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

Choices:  
A: The maximum frequency for a filter circuit using that type of amplifier  
B: The frequency at which the open-loop gain of the amplifier equals one  
C: The gain of the amplifier at a filter’s cutoff frequency  
D: The frequency at which the amplifier’s offset voltage is zero    

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

To calculate the Gain-Bandwidth (GBW) of an op-amp, remember it is defined by the unity-gain (open-loop) frequency.

Correct answer (B): The frequency at which the open-loop gain of the amplifier equals one
- This is the unity-gain frequency, often called $f_T$.
- For a single-pole op-amp, the open-loop gain falls at −20 dB/decade, so the product of closed-loop gain and bandwidth is approximately constant:
  $$GBW \approx f_T \approx A_{CL} \times BW$$
- At unity gain ($A_{CL}=1$), the bandwidth equals the GBW, which is the frequency where the open-loop gain crosses 1 (0 dB).

Why the other choices are incorrect:
- A: “Maximum frequency for a filter circuit” — Filter bandwidth depends on the entire circuit, not just the op-amp’s GBW. GBW is an op-amp parameter, not a “maximum filter frequency.”
- C: “Gain at a filter’s cutoff frequency” — That describes a filter characteristic (e.g., −3 dB point), not the op-amp’s GBW definition.
- D: “Frequency where offset voltage is zero” — Offset voltage is a DC parameter; it does not go to zero at some frequency and is unrelated to GBW.

Useful formulas and rules of thumb:
- For a single-pole op-amp:
  $$A_{OL}(f) \approx \frac{A_0}{\sqrt{1 + (f/f_p)^2}}$$
  where $A_0$ is DC open-loop gain and $f_p$ is the dominant pole.
- Gain-bandwidth relation (design rule):
  $$BW \approx \frac{GBW}{A_{CL}}$$
- Unity-gain frequency:
  $$GBW \equiv f_T \text{ (frequency where } A_{OL} = 1\text{)}$$