Modeling and Simulation of Simple Flux-Trapping FCGs Utilizing PSpice Software

A novel modeling and simulation method for flux-trapping flux-compression generators (FT-FCGs) is presented, which utilizes PSpice circuit-simulation software to solve complex differential equations derived from circuit analysis. The primary motivation for the model development is the desire for a technique to rapidly design and prototype FT-FCGs for use as drivers in high-power microwave sources. The derivation of FT-FCG equations will be given, both in the ideal (lossless) and nonideal cases. For the nonideal case, three flux conservation coefficients are added to the equations to account for intrinsic flux loss in the circuit. Time-varying inductance curves are calculated using zero-dimensional models found in literature and adapted to fit this model. A simple FT-FCG design is used as an example to show the steps taken to complete a simulation. The same design was also fabricated and tested for comparison with predicted results from the model. A comparison of the waveforms acquired through simulation and experiment was found to result in good agreement for a given set of values for the flux conservation coefficients. A discussion of the derived equations, both lossless and nonideal, is given, as well as a discussion on the investigation of the impact of the three flux constants on the circuit. Analysis is offered on the results of this investigation, and conclusions are given on the effectiveness of this model to predict FT-FCG behavior.

I. Introduction

Simulation models for flux-compression generators (FCGs) have been used for many years to expedite the design process and cut down on experimental costs. Almost all of the theory and code developed, however, has been for “directly seeded” FCGs (DS-FCGs), which establishes an initial (or “seed”) magnetic flux in the generator by injecting current directly into the stator and armature conductors. Numerous advanced numerical codes exist for this classification of FCG, which have been developed over several decades and can provide highly accurate predictions of FCG performance. Another class of FCGs exists, referred to as the flux-trapping FCG (FT-FCG), which uses a transformer-based configuration to establish magnetic flux in the generator volume without current injection into the stator conductor. This type of FCG is attractive because stator conductors can be kept “cold” during the seeding process, minimizing Joule heating and potential flux loss. Another advantage of the FT-FCG is that it enables cascading generators through stages coupled by this transformer configuration. This arrangement of the FT-FCG is of particular interest in applications such as high-power microwave generation [1] because it allows the generator output to be tailored for driving high-impedance loads. Due to the coupling behavior from the transformer configuration, FT-FCGs behave very differently from the DS-FCGs, most notably in the respect that the stator current is zero for the former and nonzero for the latter. Even with the advances in theory and code for DS-FCGs, very little theory and code exists for FT-FCGs, which may be a testament to their complex nature. Thus, there are usually two approaches in the design and simulation of FT-FCGs, both of which are time consuming. Designs can be carried out through the guidance of a handful of guidelines, but FT-FCGs designed from this method usually run through extensive experimental testing in order to optimize various parameters (at a high cost), and even then, might not be fully optimized. In addition, potential designs are put through simulations, which can be complicated to perform; thus optimization of the design through simulation can be time costly as well. Thus, it is desirable to have a modeling program where potential designs can be efficiently modeled and optimized without the costs (both monetary and time) inherent with device fabrication and experimentation or complex modeling techniques.