Op-Amp Fundamentals Revision Notes | A Level AQA Physics

1. Why Op-Amps Matter in Analogue Electronics

Imagine you are recording a faint signal from a microphone — the voltage might be just a few millivolts. To do anything useful with it, you need to amplify it cleanly, without distortion and without the amplifier itself loading down the source. That is precisely the problem the operational amplifier (op-amp) was designed to solve.

Op-amps sit at the heart of analogue signal processing: they appear in audio equipment, medical sensors, control systems, and instrumentation. At A-level, the focus is on understanding what an ideal op-amp does and how its connections determine circuit behaviour — a foundation that makes every subsequent amplifier circuit straightforward to analyse.

2. Power Supply and Signal Connections

Before any signal is processed, the op-amp needs power. A standard op-amp such as the 741 uses a dual (split) power supply: a positive supply rail $+V_S$ and a negative supply rail $-V_S$, both measured relative to a common earth (0 V). Typical values are $\pm 9$ V or $\pm 15$ V. This dual supply is what allows the output to swing both positive and negative — essential for amplifying alternating signals.

The op-amp has five key connections you need to know. Two are for the power supply rails. Two are signal inputs: the non-inverting input (labelled $+$) and the inverting input (labelled $-$). The fifth is the output. Circuit diagrams often omit the supply connections for clarity, but they must always be present in a real circuit — the op-amp cannot function without them.

The output voltage $V_{out}$ depends on the potential difference between the two inputs, not on the absolute voltage at either terminal. Specifically, $V_{out} = A_{OL}(V_+ - V_-)$, where $A_{OL}$ is the open-loop gain and $V_+$ and $V_-$ are the voltages at the non-inverting and inverting inputs respectively. This differential action is the defining feature of the op-amp.

3. Characteristics of an Ideal Operational Amplifier

Real op-amps are complex devices with many imperfections. To make circuit analysis tractable at A-level — and indeed in most professional engineering work — we use the ideal op-amp model. This model assigns extreme (often infinite or zero) values to key parameters, which simplifies calculations enormously while remaining a very good approximation for most practical circuits.

There are four ideal characteristics you must know precisely. Each one has a physical reason behind it, and each one has a direct consequence for how you analyse circuits. Work through them in order — they build on each other.

Think of this characteristic as a very strict controller. If the gain is infinite, even the tiniest difference between the two inputs would drive the output to the supply rail — unless a feedback path is used to keep the inputs balanced. This is why negative feedback is so powerful with op-amps: it exploits infinite gain to enforce precise, predictable behaviour.

This is enormously useful. Because no current enters the input terminals, all the current flowing through an input resistor in a feedback circuit must continue into the feedback network — a rule that makes Kirchhoff's current law analysis straightforward. You will use this assumption constantly when deriving gain expressions for inverting and non-inverting amplifiers.

In a real op-amp the output impedance is small but not zero — typically a few tens of ohms. For the ideal model, setting it to zero means the output voltage is independent of the load connected to it. This pairs neatly with infinite input impedance: the op-amp takes nothing from its source and gives everything to its load.

Real devices show a gain that falls off at higher frequencies — a consequence of internal capacitances within the chip. The ideal model ignores this entirely. For AQA A-level questions, you will not be asked to calculate bandwidth limitations, but you should be able to state that infinite bandwidth is one of the ideal characteristics and recognise that real op-amps deviate from this at high frequencies.

4. Summarising the Ideal Characteristics

It helps to see all four ideal characteristics together so you can recall them quickly in an exam. The table below also notes the real-device approximation, which gives you context for why the ideal model works so well in practice.

Notice that real values are extreme enough that the ideal approximation introduces very little error for most audio-frequency circuits. A real input impedance of 2 M$\Omega$ is so large compared with typical source resistances that treating it as infinite changes calculated results by a fraction of a percent.

5. Open-Loop Behaviour and Saturation

Without any feedback, the op-amp operates in open-loop mode. Because the open-loop gain is so enormous (ideally infinite, realistically around $10^5$), even a differential input of a fraction of a millivolt is enough to drive the output to the supply rail. The output cannot exceed the supply voltage, so it saturates at approximately $+V_S$ or $-V_S$.

This saturation behaviour makes the open-loop op-amp useful as a comparator: it compares $V_+$ and $V_-$ and outputs a high or low voltage depending on which is larger. If $V_+ > V_-$, the output saturates positive; if $V_+ < V_-$, the output saturates negative. The output is essentially a digital-style decision about the analogue inputs.

Worked example: Predicting Open-Loop Output State

An op-amp is powered by $\pm 9$ V rails. The non-inverting input is held at $+0.5$ V and the inverting input is held at $+0.8$ V. Predict the output voltage.

1. $V_+ - V_- = 0.5 - 0.8 = -0.3\ \text{V}$ — The differential input is the voltage at the non-inverting input minus the voltage at the inverting input. Here it is negative.
2. $V_{out} = A_{OL} \times (V_+ - V_-)$ — For an ideal op-amp, $A_{OL} \rightarrow \infty$. A negative differential input multiplied by an infinite positive gain gives a very large negative output.
3. $V_{out}$ cannot go below $-V_S = -9\ \text{V}$ — The output is limited by the supply rails. Since the calculated output would be $-\infty$, the op-amp saturates at the negative rail.
4. $V_{out} \approx -9\ \text{V}$ — The output saturates at the negative supply rail because $V_+ < V_-$. In practice, saturation occurs a volt or two inside the rail for most op-amps, but for ideal analysis we use $-V_S$.

Answer: $V_{out} \approx -9\ \text{V}$ (saturated at the negative supply rail)

Open-loop saturation is the key reason why negative feedback is used in almost all linear amplifier circuits. Feedback reduces the effective gain to a controlled, finite value and keeps the output in the linear region between the supply rails — allowing faithful amplification rather than a two-state switch.

6. The Virtual Earth Principle (Consequence of Ideal Characteristics)

The ideal characteristics combine to produce one of the most powerful analytical tools in op-amp circuit analysis: the virtual earth (also called virtual ground). This arises specifically in the inverting amplifier configuration, where negative feedback is applied from the output back to the inverting input.

Here is the reasoning chain. Because the open-loop gain is infinite, the differential input $(V_+ - V_-)$ must be zero for the output to remain finite and in the linear region. If the non-inverting input is connected to earth (0 V), then $V_+ = 0$ V, and therefore $V_- = 0$ V as well. The inverting input is held at 0 V by the action of feedback — not because it is connected to earth, but because the circuit forces it there. That is why it is called a virtual earth.

Combined with infinite input impedance (no current into the inverting terminal), the virtual earth rule lets you write Kirchhoff's current law at the inverting input node with confidence: all current arriving through the input resistor must leave through the feedback resistor. This is the starting point for deriving the gain of an inverting amplifier — a topic you will meet in the next part of this unit.

7. Exam Technique and Mark-Winning Strategies

AQA questions on op-amp fundamentals tend to target three areas: recalling ideal characteristics with correct values, explaining the consequence of a characteristic for circuit behaviour, and predicting output states. Each requires a slightly different approach to secure full marks.

For a 'describe or explain' question worth 2–3 marks, structure your answer as: state the characteristic with its ideal value, state the consequence for the circuit, and link back to the specific scenario in the question. This three-part structure reliably picks up all available marks.

Mastering the ideal op-amp model — its five connections, four ideal characteristics, and the virtual earth consequence — gives you the analytical toolkit needed for every op-amp circuit at A-level, from inverting and non-inverting amplifiers to summing amplifiers and comparators.