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IVEC Summary, Session 18, Intermodulation Distortion II 
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Session chairperson and summary author: John Booske

The second session on intermodulation distortion started with a keynote presentation by Carol Kory of Analex and NASA Glenn Research Center. Dr. Kory described the use of MAFIA (a commercially-available 3D particle-in-cell or PIC code) to model intersymbol interference effects during TWT amplification of digital modulations of a single frequency carrier. The motivation was to study internal-reflection memory effects on high-order-modulations (e.g., 16 or 64 QAM). The advantages of the 3D PIC code included its time-domain representation (necessary for this problem) and its exact representation of all dispersive effects through a physically exact three-dimensional model of the helix circuit. Through the use of constellation and eye diagrams, the degradation of high-order-modulations due to internal reflections was dramatically illustrated. A disadvantage of the 3D PIC code was also revealed: using current high-end desktop PCs (excess of 1 GHz clock speed, dual processor), a single simulation required 20 days to complete. Until computer speeds and memory technologies are significantly increased, it was concluded that time domain block models that incorporate physical characterization "data" (from computer TWT models or experiments) would be the recommended approach.

Joe Qiu of the U.S. Naval Research Laboratory (NRL) described a new TWT characterization system suitable for wide bandwidth (approaching 1 GHz), large-record-length testing of TWTs for amplifying digital signal modulations. He also identified and illustrated the value of "power margin in a digital communications link" as a system-level figure of merit for designing linear TWT amplifiers. Power margin is defined as the ratio of the available power to the power needed to sustain a given symbol error rate given a particular noise level in a communications link. Dave Abe, also from NRL, described the optimized helix circuit design and subsequent fabrication of linear C-Band TWT for digital communication experiments. Optimizations that were investigated included maximized efficiency, minimized AM/PM distortion, and a compromise between AM/PM and AM/AM distortions. It was discovered that the third choice (also called "complex gain" optimization) produced the best overall combination of performance, especially with regard to third order intermodulation distortions. Preliminary drive curve measurements indicate the tube is working as designed, with more extensive measurements and model comparisons in progress.

The next two papers described complementary methods to realize time-domain block models of TWTs as predictors of digital modulation distortions, including memory effects. The first paper (fourth paper overall in the session) presented by Christopher Silva of the Aerospace Corporation, described a block model approach based on a simplified version of Volterra series. This work represented a cross-over application of prior similar work in nonlinear mechanical systems modeling. A principle motivation for developing this predictive model was the recent successful development (by Aerospace Corporation) of a patented, highly-resolving, time-domain characterization instrument. This instrument makes it possible to experimentally measure the time-domain based parameters needed to implement the Volterra type block models for the TWT. The following paper, presented by Pedro Safier (SAIC) described latest results developing a time-domain block model built around frequency-domain characteristics of a TWT. These frequency-domain inputs can be acquired from steady state simulation models (such as CHRISTINE) or from laboratory measurements of experimental devices. The recent advances include the incorporation of frequency dependence into the nonlinear gain, i.e., nonlinear gain with memory.

The final talk in the session, presented by Juliette Plouin, a Ph.D. student at Ecole Polytechnique in Paris, described a theoretical re-examination of mechanisms for saturation in a traveling wave tube. The first determination was that inertial bunching dominates any space charge force effects, for parameters typical of many helix TWTs. This insight led to interesting speculative proposals that a departure from the sinusoidal carrier wave paradigm might be better suited to get more uniform bunching and thus more linear TWT amplification near saturation. An example cited was to consider sawtooth carriers, rather than sinusoids. A first order approximation to the sawtooth waveform would be a combination of fundamental and second harmonic signal. This prompted the observation that this proposed approach and TWT linearization by second harmonic injection (described in talks in a prior session) might be the same idea, but approached from two complementary perspectives.

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