3184 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 56, NO. 12, DECEMBER 2009 Equivalent Circuit Analysis of a Ring–Bar Slow-Wave Structure for High-Power Traveling-Wave Tubes Subrata Kumar Datta, Member, IEEE, Vemula Bhanu Naidu, Pamisetty Raja Ramana Rao, Lalit Kumar, Senior Member, IEEE, and Baidyanath Basu, Member, IEEE Abstract—A simple equivalent circuit analysis of the ring–bar slow-wave structure of a traveling-wave tube is developed, using the coupled transmission-line approach, for the dispersion and interaction-impedance characteristics of the structure. The effects of the ring and the bar widths of the structure are included in the analysis. The analysis is validated, with respect to 1) an X-band structure, against both measurement and simulation, as well as 2) a Q-band structure, against simulation. Index Terms—Coupled transmission line, equivalent circuit analysis, high-power traveling-wave tubes (TWTs), ring-and-bar structure analysis, slow-wave structure (SWS). I. I NTRODUCTION A RING–BAR or slotted variant of the contrawound he- lical slow-wave structure (SWS) [1], [2], also known as a Birdsall and Everhart structure [3], has potential for use as the interaction structure of traveling-wave tubes (TWTs) in the high-power high-frequency regime [4]–[9]. A typical ring–bar SWS consists of a ring–bar tubing, usually made of refractory metal like molybdenum, which is supported with the help of dielectric support rods symmetrically arranged at a regular angular interval in a metal envelope (Fig. 1). Due to the longitudinal and periodic skew symmetries, the struc- ture supports two principal modes: 1) the symmetric mode or E-mode and 2) the antisymmetric mode or H-mode (ring mode) [1]–[3]. The symmetric mode in the structure, providing axial electric field, is useful for the forward-wave interaction and amplification in TWTs. Compared with its conventional single- helix SWS counterpart, the ring–bar structure (supporting a symmetric E-mode) provides a number of advantages. 1) It provides a higher interaction impedance and a higher interaction efficiency. 2) It allows the use of a thicker beam at higher beam voltages and currents and with reduced focusing magnetic fields. Manuscript received May 15, 2009; revised July 29, 2009. First published October 30, 2009; current version published November 20, 2009. The review of this paper was arranged by Editor W. Menninger. S. K. Datta, V. B. Naidu, P. R. R. Rao, and L. Kumar are with the Microwave Tube Research and Development Center, Defence Research and Development Organization, Bangalore 560013, India (e-mail: skd@mtrdc.drdo.in). B. Basu is with the College of Engineering and Technology, Moradabad 244 001, India (e-mail: drbnbasu@gmail.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2009.2030710 Fig. 1. Ring–bar structure. 3) It provides greater immunity from backward-wave insta- bility, owing to lower interaction impedance in the spatial harmonics. 4) It makes the structure robust, enabling it to handle large powers and withstand a larger beam interception, even at higher frequencies. 5) It makes the construction of the structure easy, particu- larly for tiny structure sizes at higher frequencies, in that the structure can be fabricated simply by precision cuts in a hollow metallic tube. The aforementioned advantages of the ring–bar SWS over its single-helix SWS counterpart, although gained at the price of the bandwidth due to the larger amount of dispersion of the former, have resulted in the development of a number of commercially available high-power ring–bar TWTs [4]–[9]. The slow-wave characteristics of a contrawound helix (CWH) and its ring–bar variant have been studied experimen- tally [1]–[3] as well as by field analysis [2], [10]–[12] and simu- lation [11]. Chodorow and Chu [2] carried out the field analysis of the structure using the approximate variational technique, which was subsequently extended to a structure with dielectric support rods in a metal envelope by Cain and Grow [10]. Recently, Lopes and Motta [11] revisited the approximate vari- ational technique and evaluated its limitations and inaccuracies by comparison with 3-D electromagnetic simulation and mea- surement. Another approach is based on quasi-TEM analysis, which was carried out for the ring–bar structure by Ash et al. [12] and which predicted the structure characteristics with reasonable accuracy. Although rigorous, it is somewhat difficult to implement their approach because of its complexity. There is yet another approach in which a transmission-line equivalent of 0018-9383/$26.00 © 2009 IEEE