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
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Identify the given values: GBW = 1 MHz, A 0 = 100,000 V/V
- S2
Use the formula for gain-bandwidth product: GBW = A 0 × f c
- S3
Rearrange the formula to solve for f c : f c = GBW / A 0
- S4
Substitute the given values: f c = 1 MHz / 100,000 V/V
- S5
Calculate the result: f c = 10 Hz
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Identify the given values: GBW = 1 MHz, A 0 = 100,000 V/V
- S2
Use the formula for gain-bandwidth product: GBW = A 0 × f c
- S3
Rearrange the formula to solve for f c : f c = GBW / A 0
- S4
Substitute the given values: f c = 1 MHz / 100,000 V/V
- S5
Calculate the result: f c = 10 Hz
Final answer: f c = 10 Hz
Common mistakes
- Confusing the gain-bandwidth product (GBW) with the open-loop gain (A 0 ) — 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 — 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 — 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 — 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 — 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 — 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
- Full worked solution (all marking points)4 marks