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In resonant circuits, impedance bandwidth is mostly the difference between the frequencies where the impedance increases with factor 1.414 (series resonant circuit), or decreases with factor 1.414 (parallel resonant circuit). BWimp = Fcenter/Q. In antennas it can be the difference between the frequencies where the VSWR reaches a certain value (for example SWR=2).
Power bandwidth of a system is mostly the difference in frequencies where the power dropped with a certain percentage below the mid-band output power. Half-power bandwidth is frequently used.
In signal analysis, the power bandwidth can be that frequency bandwidth that contains a certain part of the total available power (for example 50% or 99%). This definition can also be applied to filters that have noisy input signal. A lossless filter that outputs 1uW based on an input signal of 1nW/Hz has a power / noise bandwidth of 1u/1n=1000 Hz.
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