Theoretical Investigation on Matching Multistage Circular Pulse-Forming Line to Transmission Line

Abstract

A connecting line (CL) is needed when a multistage circular series pulse-forming line (PFL) connects to a transmission line (TL) in order to generate an ideal nanosecond square pulse. Two conditions are needed to design such a CL: 1) the impedance matching condition and 2) the electrical-length matching condition. The first condition means that the impedance of the CL should match that of the series PFL which can affect the top of the square pulse, and the second condition means that the electrical length of the CL plus that of each stage of PFL should be a constant which can affect the tail of the square pulse. Theoretical formulas about the two conditions are presented, and different mismatch cases are analyzed. First, if the electrical-length matching condition is not met, the fall time of the square pulse would increase. Second, if the impedance matching condition is not met, two subcases exist: first, when the characteristic impedance of each stage of PFL $Z_{i}$ is not a constant, but the sum of $Z_{1}$ to $Z_{i}$ is equal to the characteristic impedance of the TL $Z_{0}$ , an ideal square pulse can still be generated; second, when the impedance decrement of each segment of CL is not a constant, fluctuation would add on the top of the main square pulse. PSpice circuit simulation is employed to give support for each case. In the end, a 3-D model of a multistage circular PFL connecting to TL via a coaxial CL is constructed, and transient simulation result shows that the pulse top distortion can be reduced within 5% compared with 20% of the previous result, which verifies the theory.