Analysis of pulse-width modulation with a variable transport lag in a rendezvous radar

The application involves two solid-state transmitters, separated in space but moving with respect to one another. One in an interrogator and another in a transponder, reduce peak power by simultaneously transmitting to each other a maximum pulse width equal to the varying transmission time between them. Although difficult to visualize or to analyze intuitively on a continuous basis, system operation may be determined approximately from error-detector difference equations, state variables, flow graphs, and discrete transforms. As shown, interrelated control loops exist. One, a phase-lock loop, equates both transmitted pulses in width and in time; another, a range-track loop, equates both pulse widths to the transmission time. Statically and dynamically these loops differ, and their design for a required system performance is described. Examples illustrate the performance of the control loops, and the occurrence of this type of control problem in other applications is discussed.