Gain-Bandwidth Product
GBW = A₀ · f₋₃dB. The product of DC gain and bandwidth is constant for a single-pole system.
Open-loop f₋₃dB
1.00 kHz
GBW / A₀
Closed-loop Gain
90.91 V/V
A₀ / (1 + β·A₀)
Closed-loop BW
11.00 kHz
GBW / A_cl
A(f) = A₀ / (1 + j·f/f₀), GBW = A₀·f₀
A_cl(f) = A₀ / (1 + β·A₀ + j·f/f₀): gain A₀/(1 + β·A₀), bandwidth f₀·(1 + β·A₀)
The closed-loop gain shown is A₀/(1 + β·A₀), the non-inverting (noise) gain; an inverting stage has the same bandwidth but signal gain −(1 − β)/β.
Single-pole op amp; higher poles, slew rate and phase margin are left out.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Single-pole op amp with frequency-independent feedback fraction β. Higher-order poles, phase margin, slew rate and output limits are left out.
- Franco S. (2015). Design with Operational Amplifiers and Analog Integrated Circuits, 4th ed. McGraw-Hill. Ch. 6: single-pole open-loop response, constant gain-bandwidth product.