Tapered transmission-line transformers for fast high-voltage transients

One technique for raising the voltage in a fast pulse involves the use of a tapered transmission line transformer, whose transit time is large compared to the risetime of the pulse. For continuous variation of the characteristic impedance, the high-frequency/early-time voltage gain is given by the square root of the impedance ratio of each end of tapered line. An undesirable product of the tapered or transmission line transformer is the droop of the pulse after the initial step rise at the transmission line output. A formulation based on the voltage/current variables and renormalized wave variables has been used to examine the pulse droop with the idea of minimizing it. In the analysis, when the dominant term in expansion is optimized, the resulting geometry is that of the exponentially tapered line. The case of the exponentially tapered transmission line is discussed in detail and is shown to have an optimal transfer function in terms of early time voltage gain and improved droop characteristics.