A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Limitations of Real Operational Amplifiers and Frequency Response — mark scheme explained
The short answer
In the realm of electronics, operational amplifiers (op-amps) are fundamental components used in a wide array of circuits. While ideal op-amps have certain characteristics that make them perfect for theoretical analysis, real-world op-amps come with limitations that must be understood to design effective circuits.
The question
An operational amplifier has a gain-bandwidth product (GBW) of 1 MHz. If the open-loop gain (A 0 ) is 100,000 V/V, what is the cutoff frequency (f c )?
[Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For calculation questions, marks are typically awarded for correct use of formulas, substitution of values, and the final answer. For explanation questions, marks are given for clarity, completeness, and accuracy of the response.
What the command words demand
- Calculate
- Perform a numerical calculation using the given data and appropriate formulas
- Explain
- Provide a detailed explanation of a concept or phenomenon, including relevant principles and relationships
- Determine
- Find a specific value or parameter based on given information and calculations
- Compare
- Identify and describe similarities and differences between two or more concepts or systems
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate approximately 2-3 minutes per mark to ensure you have enough time to carefully read the question, perform calculations, and provide well-structured answers.
- Identify the given values: GBW = 1 MHz, A 0 = 100,000 V/V0 marks
- Use the formula for gain-bandwidth product: GBW = A 0 × f c1 mark
- Rearrange the formula to solve for f c : f c = GBW / A 01 mark
- Substitute the given values: f c = 1 MHz / 100,000 V/V1 mark
- Calculate the result: f c = 10 Hz1 mark
Final answer: f c = 10 Hz
Work through every step correctly and you earn all 4 marks.
Another worked example
A closed-loop op-amp circuit has a feedback factor (β) of 0.01 and an open-loop gain (A OL ) of 10,000 V/V. Calculate the closed-loop gain (A CL ).
- Identify the given values: β = 0.01, A OL = 10,000 V/V0 marks
- Use the formula for closed-loop gain: A CL = A OL / (1 + βA OL )1 mark
- Substitute the given values: A CL = 10,000 V/V / (1 + 0.01 × 10,000 V/V)1 mark
- Calculate the denominator: 1 + 0.01 × 10,000 = 1 + 100 = 1011 mark
- Divide to find the closed-loop gain: A CL = 10,000 V/V / 101 ≈ 99.01 V/V2 marks
Final answer: A CL ≈ 99.01 V/V
Work through every step correctly and you earn all 5 marks.
Common mistakes
Confusing the gain-bandwidth product (GBW) with the open-loop gain (A 0 )
Why it happens: Students sometimes mix up these two concepts, leading to incorrect calculations and misunderstandings of how op-amps behave at different frequencies.
Fix: Always remember that GBW is a product of A 0 and f c , and it remains constant for a given op-amp. Practice using the formula GBW = A 0 × f c in various contexts.
Forgetting to convert units when calculating frequency
Why it happens: Students often forget to ensure that all units are consistent, especially when dealing with MHz and Hz. This can lead to significant errors in calculations.
Fix: Always double-check the units of your given values and make sure they are consistent before performing any calculations. Convert units as necessary.
Misinterpreting the -3 dB point
Why it happens: The -3 dB point is a critical concept in frequency response, but students sometimes misunderstand what it represents. They might think it means the gain drops to zero or that it is always at 1 kHz.
Fix: Understand that the -3 dB point is where the gain has dropped by 3 dB from its maximum value. This is a standard reference point in frequency response analysis.
Incorrectly applying the feedback factor (β) in closed-loop calculations
Why it happens: Students sometimes apply the feedback factor incorrectly, leading to errors in calculating closed-loop gain and bandwidth. They might use β instead of 1 + βA OL in the denominator.
Fix: Always use the correct formula for closed-loop gain: A CL = A OL / (1 + βA OL ). Practice with different values of β and A OL to reinforce this concept.
Overlooking the impact of gain-bandwidth product on stability
Why it happens: Students might focus solely on gain and bandwidth without considering how these parameters affect circuit stability. They might not realize that a large phase shift at certain frequencies can lead to oscillations.
Fix: Understand that the gain-bandwidth product affects both gain and phase response, which in turn impacts stability. Always consider the potential for instability when designing high-frequency circuits.
Failing to account for other limitations of real op-amps
Why it happens: Students sometimes focus only on the gain-bandwidth product and overlook other important limitations such as input offset voltage, input bias current, and power supply rejection ratio (PSRR). This can lead to incomplete circuit designs.
Fix: Always consider all relevant limitations of real op-amps when designing circuits. Practice identifying and addressing these limitations in different scenarios.
Where the marks go
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Calculate Cutoff Frequency | Rearrange the gain-bandwidth product relationship to find the cutoff frequency of an op-amp. | 4 |
| Calculate Closed-Loop Gain | Use the negative-feedback formula to find the closed-loop gain from open-loop gain and feedback factor. | 5 |
| Closed-Loop Bandwidth | Calculate the closed-loop bandwidth of an op-amp using gain-bandwidth product and feedback factor. | 6 |
| Closed-Loop Gain Calculation | Calculate an op-amp's closed-loop gain from open-loop gain and feedback factor. | 5 |
| Total across these question types | 20 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.