DESIGN AND FABRICATION OF CAVITY RESONATORS

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Peregrine Carr
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1 DESIGN AND FABRICATION OF CAVITY RESONATORS

2 CHAPTER 3 DESIGN AND FABRICATION OFCAVITY RESONATORS 3.1 Introduction In the cavity perturbation techniques, generally rectangular or cylindrical waveguide resonators are employed. The availability of sweep oscillators and network analyser makes it possible to measure the dielectric and magnetic parameters at a numher of frequencies in single band. In most of the works done by earlier researchers, measurements were done at single frequency using the cavity. The first part of this chapter describes the design and fabrication of rectangular waveguide cavity resonators used for the measurements over a numher of frequencies in a single band. In the second part, the design details and fabrication of coaxial resonators for broad hand measurements are presented. For properly positioning the sample at maximum electric or magnetic fields in the cavity sample chamhers are needed. The detailed report of designing of sample chambers is also incorporated in this chapter. 3.2 General aspects of design of rectangular waveguide cavities Generally, the cavity resonators are constructed from sections of brass or copper waveguides. If a hollow rectangular waveguide is sealed with conductive walls perpendicular to the direction of propagation, the incident and reflected waves are superimposed to generate a standing wave. The tangential electric and normal

3 magnetic field components equal zero at this wall and at distances of integral half wavelengths from it. In such a nodal plane, a second conductive wall can he placed without disturbing the field distribution in the waveguide, and thereby one obtains a cavity resonator. If the resonator is excited through a coupling mechanism, the field intensity building up within it becomes maximal when the length of the resonator in the direction of propagation is equal to an integral multiple of the half wavelength. Because of the different field modes possibly existing in the waveguide, a number of resonant frequencies can occur. In general, where X g is the guided wavelength and P = 1, 2, 3,... is an integer. The relation for the guided wavelength where A, is the wavelength in free space and A, is the cut-off wavelength for the given waveguide. Then re.wnant wavelength This expression is valid for resonators with rectangular cross section as well as for those with circular cross section. The unloaded Q-factor of rectangular cavity resonator is given by

4 where uc : Conductivity of the material of the walls of cavity 6. Skin depth P -: Permeability of the medium inside the cavity a -I Breadth of the cavity b Height of the cavity d - Length of the cavity flop - Resonant frequency (for TEIq mode) Also, the skin depth at resonant frequency is Resonant frequency and Q-factor are the fundamental parameters of a resonator. Using the above equations these parameters can be evaluated. 3.3 Fabr.ication of rectangular waveguide cavity resonators The S-band rectangular waveguide cavity resonator is constructed from a section of standard WR-284 waveguide. For C-band cavity, a section of WR-159 waveguide is used. A section of WR-90 waveguide is selected for the fabrication of X-band resonator. Table 3.1 shows the design details of S, C and X hand rectangular waveguide cavities.

5 Table 3.1 Design parameters of S, C and X hand cavities. Dimensions of the cavity (mm) S band C band X band Length, d Breadth, a Height, b Diameter of the coupling hole Length of the slot on the broad wall Width of the slot The inner walls of each cavity are silvered to reduce the wall losses. All the three resonators are of transmission type, since power is coupled intolout through separate irises. From the equations discussed so far, the resonant frequencies and Q-factors of S, C and X band cavities can be calculated. Table 3.2 shows the characteristics of each cavity. The amplitude responses of S, C and X band cavities are shown in Figures

6 St 1 REF db db/ V db START STOP GHz GHz Figure 3.1 Amplitude response of the S band rectangular waveguide cavity

7 52 1 REF db 10.0 db/ START GHr STOP thz Figure 3.2 Amplitude response of C-band rectangular waveguide cavity

8 52 1 REF db 10.0 db/ Figure 3.3 Amplitude response of X-band rectangular waveguide cavity

9 Table 3.2 Resonant frequencies and Q-values of S, C, and X band cavities. Resonant frequency(ghz) Unloaded Q-factor Type of cavity Theore- Exper i - Theore- Exper i - tical mental tical mental S-band x lo cavity x lo (TE103 - TE107) x lo C-band x lo cavity x lo (TE103 - TE107) x lo X-band x lo cavitv

10 For properly orienting the sample in the cavity at the positions of maximum electric or magnetic fields, metallic sample chambers are constructed. The bottom portion of the sample chamber consists of a heating coil and thermocouple which are the integral parts of a precision temperature controller (accuracy f 0.1 'c) (Figure 3.4). Design details of the sample chamber are given in Table 3.3. Table 3.3 Design parameters of the sample chamber. Dimensions of the chamber (mm) S band C band X band Length, Breadth, c Height, h Sample insertion length in the bottom lid of the chamber 20 10

11 INSULATING LID COPPER PLUG SAMPLE INSERTION BOLE It?l'ERIOR REGION OF CAVITY,METALLIC CHAMBER THERMOCOUPLE THERMAL I NSULATIOH Figure 3.4 Cross-sectional view of the sample chamber

12 3.4 Design and fabrication of coaxial transmission line resonators Coaxial transmission line resonators are sections of coaxial lines with both or one end shorted by a conductor of very high conductivity. Electromagnetic fields excited in the resonator are reflected from the ends. The waves add in phase. The total phase shifts in the propagating waves must be 2x or its multiple. If 4, and 4 are the phases introduced by the reflections at the two ends and d is the length of the resonator, then the condition for the resonance will be For an open end resonator, 4, = 0, b2 = T, so where h, is the resonantt wavelength. Thus the length of the coaxial line section with one end open acts as a resonator when its length is an odd multiple of quarter wavelength. Various resonant modes are possible for a resonator of detinite length d. The field configurations of these modes may easily be inferred from the propagating TEM mode in a coaxial line. However, care must be taken so that the higher order TE and TM modes are not excited in such a resonator. The basic condition is where a is the outer radius of the imer conductor and b is the inner radius of the outer conductor. It is found that in open end resonator, there is a possibility of radiation loss from the open end. It results in a low value of quality factor. In

13 order to overcome this, the outer conductor is extended beyond the end of the inner conductor such that it forms a cylindrical waveguide operating below cut-off for a given frequency band. In the present investigation, the basic coaxial transmission line resonator consisting of a circular waveguide which operates below cut-off for the TMol mode is used. There is a removable centre conductor along the axis of the circular waveguide. The TEM mode can propagate up to the end of the centre conductor. The resonator (Figure 3.5) is fed by a rectangular feed loop. The coupling mechanism will generate spurious, higher order modes. usually below cut-off and have an evanescent nature. But, these modes are Hence they will not propagate. Since the energy is coupled into or out of the resonator through the same coupling mechanism, the resonator is of reflection type. The physical dimensions of two coaxial transmission line resonators are given in Table 3.4. Table 3.4 Design parameters of coaxial transmission line resonators. Dimension (nun) Resonator I Resonator I1 Length of the resonator (D) 250 Lengths of the centre conductors (L) 168,88,113 Inner radius of the resonator (b) Radius of the centre conductor (a) Distance from centre conductor to feed loop (c) Feed loop, inner dimension ( h x 1)

14 CAPILLARY TUBE FEED LOOP MOVABLE CHAMBER NON-RADIATING SLOT CENTRE CONDUCTOR Figure 3.5 Coaxial transmission line resonator

15 A comparatively wide range of frequency can be covered by changing centre conductor and utilising frequencies where the centre conductor is several wavelengths long. The cut-off frequencies can be calculated from the separation equations [60]. For TM mode, For TE mode, where k is the wavenumber, kz the wave number in the propagation direction and SP the pth order zero of the Bessel function of the tirst kind and order n. In vacuum, the TMol mode has cut-off at GHz and the TEll mode at GHz in resonator I. In resonator 11, the TMol mode has cut-off at GHz and the TEll mode at GHz. Table 3.5 shows the characteristic features of resonators I and 11.

16 Table 3.5 Characteristic features of coaxial resonators. Length of Characteristics of resonators TYPe of cavity centre conductor Resonance Loaded (mm) frequency (GHz) Q-factor (Qo) Resonator I 168 Resonator I1 100

Waveguides. Metal Waveguides. Dielectric Waveguides

Waveguides. Metal Waveguides. Dielectric Waveguides Waveguides Waveguides, like transmission lines, are structures used to guide electromagnetic waves from point to point. However, the fundamental characteristics of waveguide and transmission line waves