OVERSHOOT-CONTROLLED RLC INTERCONNECTIONS

As circuit speeds increase, line inductance introduces propagation delay and reflections in long lines, and ringing and overshoot in short lines. For resistive drivers and capacitive loads, control of these effects is accomplished using a simple relation derived here between driver resistance RD, load capacitance CL, and the line parameters per unit length R, L, and C, thus generalizing the usual impedance matching condition RD √L/C. The relation is [formula omitted] where l is the line length, and with rl and rD the line and driver resistance divided by √L/C, and b, d,f, and g related to CL/Cl. The derivation of this result is based upon a “no-peak” condition upon the transfer function of the circuit in the frequency domain, a condition that can be derived with no sacrifice of generality using a low-frequency ladder approximation to the transfer function. This “no-peak” condition in the frequency domain allows only a 4% overshoot at the load end of the line in the time domain. By restricting consideration to such “overshoot-controlled” circuits, simple estimates of bandwidth, delay, and time-domain step response are derived. The results allow improved circuit response without risk of overshoot, for example, by reduction of driver resistance below √L/C for cases where line resistance is unavoidable and/or where load capacitance is not negligible compared to line capacitance. The algebraic formulas derived here are more effective than case-by-case numerical simulations for analyzing scaling and technology issues, whether on-chip, or at the packaging, board, or system levels. © 1991 IEEE