Generation of Reference Waveforms by Uniform Lossy Transmission Lines

This paper describes a method for generating fractional nanosecond pulsed waveforms of known shape thereby providing an a priori means for establishing reference waveform generators or standards to be used in pulsed measurements and other applications. The method employs the band-limiting properties of a lossy uniform transmission line to produce a known waveform and generator impedance. A theory for generator characterization and application is presented that defines a given generator in terms of time-domain or frequency-domain functions. A new term called the "available" waveform is defined. Rms error is employed as the error criteria. An example of generator design is given that employs planar skin-effect loss and provides an output response having 0.2 percent rms error over the interval 0 ≤ t ≤ 600 ps referred to the inherent step response of the waveshaping line. The input transition generator is assumed to be a 30-ps unit ramp generator. Also, an application example is given that employs a reference waveform generator to evaluate a sampling oscilloscope. The reference waveform generator uses a Debye dielectric lossy transmission line. The rms error of the oscilloscope time-domain response is determined as a function of time.