V of supply rails). The output cannot exceed the supply voltages.