Question E7G08:
How does the gain of an ideal operational amplifier vary with frequency?  

Choices:  
A: It increases linearly with increasing frequency  
B: It decreases linearly with increasing frequency  
C: It decreases logarithmically with increasing frequency  
D: It does not vary with frequency    

Correct Answer is  D: It does not vary with frequency  

To calculate the ideal op-amp’s frequency response:

1) Why the correct answer is correct (D)
- In the ideal op-amp model, the open-loop gain is infinite and bandwidth is infinite, so gain is constant for all frequencies.
- Mathematically: $A_{OL}(f)$ is a constant (ideally $A_{OL} \to \infty$), so it does not vary with frequency.

2) Why the other choices are incorrect
- A: Increases linearly with frequency — Not true for an ideal op-amp. No part of the ideal model implies gain rising with frequency.
- B: Decreases linearly with frequency — Real op-amps don’t decrease linearly in the linear frequency domain; this is not the ideal model.
- C: Decreases logarithmically with frequency — This describes real (non-ideal) op-amps whose open-loop gain rolls off with a slope of about −20 dB/decade after a dominant pole, but the question explicitly asks about an ideal op-amp.

3) Useful formulas and rules of thumb
- Ideal op-amp: $A_{OL}(f) = \text{constant}$ (independent of $f$), infinite bandwidth.
- Real op-amp (for comparison):
  - Single-pole model: $$A_{OL}(f) \approx \frac{A_0}{\sqrt{1+(f/f_p)^2}}$$
  - High-frequency roll-off: about −20 dB/decade beyond $f_p$.
  - Gain-bandwidth product (approximately constant): $$GBW \approx A_{CL} \cdot f_{BW}$$
  
For the exam, remember: ideal op-amp gain does not vary with frequency.