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

*Correct Answer is  D: It does not vary with frequency*  

### AI Response: (may contain errors)  

An ideal operational amplifier (op-amp) is a theoretical device with certain perfect characteristics. One of these characteristics is that its gain is infinite and does not vary with frequency. This is why the correct answer is:

**D: It does not vary with frequency**

### Explanation:

1. **Why the correct answer is correct:**
   - An ideal op-amp is assumed to have infinite gain across all frequencies. This means that its gain is constant and does not change with frequency. In reality, practical op-amps have a gain that decreases with increasing frequency, but the question specifically asks about an "ideal" op-amp.

2. **Why the other choices are incorrect:**
   - **A: It increases linearly with increasing frequency**  
     This is incorrect because an ideal op-amp's gain is constant and does not increase with frequency.
   
   - **B: It decreases linearly with increasing frequency**  
     This is incorrect for an ideal op-amp. However, in practical op-amps, the gain does decrease with frequency, but not linearly. It typically decreases at a rate of -20 dB/decade after a certain frequency.
   
   - **C: It decreases logarithmically with increasing frequency**  
     This is incorrect for an ideal op-amp. In practical op-amps, the gain decreases at a logarithmic rate (in dB), but the question is about an ideal op-amp.

### Useful Formulas or Rules of Thumb:

- For a practical op-amp, the gain-bandwidth product is constant. This means:
  $$ A_v \times f = \text{constant} $$
  where $A_v$ is the voltage gain and $f$ is the frequency. This relationship does not apply to an ideal op-amp, which is assumed to have infinite gain at all frequencies.