Ideal Op-Amp Properties: Gain and Resistance Revision Notes | A Level AQA Physics

1. Why Ideal Properties Matter

An operational amplifier (op-amp) is the workhorse of analogue electronics. Before you can analyse any op-amp circuit — inverting amplifier, summing amplifier, comparator — you need a mental model of how the device behaves. That model is built on two ideal properties.

Real op-amps are complicated: their gain varies with frequency, their input terminals do draw tiny currents, and their output can only swing so far. For A-level analysis, though, the ideal model gives answers that are accurate enough for exam purposes and, crucially, reveals the underlying physics with complete clarity.

The two properties you must know are: infinite open-loop gain and infinite input resistance. Everything else in op-amp circuit analysis flows from these two starting points.

2. Infinite Open-Loop Gain

The open-loop gain $A_{OL}$ is the gain of the op-amp with no feedback path connected. For an ideal op-amp, $A_{OL} = \infty$. The output voltage $V_{out}$ is related to the differential input voltage $V_d = V_+ - V_-$ by:

Think of it this way: if $A_{OL}$ is infinite, then even a difference of one microvolt between the two inputs would theoretically produce an infinite output. In practice, the output is limited by the supply voltage — but the ideal assumption of infinite gain is what makes the maths of feedback circuits so clean.

Here is the key consequence. When a negative feedback network is added (as in an inverting or non-inverting amplifier), the circuit automatically adjusts until $V_+ - V_- \approx 0$. Because any non-zero difference would be multiplied by infinity, the feedback loop is forced to keep the two inputs at virtually the same potential. This is the origin of the virtual earth assumption you will use in gain calculations.

The virtual earth is not a real connection to 0 V — no current flows to earth through that node. It is a consequence of the gain being so large that the feedback loop cannot tolerate any measurable difference between the inputs. Examiners test this distinction regularly.

3. Infinite Input Resistance

The second ideal property concerns the input terminals themselves. For an ideal op-amp, the resistance between the two input terminals — and between each terminal and earth — is infinite. This means no current flows into or out of either input terminal.

Picture a voltmeter with a very high internal resistance: it reads the voltage across a component without drawing any current and therefore without disturbing the circuit. An ideal op-amp input behaves the same way — it senses the voltage at each terminal without loading the source that provides it.

The practical consequence is significant. When you write Kirchhoff's current law at the inverting input node of an inverting amplifier, you can state that all the current flowing through the input resistor $R_1$ must continue through the feedback resistor $R_f$ — none of it disappears into the op-amp input. This single assumption is what allows the standard gain formula $A_v = -R_f / R_1$ to be derived cleanly.

4. Connecting the Two Properties: A Worked Example

The two ideal properties work together every time you analyse an op-amp circuit. The worked example below shows how they combine to derive the voltage gain of an inverting amplifier — a standard exam task.

Worked example: Deriving the Gain of an Inverting Amplifier Using Ideal Properties

An inverting amplifier has an input resistor $R_1 = 10\text{ k}\Omega$ and a feedback resistor $R_f = 47\text{ k}\Omega$. The non-inverting input is connected to 0 V. Use the ideal op-amp properties to find the voltage gain $A_v$.

1. $A_{OL} = \infty \Rightarrow V_+ - V_- = 0$ — Because the open-loop gain is infinite, the feedback loop forces the differential input voltage to zero. Since $V_+ = 0\text{ V}$, the inverting input is also at 0 V. This is the virtual earth. [B1]
2. $I_{in} = 0\text{ A}$ at the inverting input terminal — Because input resistance is infinite, no current enters the op-amp at the inverting input. All current through $R_1$ must therefore flow through $R_f$. [B1]
3. $I = \dfrac{V_{in} - 0}{R_1} = \dfrac{V_{in}}{10\text{ k}\Omega}$ — The voltage at the left end of $R_1$ is $V_{in}$; the right end is at virtual earth (0 V). Ohm's law gives the current. [M1]
4. $V_{out} = 0 - I \times R_f = -\dfrac{V_{in}}{10\text{ k}\Omega} \times 47\text{ k}\Omega$ — The current flows from the virtual earth node through $R_f$ to the output. The output is below the virtual earth, hence the negative sign. [M1]
5. $A_v = \dfrac{V_{out}}{V_{in}} = -\dfrac{R_f}{R_1} = -\dfrac{47}{10} = -4.7$ — The gain is negative (inverting) and has magnitude 4.7. The formula $A_v = -R_f / R_1$ is a direct result of both ideal properties acting together. [A1]

Answer: $A_v = -4.7$ (the output is inverted and 4.7 times larger in magnitude than the input)

Notice that neither the value of $A_{OL}$ nor any current into the op-amp appeared in the final answer. The ideal properties did their job silently: they justified the virtual earth and the current continuity, and then stepped aside. That is exactly how you should present this reasoning in an exam.

5. Comparing Ideal and Real Op-Amp Behaviour

The ideal model is a deliberate simplification. Real op-amps, such as the 741, have a large but finite open-loop gain (typically around $10^5$ at low frequencies) and a large but finite input resistance (around $2\text{ M}\Omega$ for a bipolar-input device). For most A-level calculations, these values are close enough to the ideal that the error introduced is negligible.

The table shows that real values are large, not infinite — but the ideal assumption introduces only a tiny percentage error in most circuits. Where real behaviour matters (for example in precision instrumentation or high-frequency applications) engineers must account for these departures, but that analysis is beyond the A-level specification.

6. Exam Technique and Common Mistakes

AQA questions on ideal op-amp properties tend to fall into three categories: state a property, explain a consequence, or use a property to justify a step in a calculation. Each requires a slightly different approach.

When a question says state, give the property in precise terms — 'infinite open-loop gain' or 'infinite input resistance' — and nothing more. Adding an unprompted explanation wastes time and risks introducing an error that costs marks.

When a question says explain, you need a two-part answer: state the ideal property, then state its consequence. For example: 'The input resistance is infinite, so no current flows into the inverting input terminal. Therefore, the current through $R_1$ is equal to the current through $R_f$.' That chain of reasoning is what earns the marks.

Together, infinite open-loop gain and infinite input resistance form the complete ideal model that underpins every op-amp calculation at A-level: the first property gives you the virtual earth, and the second gives you current continuity through the feedback network.