Linearized Dispersion Relation and Green's Function for Discrete-Charge-Transfer Devices with Incomplete Transfer

In an important new class of discrete-charge-transfer devices including charge-coupled devices1 (CCD's), bucket-brigade shift registers,2-3 and other shift-register or image-detection or display devices, externally applied time-dependent voltages step captive charge along a chain of equivalent discrete .storage stations. In some of these devices the charge transfer is imperfect with a fraction of the charge failing to advance and a fraction lost altogether during each step. Explicit expressions are constructed here for the dispersion relations and Green's functions which describe this imperfect performance under conditions when the fractions of charge that go astray can be described by constant parameters characteristic of the particular device. The theory of analog signal processing is based on the properties 1741 1742 THE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1971 of sine waves, and analog devices are conventionally characterized by the dispersion, attenuation, etc., which they cause. A second standard method of characterization is based on the distortion and attenuation of pulses. In contrast, discrete-charge-transfer devices are presently characterized by their charge-transfer efficiencies (fractions). The solutions given here were chosen to facilitate the application of conventional signal processing theory to these new discrete devices. That is, they show the equivalence of these three methods of characterization in the .small-signal limit and provide the appropriate interrelating formulas.