Skip to main content
WalesElectronicsSyllabus dot point

How does negative feedback set the gain of inverting and non-inverting op-amp amplifiers?

Inverting and non-inverting amplifiers: negative feedback, the virtual earth, the closed-loop gain equations, and the voltage follower (buffer).

A focused answer to WJEC A-Level Electronics inverting and non-inverting op-amp amplifiers, covering negative feedback, the virtual earth concept, the closed-loop gain equations for both configurations, and the voltage follower used as a buffer.

Generated by Claude Opus 4.812 min answer

Reviewed by: AI editorial process; not yet individually human-reviewed

Have a quick question? Jump to the Q&A page

Jump to a section
  1. What this dot point is asking
  2. The answer
  3. Examples in context
  4. Try this

What this dot point is asking

Once an op-amp has negative feedback, it becomes a precise, predictable amplifier whose gain is set by two resistors. WJEC expects you to apply negative feedback, explain the virtual earth, use the closed-loop gain equations for inverting and non-inverting amplifiers, and describe the voltage follower as a buffer. Gain calculations and the virtual-earth and buffering explanations are core, frequently examined content.

The answer

Negative feedback

Feedback trades gain for stability, accuracy and bandwidth: the circuit no longer depends on the exact (and variable) open-loop gain of the chip.

The inverting amplifier and virtual earth

The input signal goes through RinR_{in} to the inverting input; RfR_f feeds back from the output. Because the non-inverting input is grounded and the inputs are forced equal, the inverting input sits at almost 0 V0\,\text{V}: a virtual earth. The minus sign shows the output is inverted.

The non-inverting amplifier

Here the signal goes to the non-inverting input, so the output is in phase. The gain is always at least one, and the configuration has a high input resistance, which is useful when the source is weak.

The voltage follower (buffer)

Examples in context

Example 1. Scaling a sensor output
A sensor producing only tens of millivolts is fed to a non-inverting amplifier with a gain of 100 to bring it into the range an ADC needs. The high input resistance of the non-inverting configuration means the amplifier does not load the sensor and distort its reading.
Example 2. A virtual-earth mixer input
Because the inverting input is a virtual earth, several signals can be summed there through their own resistors without interacting, which is the basis of the audio summing amplifier. The virtual earth keeps each input independent of the others.
Example 3. Buffering a potential divider
A potential divider feeding a heavy load would sag, because the load draws current and changes the divider ratio. Inserting a voltage follower between the divider and the load fixes this: the follower draws negligible current from the divider yet supplies the load, so the set voltage holds.

Try this

Q1. A non-inverting amplifier has Rf=90 kΩR_f = 90\,\text{k}\Omega and Rin=10 kΩR_{in} = 10\,\text{k}\Omega. Find its voltage gain. [2 marks]

  • Cue. Av=1+RfRin=1+9010=10A_v = 1 + \frac{R_f}{R_{in}} = 1 + \frac{90}{10} = 10.

Q2. Explain why negative feedback makes the gain of an op-amp amplifier independent of the exact open-loop gain. [2 marks]

  • Cue. Feedback forces the input difference to nearly zero, so the closed-loop gain is fixed by the resistor ratio; as long as the open-loop gain is very large, its precise value does not matter.

Exam-style practice questions

Practice questions written in the style of WJEC exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

WJEC Eduqas 20205 marksAn inverting amplifier uses an input resistor of 10 kΩ10\,\text{k}\Omega and a feedback resistor of 47 kΩ47\,\text{k}\Omega. Calculate the voltage gain, the output for a 0.20 V0.20\,\text{V} input, and explain the meaning of the virtual earth at the inverting input.
Show worked answer →

The inverting amplifier gain is minus the ratio of the feedback resistor to the input resistor.

Gain: Av=−RfRin=−4710=−4.7A_v = -\dfrac{R_f}{R_{in}} = -\dfrac{47}{10} = -4.7.

Output for a 0.20 V0.20\,\text{V} input: Vout=Av×Vin=−4.7×0.20=−0.94 VV_{out} = A_v \times V_{in} = -4.7 \times 0.20 = -0.94\,\text{V} (inverted).

Virtual earth: with the non-inverting input grounded and huge open-loop gain, the inverting input is held at almost exactly 0 V0\,\text{V} even though it is not directly connected to ground. Negative feedback forces the voltage difference between the inputs to nearly zero, so the inverting input sits at virtual earth.

Markers reward the gain of −4.7-4.7, the output of about −0.94 V-0.94\,\text{V}, and the virtual-earth explanation via negative feedback.

WJEC Eduqas 20184 marksState the gain equation for a non-inverting amplifier and explain why a voltage follower, despite having a gain of one, is so useful.
Show worked answer →

Non-inverting gain: Av=1+RfRinA_v = 1 + \dfrac{R_f}{R_{in}}, where RinR_{in} is the resistor from the inverting input to ground and RfR_f is the feedback resistor. The gain is always at least one and the output is in phase with the input.

A voltage follower is a non-inverting amplifier with the output fed straight back, so Rf=0R_f = 0 and the gain is exactly one. It is useful because of its impedance properties: it has a very high input resistance (drawing almost no current from the source) and a very low output resistance (able to drive a load). It therefore buffers a high-impedance source from a low-impedance load, preventing the load from disturbing the source.

Markers reward the non-inverting gain equation and the buffering role (high input resistance, low output resistance) of the follower.

Related dot points

Sources & how we know this