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If you build an op-amp circuit with a gain of 100 to amplify high-frequency signals, you might find that your output voltage unexpectedly collapses to almost zero.
Op-amps cannot deliver maximum amplification across all frequencies because internal compensation limits their speed to ensure circuit stability.

The Gain-Bandwidth Trade-Off

In the 1930s, Hendrik Bode at Bell Labs studied feedback amplifiers and demonstrated that adding a controlled high-frequency roll-off prevents circuits from oscillating out of control.
An op-amp's open-loop gain (AOLA_{OL}) is its raw amplification without feedback, while the gain-bandwidth product (GBP) is the constant value representing the product of gain and frequency along the standard βˆ’20Β dB/decade-20\text{ dB/decade} roll-off slope.
Because the slope falls at a constant rate, any decrease in closed-loop gain produces an equal proportional increase in available bandwidth: GBP=ACLΓ—fβˆ’3dB\text{GBP} = A_{CL} \times f_{-3\text{dB}}
The βˆ’3Β dB-3\text{ dB} cut-off frequency (fβˆ’3dBf_{-3\text{dB}}) is the upper frequency limit where the closed-loop voltage gain drops to 1/2β‰ˆ0.7071/\sqrt{2} \approx 0.707 (or βˆ’3Β dB-3\text{ dB}) of its mid-band value.
How do we apply this relationship to determine the operational limit of a practical amplifier?

Calculating Non-Inverting Bandwidth

For a non-inverting op-amp configuration, the closed-loop voltage gain is ACL=1+RfR1A_{CL} = 1 + \frac{R_f}{R_1}, where RfR_f is the feedback resistor and R1R_1 connects the inverting terminal to ground.
Suppose you design an amplifier using an op-amp with a rated GBP=4Β MHz\text{GBP} = 4\text{ MHz}, using resistors Rf=39Β kΞ©R_f = 39\text{ k}\Omega and R1=1Β kΞ©R_1 = 1\text{ k}\Omega.
First, calculate the closed-loop gain: ACL=1+39Β kΞ©1Β kΞ©=40A_{CL} = 1 + \frac{39\text{ k}\Omega}{1\text{ k}\Omega} = 40