Consider a closed loop (feedback) system with the reference input being r and the output being y. Bandwidth is defined as the maximum frequency at which the output (y) of this closed loop system will track an input sinusoid in a satisfactory manner. By convention, it is the frequency w at which y is attenuated to a factor of 0.707 times r, i.e., the frequency at which |y|/|r|=0.707. In terms of the Bode magnitude plot, this translates to the frequency w at which the magnitude of the closed loop transfer function is approx.=3dB (-20log10(0.707) =3.0116).