E12: Amplifier Circuits
Gain, bandwidth, feedback, inverting amplifier and summing amplifier
Amplifier Circuits
Gain, bandwidth, feedback, inverting amplifier and summing amplifier
Key Fact: Voltage gain is the ratio of output voltage to input voltage: Av = Vout/Vin; it can be expressed as a number or in decibels (dB).
Key Fact: Gain in decibels: G(dB) = 20 log₁₀(Av); a gain of 10 equals 20 dB, a gain of 100 equals 40 dB.
Key Fact: Bandwidth is the range of frequencies over which the amplifier operates within specification, typically defined between the −3 dB points.
Key Fact: The gain-bandwidth product (GBW) is constant for a given op-amp: as closed-loop gain increases, bandwidth decreases proportionally.
Key Fact: Negative feedback reduces gain but increases bandwidth, improves linearity and stabilises the circuit against component variations.
Key Fact: The inverting amplifier has Av = −Rf/Rin; its input impedance equals Rin (not the op-amp's input impedance).
Key Fact: The summing amplifier (inverting) combines multiple inputs: Vout = −Rf(V1/R1 + V2/R2 + V3/R3).
Key Fact: A summing amplifier with equal input resistors gives Vout = −(Rf/R)(V1 + V2 + V3); it acts as an analogue adder.
Key Fact: If Rf = R for each input, the output is the negative sum of all input voltages.
Key Fact: The output resistance of an op-amp with negative feedback is very low, making it close to an ideal voltage source.
Key Fact: Power bandwidth is the maximum frequency at which the output can swing fully without slew-rate-induced distortion.
Key Fact: Input offset voltage is a small differential voltage needed to zero the output; it can be corrected with a trimming potentiometer.
📋 Key Vocabulary and Concepts
For Amplifier Circuits, you must know:
- Voltage gain: The ratio of output voltage to input voltage; Av = Vout/Vin.
- Bandwidth: The frequency range between the upper and lower −3 dB points of an amplifier.
- Gain-bandwidth product: The product of closed-loop gain and bandwidth; constant for a given op-amp (e.g. 1 MHz for 741).
- Summing amplifier: An inverting op-amp circuit that produces an output proportional to the weighted sum of multiple inputs.
- Decibel (dB): A logarithmic unit for gain: G(dB) = 20 log₁₀(Av).
- −3 dB point: The frequency at which the output power has fallen to half its mid-band value; gain is 0.707 of maximum.
❓ Practice Questions
Q: An amplifier has an input of 50 mV and an output of 2 V. Calculate the voltage gain and express it in dB.
Q: A summing amplifier has Rf = 100 kΩ and three inputs each with R = 20 kΩ. If V1 = 1 V, V2 = 2 V, V3 = 0.5 V, find Vout.
Q: An op-amp has a GBW of 1 MHz. If the closed-loop gain is 100, what is the bandwidth?
Q: State two advantages of using negative feedback in an amplifier.
Q: What is the input impedance of an inverting amplifier with Rin = 22 kΩ?
✅ Answers
- Av = 2/0.05 = 40. G(dB) = 20 log₁₀(40) = 20 × 1.602 = 32.0 dB.
- Vout = −Rf(V1/R1 + V2/R2 + V3/R3) = −100(1/20 + 2/20 + 0.5/20) = −100 × 0.175 = −17.5 V.
- Bandwidth = GBW/Av = 1 × 10⁶/100 = 10 kHz.
- Negative feedback stabilises gain against component variation and increases bandwidth (also reduces distortion and noise).
- The input impedance equals Rin = 22 kΩ, because the inverting input is a virtual earth.
🎯 Exam Tips
- Convert between linear gain and dB: G(dB) = 20 log₁₀(Av); Av = 10^(G/20).
- For summing amplifier questions, write the full equation first, then substitute values step by step.
- Remember the output of a summing amplifier is inverted — include the minus sign.
- When discussing bandwidth, always refer to the −3 dB point as the definition of bandwidth.
- Use the gain-bandwidth product to find bandwidth: BW = GBW/closed-loop gain.
📝 Exam Technique
GCSE Electronics Exam Tips — Amplifier Circuits:
1. For Amplifier Circuits questions, use correct electronic symbols and terminology
2. Always show your working in calculations, including units at each step
3. When analysing circuits, state which law or rule you are applying first
4. For evaluation questions on Amplifier Circuits, compare component choices and consider cost, reliability and tolerance
5. Draw circuit diagrams neatly with conventional symbols
1. For Amplifier Circuits questions, use correct electronic symbols and terminology
2. Always show your working in calculations, including units at each step
3. When analysing circuits, state which law or rule you are applying first
4. For evaluation questions on Amplifier Circuits, compare component choices and consider cost, reliability and tolerance
5. Draw circuit diagrams neatly with conventional symbols
⚠️ Common Errors
✗ Using power gain formula (10 log₁₀) for voltage gain in dB. ✓ Voltage gain in dB uses 20 log₁₀(Av); power gain uses 10 log₁₀(Pout/Pin).
✗ Assuming the input impedance of an inverting amplifier equals the op-amp's input impedance. ✓ The input impedance of an inverting amplifier equals Rin, because the inverting input is a virtual earth.
✗ Forgetting that a summing amplifier's output is inverted. ✓ The output of a summing amplifier is negative (inverted); Vout = −Rf(Σ Vi/Ri).
✗ Confusing open-loop bandwidth with closed-loop bandwidth. ✓ Open-loop bandwidth is very small (a few Hz); closed-loop bandwidth = GBW/closed-loop gain.
✍️ Model Answer
Full-Mark Response
Explain the concept of gain-bandwidth product and describe how a summing amplifier combines multiple input signals.
The gain-bandwidth product (GBW) is a constant for a given op-amp, representing the frequency at which the open-loop gain falls to unity (0 dB). For any closed-loop configuration, the product of gain and bandwidth equals the GBW: as closed-loop gain increases, bandwidth decreases proportionally. For example, a 741 op-amp with GBW = 1 MHz has a bandwidth of 1 MHz at unity gain, 100 kHz at Av = 10, and 10 kHz at Av = 100. A summing amplifier is an inverting op-amp circuit with multiple input resistors connected to the inverting input. Each input voltage is weighted by the ratio Rf/Ri, and the output is the inverted sum: Vout = −Rf(V1/R1 + V2/R2 + … + Vn/Rn). When all input resistors are equal (Ri = R), the output is simply −(Rf/R)(V1 + V2 + … + Vn), making it a true analogue adder. This circuit is used in audio mixing, DACs and analogue computation.
📊 AO Deep Dive
Assessment Objective Analysis
AO1 (Knowledge & Understanding): Demonstrate knowledge and understanding of amplifier circuits, including electronic components, circuit theory and systems concepts relevant to WJEC Eduqas C690QS.
AO2 (Application): Apply knowledge and understanding of amplifier circuits to analyse, design and construct electronic circuits and systems.
AO3 (Evaluation): Evaluate electronic circuits and systems, making reasoned judgements about design choices, performance and practical considerations, constructing supported arguments.
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