Vacuum microwave tubes, such as klystron, traveling-wave tube, gyrotron are high efficiency devices, where the RF interaction structure facilitates efficient energy transfer from the kinetic energy of the high energy electron beam to the electromagnetic wave. Traveling-wave Tube is the most versatile microwave power amplifier widely used for terrestrial communication, radar and aerospace applications. The waveguide based slow-wave structures like Millman, Karp, inter digital, grated waveguide, ring-plane, ring-bar, millitron and folded-waveguide structure gathered importance for application in millimeter-wave traveling-wave tubes. Among these millimeter-wave interaction structures, the folded-waveguide slow-wave structure became the most popular due to its robust structure, high power capability, low RF loss, simpler coupling, reasonably wide bandwidth and ease of fabrication for millimeter-wave to terahertz frequencies. Hence this thesis aims to analyse the folded-waveguide slow-wave structure for broad-banding and efficiency enhancement. The existing approaches for the analysis of cold circuit parameters (dispersion and interaction impedance characteristics) of folded-waveguide slow-wave structure are reinvestigated and found that these have limitation, as the effects of E-plane bend and beam-hole discontinuities are ignored in the parametric analysis. A cascaded matrix equivalent circuit model includes the effect of E-plane and beam-hole discontinuities for the analysis, but reported only for the serpentine folded-waveguide slow-wave structure. The cold test measurement technique was reported only for the dispersion characteristics. Hence the measurement technique has to be extended for the measurement of interaction impedance. The author proposes to orient the present doctoral work to (i) extend the proposed cascaded transmission matrix equivalent model for the analysis of rectangular folded-waveguide slow-wave structure, (ii) develop a non-resonant perturbation technique for the measurement of interaction impedance characteristics of the folded-waveguide slow-wave structure and also to (iii) establish new analysis models for the folded-waveguide slow-wave structure. The effect of E-plane bend and beam-hole discontinuities on the RF characteristics have been considered and simple, yet accurate closed form expressions for the computation of dispersion and interaction impedance characteristics have been established by three different approaches namely: transmission line equivalent circuit model, conformal mapping equivalent circuit model and quasi-TEM approach. The analysis results are benchmarked against 3-D electromagnetic modeling. The non-resonant perturbation theory is developed for the interaction impedance measurement. Typical Ka-band structures are fabricated by wire-EDM process and cold test measurements are carried out to benchmark the analysis approaches. The equivalent circuit models based on lumped circuit model are simpler than the cascaded matrix equivalent circuit model and can give closed form expressions for the prediction of dispersion and interaction impedance characteristics. The quasi-TEM approach can be extended for the complicated structure like ridge-loaded FWG-SWS. Broad-banding of the conventional folded-waveguide slow-wave structure is attempted by ridge-loading on the broad wall of the structure. The ridge-loaded folded-waveguide slow-wave structure is analyzed by parametric approach, cascaded transmission matrix equivalent circuit model and quasi-TEM approach and validated against numerical simulation. The analysis is extended for exploring the efficacy of the ridge-loading on broad-banding of the traveling-wave tube. Finally efficiency enhancement of the folded-waveguide slow-wave structure is attempted by introducing grating on the broad wall of the structure. The analysis is carried out by numerical simulation for exploring the efficacy of the grating on efficiency enhancement of the traveling-wave tube.