Virtual Time-Domain Reflectometry (TDR)

Time-Domain Reflectometry (TDR) is one of the important techniques to identify, diagnose circuit systems, especially in high-speed digital applications. The fundementals of TDR is usually addressed in the transmission-line theory. In order to help people who like to know the basics of TDR, a simple applet is provided here to solve the time-domain step-response recorded at the source end of a transmission-line which is loaded at the other end.

Brief User's Guide

The user needs to first supply information about the transmission-line:

• Z0: the characteritic impedance
• Rg: internal resistance of the source generator
• v: wave velocity inside the line
• d: length of the line

The load-impedance value is entered through the combination of text field for R, C, L and the drop-down choice box. The drop-down choice box allows the load condition to be OPEN, SHORT or other parallel or series connections using the R, C, L values. Furthermore, an arbitrary load can be specified by entering a rational polynomial for the s-domain impedance expression. The voltage wave created by the step function at the source generator (located at x=0) is lauched at "t=0", and travels for "tau=d/v" seconds to reach the load. It takes another "tau" seconds to come back to the generator. Thus, "2*tau" represents the time for a round-trip of the voltage wave. The user should specify the number of round-trip bounces desired, default is 5, to be recorded. Also, the total number of sampling points can be adjusted. A click on the "Calculate" button triggers the computation, followed by the results for both voltage and current in two plots. This is essentially a simple demonstration of what a TDR instrument can do, hence the name of this applet. In the plots, the voltage and current signals are normalized, and the blue traces represent the settling signal levels (when time approaches infinity.)

NOTE: In order to enter an s-domain impedance expression for an arbitrary load, the drop-down choice box should select the last choice before entering text for the rational polynomial.

CAUTION: The current implementation has problems in handling large number of bounces, say, greater than 5, when the load involves reactive elements. However, for cases involve only resistive load, including OPEN and SHORT, there should be no problem in choosing a large number of bounces.

References

J. Duncan Glover and Mulukutla Sarma, "Power System Analysis and Design", Chapter 11, PWS-Kent, Boston.