Joaquim P. Leite Neto

Design of coaxial Bragg reflectors

A coaxial line periodically loaded by circular disks on the inner conductor is specifically designed to act as Bragg reflector to prevent radio-frequency fields from leaking out of a 6.6-GHz monotron. Design criteria to ensure a stopband as wide as possible are presented and a discussion is given on how band gap width, center frequency, and reflectivity arise from the geometry of the periodic structure

Examining by the Rayleigh-Fourier method the cylindrical waveguide with axially rippled wall

Axially corrugated cylindrical waveguides with wall radius described by R/sub 0/(1+/spl epsi/cos2/spl pi/z/L), where R/sub 0/ is the average radius of the periodically rippled wall with period L and amplitude /spl epsi/, have been largely used as slow-wave structures in high-power microwave generators operating in axisymmetric transverse magnetic (TM) modes. On the basis of a wave formulation whereby the TM eigenmodes are represented by a Fourier-Bessel expansion of space harmonics, this paper investigates the electrodynamic properties of such structures by deriving a dispersion equation through which the relationship between eigenfrequencies and corrugation geometry is explored. Accordingly, it is found that for L/R/sub 0//spl ges/1 a stopband always exists at any value of /spl epsi/; the condition L/R/sub 0/=1 gives the widest first stopband with the band narrowing as the ratio L/R/sub 0/ increases. For L/R/sub 0/=0.5 the stopband sharply reduces and becomes vanishingly small when /spl epsi/<0.10. Illustrative example of such properties is given on considering a corrugated structure with L/R/sub 0/=1,R/sub 0/=2.2 cm, and /spl epsi/=0.1, which yields a stopband of 1.5-GHz width with the central frequency at 8.4 GHz; it is shown that in a ten-period corrugated guide, the attenuation coefficient reaches 165 dB/m, which makes such structures useful as an RF filter or a Bragg reflector. It is also discussed that by varying L/R/sub 0/ and /spl epsi/ we can find a variety of mode patterns that arise from the combination of surface and volume modes; this fact can be used for obtaining a particular electromagnetic field configuration to favor energy extraction from a resonant cavity.

The Sinusoid as the Longitudinal Profile in Backward-Wave Oscillators of Large Cross Sectional Area

High-power generation in backward-wave oscillators (BWO) of large section requires that the beam electrons flowing close to the corrugated wall interact efficiently with surface waves supported by a periodic structure. Such waves are described by the superposition of slow-wave space harmonics of the operating mode. The present paper reports on design tools for BWOs operating in symmetric TM modes since these modes are able to perturb the axial velocity and electron density on rectilinear beams confined by an external magnetic field in slow-wave systems. Here we investigate whether a cylindrical guide with sinusoidally rippled wall can provide strong coupling between the guide surface waves and mildly relativistic (» 500 keV) electron beams in the 8-9 GHz frequency range for BWOs of large diameter (D » 3‚). For this purpose, the characteristic equation of a sinusoidally corrugated structure is derived on the basis of the Rayleigh-Fourier method, whereby the field solution is represented by a single expansion of TM eigenmodes. From the dispersion diagrams thus obtained we infer the appropriate periodic length and ripple amplitude of the guiding structure that optimize the beam-wave interaction.

Experimental characterization of a 6.7 GHz coaxial Bragg reflector

A coaxial line periodically loaded by circular disks on the inner conductor is designed and constructed to act as Bragg reflector in the 4.0-9.5 GHz frequency range. This is achieved by placing 10 disks (0.35 cm thick and 6.22 cm in diameter) equally spaced by the periodic distance of 1.8 cm on a coaxial waveguide with inner and outer diameters of 6.90 and 4.22 cm. Experiments on a periodic structure made from stainless steel demonstrate a band gap of 5.6 GHz centered at the 6.7 GHz design frequency in close agreement with 3D microwave computer simulations.

Experimental Study on Split-Ring Resonators with Different Slit Widths

Metamaterial one-dimensional periodic structures are composed of split-ring resonators, which can display electric permittivity and magnetic permeability simultaneously negative, are studied experimentally. In the present study, each resonator is made up of two concentric circular copper rings patterned on a substrate of kapton, with slits diametrically opposite each other and with the line of the splits along the longitudinal direction of the periodic array containing seven split rings evenly spaced. The experiments consist in inserting the metamaterial slab into a square waveguide of side length 6 mm, corresponding to a cutoff frequency of 25 GHz. Transmission bands due to magnetic and electrical responses are identified for slits with aperture widths of 1 mm and 2 mm, centered at 5.67 and 6.12 GHz frequencies, respectively, values well below the 25 GHz frequency cutoff, so characterizing a medium with negative permeability and permittivity.

Microwave propagation experiments on a waveguide loaded by an array of split-ring resonators

A study of split-ring resonators with different arrays containing two, four and six cells is conducted experimentally to verify the transmission band resulting from the electrical and magnetic responses of the metamaterial array. Microwave propagation below cutoff in an X-band waveguide loaded with an array of split-ring resonators is demonstrated. Transmission bands corresponding to magnetic and electrical frequencies are measured and compared with simulation model with good agreement.

Reentrant cylindrical cavities

Of applications ranging from electron spin resonance to detection of gravitational waves, reentrant cylindrical cavities are analyzed on the basis of a mathematically simple formalism extending the range of validity of expressions for resonant frequency and quality factor obtained from lumped RLC constant models. Several cavity configurations in the 1-3 GHz range are analytically examined in excellent agreement with frequencies obtained from Superfish code.

Electrical Conductivity Measurement Through the Loaded Q Factor of a Resonant Cavity

We present a method for measuring the electrical conductivity of metallic materials that relies on the ratio of two loaded Q factors, QR/QX, with QR corresponding to a TE011-mode reference cavity made of aluminum, and QX the Q that results upon replacing the aluminum plate with the one fabricated from the material to be examined. Electrical conductivity is mathematically inferred from the ratio QR/QX where the loaded Q factors are measured by using the transmission-type method. Within a 3.0 percent accuracy, conductivities determined at 8.7 GHz for electrolytic copper (5.6 times 107 S/m) and brass (1.6 times 107 S/m) show to be in good agreement with those reported in the literature.

Coupled Circular Cavities for Transit-Time Microwave Tubes

We examine both analytically and numerically by using a 2-D electromagnetic solver the frequency tuning characteristics and electric-field patterns in a two-celled system consisting of cylindrical cavities coupled by a circular iris. It is shown that the presence of the iris introduces unique features not found in hollow circular cavities, namely, the occurrence of flat portions on the frequency tuning curves for varying iris radius and also a Q factor 10% higher than that of the otherwise smooth cavity.

Dispersion relation of split-ring resonators magnetically coupled to a TEM wave

An electromagnetic wave dispersion equation in a metamaterial consisting of an array of split-ring resonators (SRRs) is derived for the determination of stop bands and passbands, showing the kind of wave which propagates, whether it is forward or backward. This derivation takes into account the magnetic coupling between the adjacent SRRs to consider propagation of magneto inductive waves (MI). The mathematical formulation is based on a coupled circuit model of transmission lines, that is, by using lumped-element circuits to model the SRR array.