| Traveling wave tube(TWT)amplifiers are one of the most widely used vacuum electronic devices which are employed in various applications,such as radar,wireless communication.Among TWT amplifiers,helix TWTs which are of high power,high efficiency,ultra-wide bandwidth,high reliability,long life and radiation hardened are extensively used in active phased array system,satellite transmitter,data communication system,global positioning system and electronic countermeasures system.The increasing need for high data rate communications,coupled with increasing demands on already crowded RF/microwave spectrums are leading to a rapid development in the multiphase digital modulation schemes.Therefore,for the designer of helix TWTs to be utilized in these systems,the use of multilevel modulation schemes are placing stringent demands on efficiency,bandwidths and linearity of helix TWTs.However,the nonlinear beam-wave interaction(BWI)will lead to the generation of nonlinear distortion characteristics(such as group delay distortion,input-output transfer characteristics,intermodulation distortion,harmonic generation)which have undesirable impacts on systems.The group delay distortion response of a digital satellite communication channel has a significant effect on the accuracy of time synchronization and pseudo-range measurement of the navigation system.The input-output transfer characteristics can lead to the generation of undesired frequencies(such as intermodulation distortion)which will strongly influence the data transition quality as measured by bit error rate.The nonlinear BWI will also lead to the generation of harmonics,and thus reduce the output power and electronic efficiency.The harmonics can also act to create beats with the fundamental wave,and thus generate these beat frequencies which are commonly known as intermodulation products.As a result,the bit-error-rate will be increased and the system performance will be compromised.Therefore,the generation of nonlinear distiortion characteristics are of significant current interest in helix TWTs.Understanding this nonlinear effects provide strong motivation for nonlinear analysis of a helix TWT.In this doctoral dissertation,the work is mainly focused on the developments of analytic models of nonlinear distortion characteristics and the studies of the mechanisms and suppression schemes of nonlinear distortion characteristics.The main work and innovations of this dissertation are as follows:First,we focus on the derivation of revised Pierce's 3-wave theory which can achieve more accuracy than classical Pierce's 3-wave theory.Firstly,a more accurately revised Pierce's 3-wave dispersion relation is obtained by using an approximate treatment on the nonlinear term of the dispersion relation of Pierce's 4-wave BWI theory.Secondly,the boundary conditions of Pierce's 3-wave theory are also revised,and then the revised Pierce's 3-wave theory is established.Thirdly,the Pierce small-signal theories are compared to each other and Lagrangian theory.Results show that the revised Pierce's 3-wave theory agrees extremely well with Lagrangian theory and gains more accuracy than the classical Pierce's 3-wave theory in the small-signal BWI region.Second,the successive analytic model of Eulerian nonlinear BWI theory for fundamental frequency is developed.Motivated by a phase expansion Eulerian nonlinear BWI model,we have obtained a simplified Eulerian nonlinear BWI theory model.Then,derived from the Eulerian model,analytic solutions of normalized electric field are first obtained by the method of successive approximation.The successive analytic solutions are compared to Lagrangian theory and traditional Eulerian models.It is found that the fourth order analytic solution agrees well with Lagrangian theory and gains more accuracy than the first,second or third order analytic solution in nonlinear region.Interestingly,the saturation effects caused by electron overtaking cannot be found by traditional Eulerian analysis,but can be described by the fourth order analytic solution.Moreover,the fourth order analytic solution is simpler than existing approaches,and thus allow analytical progress.The study confirms that the fourth order analytic solution can outperform previous proposals.Third,based on the successive analytic model of Eulerian nonlinear BWI theory,analytic solution of group delay distortion is obtained,then the mechanism and suppression schemes of group delay are studied.Firstly,derived from this Eulerian small-signal analytic solution,the analytic solution of group delay distortion is obtained.Secondly,the mechanism of group delay is studied.It is found that the main mechanism of group delay distortion is the propagation time difference between the wave group and electron beam throughout the beam-wave interaction region.Furthermore,a series of group delay suppression schemes are discussed by using the mechanism.Finally,the Eulerian formation and the suppression schemes are validated by an in-house code based on Lagrangian theory.Results show that the analytic solutions of Eulerian model and group delay distortion agree well with Lagrangian theory in small-signal region.In addition,the suppression schemes are applied to a high efficiency Ku-band space traveling-wave tube.The group delay distortion is greatly reduced by approximately 50 percent with a slightly drop of output power.Fourth,based on the successive analytic model of Eulerian nonlinear BWI theory,analytic solutions of AM/AM and AM/PM conversion are obtained,then the mechanisms and suppression schemes of AM/PM conversion are studied.Then,a series of AM/PM conversion suppression schemes are discussed by using the mechanism.Finally,the Eulerian formation and the suppression schemes are validated by Lagrangian theory.Results show that the analytic solutions of Eulerian model,AM/AM and AM/PM conversion agree well with Lagrangian theory at 1dB gain compression point.Fifth,based on the analytic models of AM/AM and AM/PM conversion and a fast calculation model of intermodulation distiortion,the key parameters which have a great influence on intermodulation distiortion suppression ratio are obtained.Then,a suppression scheme of intermodulation distiortion is proposed.Finally,the suppression schemes are applied to high efficiency C-and Ku-bands space traveling-wave tube.The intermodulation distiortion suppression ratio is greatly reduced with a slightly drop of output power.Sixth,a nonlinear Eulerian theory considering harmonic interaction is developed.Firstly,to obtain a nonlinear Eulerian theory considering harmonic interaction,the electron phases in Lagrangian theory have been expanded into a series of harmonic components.Considering the 0th component and 1st component of the electron phases only and integrating over the initial phase distribution with the help of the relation of Bessel function,the nonlinear Eulerian theory considering harmonic interaction is established.It is found that the nonlinear Eulerian theory considering harmonic interaction agrees well with the Lagrangian theory before the saturation effect occurs.So the present nonlinear Eulerian theory considering harmonic interaction can effectively describe harmonic generation at 1dB gain compression point.The simulation results validate the correctness and effectiveness of our nonlinear Eulerian theory considering harmonic interaction.Seventh,the successive analytic model of the nonlinear Eulerian theory considering harmonic interaction is developed.Derived from the nonlinear Eulerian theory considering harmonic interaction,Eulerian nonlinear analytic solutions(the fourth order analytic solution of fundamental and the second order analytic solution of harmonic)are first obtained by the method of successive approximation.The analytic relationships between electric fields of fundamental/harmonic frequencies and electron phases are also found.Then,the Eulerian nonlinear analytic solutions and Eulerian nonlinear beam-wave interaction theory are compared to Lagrangian theory.It is found that the Eulerian nonlinear analytic solutions and Eulerian nonlinear beam-wave interaction theory agree well with Lagrangian theory at 1dB gain compression point.Moreover,Eulerian nonlinear analytic solutions are simpler than existing approaches,and thus allow analytical progress.Finally,the relationship between harmonic suppression and anomalous dispersion has been analytically studied. |
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