*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)  

The correct answer to the question about the gain of an ideal operational amplifier (op-amp) is:

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

### Explanation of the Correct Answer:
- An ideal operational amplifier is characterized by infinite open-loop gain, which means that its gain remains constant regardless of the frequency of the input signal. This is a theoretical concept, as real op-amps do have limitations, but for the purpose of the exam, we consider the ideal case.

### Why the Other Choices are Incorrect:
- **A: It increases linearly with increasing frequency**  
  This is incorrect because the gain of an ideal op-amp does not increase with frequency. In fact, real op-amps typically exhibit a decrease in gain at higher frequencies due to various factors like internal capacitances.

- **B: It decreases linearly with increasing frequency**  
  While this might be true for some real op-amps, it does not apply to ideal op-amps. The ideal op-amp maintains a constant gain across all frequencies.

- **C: It decreases logarithmically with increasing frequency**  
  This is also incorrect for ideal op-amps. Although real op-amps can show a logarithmic decrease in gain at high frequencies, the ideal op-amp is defined to have constant gain.

### Useful Formulas or Rules of Thumb:
- For real op-amps, the gain-bandwidth product (GBP) is a key concept. It states that the product of the gain and the bandwidth of the amplifier is constant. This can be expressed as:

$$
GBP = Gain \times Bandwidth
$$

- As frequency increases, the gain of a real op-amp decreases, but for an ideal op-amp, this relationship does not apply, reinforcing the idea that its gain does not vary with frequency.

In summary, remember that for an ideal op-amp, the gain is constant across all frequencies, which is a fundamental characteristic that distinguishes it from real-world devices.