*Question E7G06:
What is the gain-bandwidth of an operational amplifier?*  

*Correct Answer is  B: The frequency at which the open-loop gain of the amplifier equals one*  

### AI Response: (may contain errors)  

The gain-bandwidth product of an operational amplifier (op-amp) is a key parameter that describes the relationship between the gain and bandwidth of the amplifier. It is defined as the frequency at which the open-loop gain of the amplifier equals one (unity gain).

### Explanation:

1. **Correct Answer (B):**  
   - The gain-bandwidth product is a constant for a given op-amp and is the product of the amplifier's bandwidth and its gain.  
   - At the gain-bandwidth frequency, the open-loop gain of the amplifier is equal to one. This means that if you increase the gain, the bandwidth decreases proportionally, and vice versa.  
   - This is a fundamental characteristic of op-amps and is used to determine how the amplifier will perform at different frequencies and gains.

2. **Why the Other Choices are Incorrect:**
   - **Choice A:** The maximum frequency for a filter circuit using that type of amplifier is not directly related to the gain-bandwidth product. The filter's cutoff frequency depends on the specific filter design and components used, not just the op-amp's gain-bandwidth.
   - **Choice C:** The gain of the amplifier at a filter’s cutoff frequency is not the definition of gain-bandwidth. The cutoff frequency is specific to the filter design and does not define the gain-bandwidth product.
   - **Choice D:** The frequency at which the amplifier’s offset voltage is zero is unrelated to the gain-bandwidth product. Offset voltage is a separate parameter that deals with the DC performance of the op-amp, not its frequency response.

### Useful Formula:

- **Gain-Bandwidth Product (GBP):**  
  $$ \text{GBP} = A_{\text{open-loop}} \times f_{\text{bandwidth}} $$  
  where:
  - $A_{\text{open-loop}}$ is the open-loop gain of the amplifier.
  - $f_{\text{bandwidth}}$ is the frequency at which the gain is measured.

This concept is crucial for understanding how op-amps behave in different circuit configurations and is essential for designing stable and effective amplifier circuits.