Characteristic Eq. of coupled-bunch motion of beam governed by a feedback (FB) is given to find FB's stabilizing effect against coherent instabilities or, say, injection error damping rates. Quite a general FB's schematics is involved: (ⅰ) it has two paths, the in-phase and quadrature (or amplitude and phase in a small-signal approach), with unequal gains; (ⅱ) may employ distinct RF-bands to pick-up beam data and feed correction back to the beam. To account for cross-talk between various field and beam current harmonics inflicted by frequency down- and up-mixing, an impedance matrix (with, at most, three non-trivial elements per row) is introduced as a natural concept to gain insight into 'FB & beam' dynamics. The important class of FBs to counteract heavy beam loading of accelerating cavities is included into analysis as a particular case.
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