Contains reports on four research projects

Berk, A. D.

Fontana, J. R.

Rose, P. H.

Schetzen, M.

Sciegienny, J.

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XI. MICROWAVE COMPONENTSProf. L. J. Chu L. D. Smullin P. H. RoseProf. J. B. Wiesner A. D. Berk M. SchetzenProf. H. J. Zimmermann J. R. Fontana J. SciegiennyA. STRIP TRANSMISSION SYSTEMA strip transmission system was further investigated. It was shown (QuarterlyProgress Report, Research Laboratory of Electronics, Jan. 15, 1953, p. 53) that theassumption of a TEM mode in the strip system is, at best, a first approximation.In order to explain the observed beat pattern in the standing wave along the strip(see Fig. X-5, Quarterly Progress Report, Jan. 1953, p. 55) the following assumptionssuggested by H. A. Haus were made (see Fig. XI-1):a. A TEM mode exists in the region between the strip and the ground plane.b. In the region far from the strip, a TM mode (surface wave) exists.Thus the observed standing-wave pattern would be due to the interference between thetwo modes, the "beat wavelength" being given by the relationTM TEMbeat = -Xb TM XTEMA graph of XTEM, XTM' and Xbeat vs frequency for a given system is shown in Fig. XI-2.The observed "beat wavelength" was comparable with the one calculated.An investigation has been started on the behavior of ferrites in the strip system. Theexperimental setup is shown in Fig. XI-3, and the typical results obtained are shown inFig. XI-4. An exact theory explaining the results obtained has not yet been derived.A ASTRIP DIELECTRICa GROU ND PLANETM REGION I TEM REGIONI TM REGIONSECTION A-AFig. XI-1Approximate approach to strip transmission problem.-83-1412:Eo 8J:f-l!lZlJJ...J~ 6~42STRIP SYSTEMBEAT WAVELENGTH BETWEEN_____ TM AND TEM MODESCALCULATED WAVELENGTH FORTM MODE IN DIELECTRIC SHEETMEASURED WAVELENGTH---- ABOVE STRIPCALCULATED WAVELENGTH ~CALCULATED WAVELENGTH FORFOR FREE MODE TEM MODE IN DIELECTRICFREQUENCY (k MC/SEC) ----Fig. XI-2Wavelength as a function of frequency for the strip system.POLYSTYRENEFig. XI-3An experimental setup for investigationof ferrite in the strip system.-84-STRENGTH OF MAGNETIC FIELD AT THE t INSERTION LOSS OF SYSTEMPOSITION OF FERRITE IN ABSENCE OF FERRITE. IN DBABOUT 300 GAUSS. FREOUENCY 9300 Me/SECINSERTION LOSS OF SYSTEM FOR NO 1800MAGNETIC FIELD 34 DB~ POSITION OF MAGNETS IN DEGREESFig. XI-4Insertion loss of system shown in Fig. XI- 3as a function of direction of magnetic field.WAVEGUIDE FILLEDWITH POLYSTYRENE(0) (h) GROUND PLANEFig. XI-5(a) A coaxial type of ferrite line (ferrite between inner and outer conductorof a coaxial line), (b) Transition from x-band waveguide to strip system.-85-(XI. MICROWAVE COMPONENTS)As a by-product of the above investigations a transition from the x-band waveguideto the strip system and a coaxial type of ferrite line (Fig. XI-5) were developed. Thelatter shows promising properties as a direct-current-controlled microwave attenuator.J. SciegiennyB. THEORETICAL ANALYSIS OF A STRIP TRANSMISSION SYSTEMFollowing a method of solution suggested by Mr. H. A. Haus, we obtained a Fourierintegral representation of the fields for the strip system (see Quarterly ProgressReport, Jan. 15, 1953, p. 53), under the following assumptions: (a) The ground planeand dielectric sheet are infinite in extent. (b) The strip is very narrow compared witha wavelength. (c) The strip is infinitesimally thin. (d) Only longitudinal currents existin the strip.The solution was obtained by solving for the fields that would be caused by a sinus-oidal current sheet distribution on the surface of the dielectricK = i K cos ax e - jyzz zA Fourier integral of all such sinusoidal currents (- oo < a < oo) was then formed so that itrepresented the fields caused by a current which is finite only over the region occupiedby the strip. Since the strip was assumed to be very narrow compared with a wave-length, it sufficed to make the tangential E fields zero only at the center of the strip(x=O).Experimental measurements of the propagation constant compared favorably withthe computed values (see Fig. XI-2).M. SchetzenC. BROAD-BAND MATCHING TO TRAVELING-WAVE TUBE HELICESIn order to utilize the broad-band characteristics of the traveling-wave tube ampli-fier or oscillator, it is necessary to match the periodic structure of the tube, which ismost commonly a helix, to a transmission line over a wide band of frequencies. Thedesign of these line-helix couplings is at present an empirical process which is compli-cated by the physical geometry of the traveling-wave tubes (see Fig. XI-6).Measurements show that a traveling-wave tube helix may be regarded as a coaxialline with a characteristic impedance generally lying between 100 to 300 ohms, and con-ventional coaxial waveguide transitions may be designed on this basis. Bandwidths of10 to 20 percent have been obtained by such transitions (see Fig. XI-7).Coaxial-helix transitions have proved to be more successful in giving a broad-band-86-ELECTRON GUN -COLLIMATING MAGNETELECTRON GUN.1 ____ ___ ___ __OUTPUT COAXIALLINESCOUPLINGFig. XI-6Typical traveling-wave tube geometry showing coupling at input end only.ELECTRONBEAM.ADJUST PISTON ANDOPEN-END TURNSFig. XI-7Waveguide helix coupling.-87-11 11 . P;0 - P 0 ly - - ,zz - -ff~TT.1.47TzTzTz7T777ZTZTTz~T777zPT/ TZzTzTcc ~L~~tL1.0 I I I ~ I .-- I6.5654kMC/SEC _3I-- 1.50 IN ·1,~ g 2.01 LW ;oJ =15t%%55twk ~ tZW Iohi a:C\l:!: ~d~ ~Iex>ex>IFig. XI-8Stanford coupling designed for backward wave oscillator; performance curve.Fig. XI-9Coupling for backward wave oscillator.Fig. XI-IOStraight coaxial transition.(XI. MICROWAVE COMPONENTS)match (2), for example, 1. 8 to 4. 0 k Mc/sec. Experiments have been completed onseveral types of coupling, and other geometries are being considered. A coupling devel-oped for a backward wave oscillator is shown in Figs. XI-8 and XI-9 together with atypical VSWR curve obtained by looking into a correctly terminated helix. Reflectionsin the coaxial line from the cavity must be avoided by designing the line carefully; other-wise, interference effects will produce variations in the VSWR which may be ascribederroneously to the coupling.The most characteristic feature of this form of coupling is the high-frequency cutoffcaused by the cavity in a manner which is not yet understood. However, experimentsindicate that it should be possible to develop more compact couplings operating on thesame principle but covering a broader band of frequencies.The straight coaxial transition (3), shown inFig. XI-10, gives a good match into the helix over anindefinitely broad band (see Fig. XI-11), and would20 have applications in a backward wave oscillator of thetype shown in Fig. XI-12, which employs a hollow3 4 5 6 electron beam flowing outside the helix.k MG/SEC Magnets for traveling-wave tube: Solenoids andcored elliptical permanent magnets may be used toFig. XI-11 provide uniform magnetic fields for traveling-waveVSWR for coaxialVS . tubes. Multiple magnetic lens systems or applicationstaper transition.of the principle of strong focusing to traveling-wavetubes are being considered, and some theoreticalexpressions for the electron trajectories have been derived.It has been shown that gaps in the collimating solenoid of widths less than one half ofthe inner radius of the solenoid may be tolerated.P. H. Rose, J. FontanaReferences1. D. C. Rogers: Travelling-wave Amplifiers for 6 to 8 cm, Elec. Commun. 26,144-52, 19482. Private communication from H. C. Poulter, Stanford University3. C. O. Lund: A Broadband Transition from Coaxial Line to Helix, RCA Rev. 11,133-42, 1950-89-OUTPUTI I84 2SCALE IN INCHESFig. XI-12A possible backward wave oscillator with annular electron beam.(XI. MICROWAVE COMPONENTS)D. CAVITIES WITH GENERALIZED MEDIAThe study of the impedance matrix of a cavity with a generalized medium has beencontinued. It has consisted of (a) refinements of the results previously given and(b) a treatment of a specific case, which may be utilized in developing a method for theexperimental determination of the magnetic susceptibility matrix.The analysis previously given (1, 2) has been extended by including in the calculationsthe possibility of having each input coupled to both of the cavity normal modes; it hasbeen refined by taking into account the effect of the wall losses. Since the new expres-sions are lengthy and of no immediate use in themselves, they will not be presented here.However, the following conclusion may be drawn: When both cavity modes are coupledto each of the two inputs, not only is the reciprocity relation violated, but the gyratorcondition (Z 12 = - Z 2 1 ) can never be realized.The second and more important aspect of the investigation consisted of utilizing thedriving-point impedance expression of a single input cylindrical cavity in developing amethod for the experimental determination of the magnetic susceptibility matrix. Theparticular cavity under consideration has been described in the illustrative example ofreference 2 where an expression for its input impedance has also been given withthe assumption that there are no wall losses. In developing an experimental method,the finite Q caused by the wall losses has to be taken into account; therefore, inthe following expression for the driving-point impedance, we have included theselosses.2 2 2 + 1 + J + 1 + Ja -Val o-j I- + 1 + Ja)] QZ = j (1)S o 2 2 _j + 1 + J c + 4o Qw a Pwhere all the symbols have been defined in reference 2 except the following:1/21 1 oo = ( a = ) the resonant angular frequency of the two degenerate TE 1 1 1 modes, anda- = the conductivity of the walls. By suitable manipulations Eq. 1 can be put into thefollowing useful form:2Z = a loo1 (2).02 12 Q2-91-(XI. MICROWAVE COMPONENTS)where1o ¢o i - + Tg (X -K Iw2 = o 1 - + Tg ( 1 +K1(3)1 1 + Tg (X2 - K 2 )Q1 w1 1S 1Q + Tg (x 2 + K2 )In these expressions X1 , X2' K 1' K2 are defined by the magnetic susceptibility matrixXm(X 1 - jXZ) -j (K 1 - jKz) 0Xm = +j (K - jK) (X 1 - jX2) 0 (4)0 0 0T is the volume of the ferrite and g a computable factor whose value depends upon thegeometry of the cavity.Figure XI-13 is an equivalent circuitfor the input impedance Z, provided XmaI remains essentially constant during the_-_resonant behavior of Z. This assumptionL C I G seems reasonable except when the fre-quency is near that of the ferromagneticresonance of the ferrite. The quantitiesL2 C2 G2 Vl 1 , Qw' and wo 1 - (1/2 Qw) can beT_ experimentally determined by taking appro-Val priate measurements at zero static mag-netic field. Consequently, if w 1' 21'Fig. XI-13 and Q2 can be determined with the staticAn equivalent circuit for the input magnetic field turned on, the terms of theimpedance Z. C 1 = o; G1= ( 1 Eo)/Q 1 ; Xm matrix can be computed by utilizingL1 1/ 0o); C 2 = ; G2 = ( 2 o)/Q 2 ; the relations in Eq. 3. It might appearL 2 = 1/(02 ). that a straightforward way of doing thiswould be to measure Z at two differentfrequencies and thus obtain four simultaneous equations for el, JZ' Q 1, and Q 2 . Unfor-tunately, this system is nonlinear and its solution would be very laborious. If this-92-Z(XI. MICROWAVE COMPONENTS)computational complexity is to be avoided, some other procedure should be developed.Attention will be given to this phase of the problem.In using Eqs. 1 and 2 it should be noted that Z represents the difference betweenthe experimentally measurable impedance and the impedance produced by all cavitymodes other than the two degenerate TE 1 11 modes. This latter impedance is essentiallyindependent of frequency and may be experimentally determined by taking appropriatemeasurements at frequencies outside the interval of the resonant behavior of Z.A. D. BerkReferences1. Quarterly Progress Report, Research Laboratory of Electronics, M. I. T. July 15,1952, pp. 60-632. Quarterly Progress Report, Research Laboratory of Electronics, M. I. T. Oct. 15,1952, pp. 32-34-93-

Microwave Components

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Microwave Components

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