Shaping Fast Rise-Time Pulses with Tapered Transmission Lines

For the purpose of checking very fast time-domain reflectometer (TDR) systems it is desirable to have a fast rise-time pulse whose parameters are known. A means for obtaining pulses meeting these requirements has been achieved by suitably tapering the inner conductor of a rigid coaxial transmission line having air dielectric, commonly referred to as an air line. The air line is driven with a pulse that has a very fast rise time compared to the rise time of the expected output pulse. A reflected pulse will be generated whose shape is dependent upon the taper of the inner conductor. A procedure is outlined for determining the proper taper to shape the leading edge of the reflected pulse to match any continuous single-valued function. Air lines that were designed and built for producing a pulse whose leading edge is a linear ramp, a truncated Gaussian function, and the integral of a truncated Gaussian function are discussed and traces of these pulses are shown. The problem of re-reflections due to the multiple discontinuities along the air line was analyzed by means of a computer. This program is described. The effect of the driving-pulse parameters on the reflected pulse is analyzed on a theoretical basis. Rise time, pulse shape, and aberrations such as overshoot and ringing of the driving pulse are considered in this analysis.