*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 is a key parameter that defines its performance in various applications. 

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

- The gain-bandwidth product is defined as the frequency at which the open-loop gain of the amplifier drops to 1 (0 dB). This means that as the frequency increases, the gain of the amplifier decreases, and the product of the gain and the frequency remains constant. This is crucial for understanding how the amplifier will behave in different frequency ranges.

### Why the Other Choices are Incorrect:

- **A: The maximum frequency for a filter circuit using that type of amplifier.**
  - This choice is misleading because the gain-bandwidth product does not directly define the maximum frequency of a filter circuit. Instead, it relates to the amplifier's gain at various frequencies, not the filter's operational limits.

- **C: The gain of the amplifier at a filter’s cutoff frequency.**
  - This is incorrect because the gain at the cutoff frequency is not the same as the gain-bandwidth product. The cutoff frequency is where the gain starts to roll off, but the gain-bandwidth product specifically refers to the frequency at which the gain is 1.

- **D: The frequency at which the amplifier’s offset voltage is zero.**
  - This choice is incorrect as well. The offset voltage is a DC parameter and does not relate to the gain-bandwidth product, which is concerned with AC performance and frequency response.

### Useful Formula:
The gain-bandwidth product can be expressed as:

$$
GBW = A_{OL} \times f
$$

where:
- $GBW$ = gain-bandwidth product (constant for a given op-amp)
- $A_{OL}$ = open-loop gain (in linear terms)
- $f$ = frequency (in hertz)

This formula illustrates that as the frequency increases, the open-loop gain decreases, maintaining a constant product. Understanding this relationship is essential for designing circuits that utilize operational amplifiers effectively.