Op-Amp Transfer Function and Comparator Revision Notes | A Level AQA Physics

1. Why the Op-Amp is a Fundamental Building Block

Picture a single chip that can amplify, compare, add, and filter signals — all by changing the components wired around it. That chip is the operational amplifier, or op-amp, and it sits at the heart of analogue electronics at A-level.

The AQA specification treats the op-amp as an important system building block. That framing matters: you are not expected to understand the transistor-level internals. Instead, you treat the op-amp as a black box with well-defined terminal behaviour, and you predict what it does in a circuit from that behaviour alone.

This lesson focuses on the open-loop case — no feedback resistors, no closed-loop gain formula yet. Understanding what the op-amp does without feedback is the foundation for everything that follows in analogue signal processing.

2. The Open-Loop Transfer Function

Every op-amp has two signal inputs: the non-inverting input ($V_+$) and the inverting input ($V_-$). The output responds to the difference between them, not to either voltage on its own.

The key insight is the magnitude of $A_{OL}$. For a real op-amp such as the 741, $A_{OL}$ is typically around $10^5$ (100,000). Multiply that by even a 1 mV difference between the inputs and you get a theoretical output of 100 V — far beyond what any real power supply can deliver.

Because the supply rails cap the output, the op-amp saturates: the output clamps to just below the positive supply rail when $V_+ > V_-$, and to just below the negative supply rail when $V_- > V_+$. For a $\pm 15$ V supply, saturation typically occurs at roughly $\pm 13$ V to $\pm 14$ V in practice.

This saturation behaviour is not a flaw — it is precisely what makes the op-amp useful as a comparator. The output snaps decisively to one rail or the other, giving a clear high or low signal depending on which input is larger.

3. Saturation in Detail: Working Through the Numbers

It is worth working through a concrete numerical example to see exactly why saturation is almost inevitable in open-loop operation. The step-by-step below walks through two scenarios using the same op-amp.

Worked example: Applying the Open-Loop Transfer Function

An op-amp has an open-loop gain $A_{OL} = 1.0 \times 10^5$ and is powered by $\pm 15$ V supply rails. The saturation output is $\pm 13$ V. Calculate $V_{out}$ for: (a) $V_+ = 2.001$ V, $V_- = 2.000$ V and (b) $V_+ = 1.998$ V, $V_- = 2.000$ V.

1. $(V_+ - V_-) = 2.001 - 2.000 = +0.001$ V $(= +1$ mV$)$ — The non-inverting input is 1 mV above the inverting input. This is a very small difference.
2. $V_{out} = A_{OL} \times (V_+ - V_-) = 1.0 \times 10^5 \times 0.001 = 100$ V — The theoretical output is 100 V. The supply rails are only $\pm 15$ V, so this is impossible to deliver.
3. $V_{out} = +13$ V (positive saturation) — Because the theoretical value exceeds the positive rail, the output clamps to the positive saturation voltage. [A1]
4. $(V_+ - V_-) = 1.998 - 2.000 = -0.002$ V $(= -2$ mV$)$ — Now the inverting input is larger, so the differential is negative.
5. $V_{out} = 1.0 \times 10^5 \times (-0.002) = -200$ V — Again, the theoretical value far exceeds the supply rails in the negative direction.
6. $V_{out} = -13$ V (negative saturation) — The output clamps to the negative saturation voltage. [A1] Notice how the sign of the differential input directly determines which rail the output snaps to.

Answer: (a) $V_{out} = +13$ V (positive saturation); (b) $V_{out} = -13$ V (negative saturation)

The pattern is clear: in open-loop operation, the output is almost never a linearly amplified version of the input. The output is essentially always at one of the two saturation voltages. The only exception would be if the differential input were so tiny — on the order of microvolts — that the theoretical output fell within the supply range, which is extremely rare in practice.

4. The Op-Amp as a Comparator

The saturation behaviour described above is not just a side effect to be aware of — it is the operating principle of the comparator circuit. A comparator uses the op-amp open-loop to answer one question: which of two voltages is larger?

Consider a practical setup: the non-inverting input ($V_+$) receives a varying sensor signal, and the inverting input ($V_-$) is connected to a fixed reference voltage $V_{ref}$. Whenever the sensor signal rises above $V_{ref}$, the output snaps to positive saturation. Whenever it falls below $V_{ref}$, the output snaps to negative saturation.

This gives a clean, decisive output transition — exactly what is needed to interface analogue sensors with digital logic circuits, trigger alarms, or control switching circuits. The comparator is one of the most widely used op-amp configurations in real engineering systems.

The chart above illustrates the transfer characteristic of a comparator. The theoretical linear response (dashed) would require an impossibly large output voltage. The actual response (solid) shows the output clamped at the saturation voltages for all but the tiniest differential inputs — the transition region is so narrow it appears as a vertical step on any practical scale.

5. Comparator Configurations and Reference Voltages

The choice of which input receives the signal and which receives the reference determines the polarity of the output transition. This is worth being precise about, because examiners frequently test it.

In both cases the underlying equation $V_{out} = A_{OL}(V_+ - V_-)$ is unchanged. The difference is purely which terminal carries the signal and which carries the reference, and this reverses the output polarity for a given input condition.

A common application is a temperature alarm: a thermistor and fixed resistor form a potential divider, and the mid-point voltage is fed to $V_+$. A reference voltage set by a second potential divider is fed to $V_-$. When the temperature rises enough to push the thermistor voltage above the reference, the output switches to positive saturation and can drive an LED or relay.

6. The Op-Amp as a System Building Block

AQA explicitly requires you to treat the op-amp as a system building block. This means thinking at the level of inputs, outputs, and transfer behaviour — not at the level of internal transistors. The op-amp is a subsystem that can be combined with other subsystems (sensors, potential dividers, logic gates, displays) to build complete signal-processing systems.

In system terms, the comparator block has one analogue input (the signal), one reference input, and one digital-style output. It acts as an analogue-to-digital interface: it converts a continuously varying voltage into a two-state output. This is why comparators appear at the boundary between analogue sensing and digital control in almost every embedded system.

• Sensor interface: thermistor, LDR, or pressure sensor voltage compared against a threshold to trigger an output
• Zero-crossing detector: reference set to 0 V; output switches each time an AC signal crosses zero
• Window comparator: two op-amps with different references detect whether a signal lies within a specified voltage range
• Analogue-to-digital conversion: comparators form the core of flash ADC architectures

Each of these applications relies on exactly the same transfer function: $V_{out} = A_{OL}(V_+ - V_-)$, with the output saturating at the supply rails. The versatility comes not from changing the op-amp itself, but from how the surrounding circuit presents voltages to its two inputs.

7. Exam Technique and Common Mistakes

Questions on op-amp comparators appear in the Electronics section of AQA A-level Physics Paper 3 (Section B, Electronics option). They tend to combine a circuit description with a calculation or a 'describe/explain' demand. The marks are often lost not through lack of knowledge but through imprecise language or arithmetic slips.

For extended-response questions asking you to evaluate the op-amp as a system building block, structure your answer as: (1) state the transfer function and what it means, (2) explain saturation and why it is useful in comparator applications, (3) give a specific application with the correct input/output description, and (4) conclude by linking back to the 'building block' idea — the same device, reconfigured, performs different functions.

The op-amp comparator is a compact demonstration of the system building block principle: one equation, $V_{out} = A_{OL}(V_+ - V_-)$, combined with the physical reality of supply-rail saturation, produces a device that converts analogue differences into decisive digital-style outputs — the foundation of analogue signal processing at A-level.