Abstract and subjects
Among other things, E. A. Guillemin is known for solving the Gibbs phenomenon relating to Fourier series components when combined to create step-function outputs. His work is frequently cited in the design of type A, B, C, D, and E pulse-forming networks (PFNs). The synthesis of type A, B and C networks is straightforward using Cauer or partial-fraction expansion techniques and the driving-point admittance or impedance functions. Types D and E are much more difficult to derive analytically. Type-E PFNs are often preferred in practice because of the single, tapped inductor and equal-value capacitors. However, the synthesis of a type-E PFN first requires the derivation of the negative inductances in a type-D PFN. What was laborious using tools of the 1940s, now, by using modern computers and especially symbolic mathematics software, the impedance and admittance functions can now be readily solved to fully synthesize these types of PFNs. This paper builds on the theory and synthesis methods developed by Guillemin and shows how to analytically derive the negative inductances in type D and then coupled inductors in type-E PFNs. Synthesis examples are given of multi-section PFNs. The validity of synthesized PFNs is verified by SPICE circuit models.