Exponential Transmission Line Design for Impedance Ratios Greater than 10

The use of an exponential transmission line as a high- pass pulse transformer has received much attention and has yielded analytic expressions for line parameters as a function of the geometrical factors, material properties, and the impedance ratio from input to output. The one- dimensional analysis applied to a stripline has been used by Arnold and Bailey for an impedance ratio of 33 or a voltage step-up/down of 5.74. Use of one-dimensional analysis to design a stripline with an impedance ratio of 100 introduces an unwanted phase variation at the low- impedance end of the line. This phase variation detracts from ideal performance. Two approaches are discussed to restore proper phasing. The first is to apply a linear taper to decrease the height of the stripline at the low- impedance end of the line. The height is greatest at the high-impedance (high-voltage) end of the line and tapers to a minimum value at the low-impedance (low-voltage) end. This taper reduces the overall width of the exponential line at the low impedance end and so reduces the overall variation of phase path length within the line. The second approach is a ray tracing algorithm that maintains coherent phase fronts in the exponential line as the impedance increases exponentially as a function of distance. This algorithm places additional geometrical constraints on the stripline. Experiments are discussed that quantify the performance of a 46-inch long exponential stripline with an impedance ratio of 100, from 50 Omega to 500 mOmega.