Gain bandwidth product

The gain bandwidth product (GBW) is the product of:

• The largest gain in the passband $T_{max}$, and
• The bandwidth of that passband ${\omega }_C$.

Operational amplifiers also by default act as low-pass filters when not in their feedback configuration (i.e., they’re in open-loop). We can write their open-loop gain as the transfer function:

$$A(j\omega )=\frac{A_0}{1+j\omega /{\omega }_C}$$ $$V_O(s)=A(s)[V_p(s)-V_n(s)]$$

where $A_0=A(j\omega ){|}_{\omega =0}$ is the DC gain. For the open-loop op amp, the GBW $=A_0{\omega }_C$.¹

Footnotes

1. Proof is in Prof Najm’s notes, lecture 29. ↩