Theory of Terminated Nonlinear Transmission Lines

Properly terminating a transmission line, in order to transfer the maximum available power to the load, is an important issue. The problem, fully analyzed in linear lines, is still considered as a persisting problem in the area of nonlinear transmission lines (NLTLs). In this paper, an accurate analysis is presented which gives a closed-form formula for the matching efficiency of the NLTLs. Using this analysis, optimal resistive terminating load for the NLTLs was extracted. These results will considerably ease the design of all kinds of the NLTL-based systems, such as high-frequency oscillators and ultrashort pulse generators. This consistent analysis also gives the reflection coefficient for the waves reflecting from the NLTLs load. It is shown that the NLTLs are far different from linear transmission lines in the both cases of matching efficiency and reflection coefficient. The obtained analytical results are verified with experimental measurements and SPICE simulations. Excellent agreements are obtained. It is also shown that the results of the introduced analysis make it possible to design the NLTL-based systems without any trial-and-error efforts.

I. Introduction

Nonlinear transmission lines have a great importance due to a variety of their important applications in passive intermodulation [1], ultra-wideband (UWB) impulse radio transmitters [2], high-power RF pulse generators [3], frequency multipliers [4], picosecond pulse generators [5], electrical oscillators [6], and pulse compressors [7]. These applications are mostly related to the lumped element nonlinear transmission lines (NLTLs) which are transmission lines that are periodically loaded with nonlinear elements. Properly terminating the NLTL with an optimal load is required for delivering the maximum available power to the load and remains as a persisting problem. Ricketts et al. [8] have mentioned that perfect termination of an NLTL is a challenging problem since its characteristic impedance changes with voltage. They have also emphasized in [9] that the termination of an NLTL is not a trivial problem. They have terminated NLTL with a resistor whose value is the average of the characteristic impedances. The importance of the problem of the NLTL termination is also emphasized in [10].