THE UN I V E R S I T Y O F MICHIGAN COLLEGE OF ENGINEERING Department of Electrical Engineering Cooley Electronics Laboratory Quarterly Progress Report No. 5 Period Covering April 1, 1961, to July 1, 1961 STUDY AND INVESTIGATION OF A UHF-VHF ANTENNA A. T. Adams R. M. Kalafus J. C. Palais A. I. Simanyi Approved by:' /Zohn A. M. Lyon //Project Director ORA Project 03667 under contract with: UNITED STATES AIR FORCE AIR FORCE SYSTEMS COMMAND AERONAUTICAL SYSTEMS DIVISION CONTRACT NO. AF 33(616)-7180 WRIGHT-PATTERSON AIR FORCE BASE, OHIO administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR September 1961

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TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS iv ABSTRACT v PURPOSE v 1. REPORTS, TRAVEL, AND VISITORS 1 2. FACTUAL DATA 1 2.1 The Problem of a Plane Wave Incident on a Material Sphere 1 2.1.1 Higher Modes 1 2.1.2 Power Flow 5 2.2 The Problem of a Plane Wave Incident Upon a Composite Structure Consisting of a Metal Sphere Inclosed Within, and Concentric with, a Material Sphere 7 2.3 Scattering of a Normally Incident Plane Wave by a Magnetized Ferrite Cylinder 11 2.4 Theory of Loop. Antenna 18 2.4.1 Analysis of the Shielded, Balanced-Loop Antenna 18 2.4.2 Broadbanding Discussion 25 2.5 Waveguide Radiators 26 2.5.1 General Discussion 26 2.5.2 Theoretical Results 28 2.6 Materials 34 2.6.1 Powdered Ferrite 34 2.6.2 Experimental Results on Material Measurements 35 3. ACTIVITIES FOR THE NEXT PERIOD 36 4. SUMMARY 37 5. REFERENCES 38 BIBLIOGRAPHY 39 DISTRIBUTION LIST 61 iii

LIST OF ILLUSTRATIONS Table Page I. Manufacturer's Data on Powdered Ferrite 34 II. Results of Laboratory Tests 35 III. Measured Values of Permeability and Permittivity 36 Figure 1. Coefficients for ferrite sphere for. = e = 10. 3 2. Coefficients for ferrite sphere for. = 3. 4 5. Resonance plot for. = e = 10. 6 4. Power flow diagram for ferrite sphere. 8 5 Conducting sphere problem. 9 6. Coefficients of ferrite sphere with conducting inner sphere. Inner radius = 0.1 km. 12 7. Coefficients of ferrite sphere with conducting inner sphere. Inner radius = 0.5 nm. 13 8. Shielded balanced-loop antenna. 19 9. Equivalent circuit of shielded-loop antenna. 20 10. pro as a function of frequency needed to resonate the shieldedloop antenna of Fig. 8. 24 11. (a) Open-end rectangular waveguide radiator. (b) Coordinate system for the representation of the far fields, 27 12. Theoretical patterns for material-filled rectangular waveguide radiator. 33 iv

ABSTRACT Several theoretical and experimental problems were studied during this period. The study of diffraction of a plane wave by a ferrite sphere was extended to include a metal sphere enclosed within and concentric with the ferrite sphere. Computer results showed that resonant frequencies were changed slightly with the addition of the metal sphere. A study of plane-wave diffraction by a longitudinal magnetized ferrite cylinder was begun. A computer program is being prepared to evaluate the fields for various values of. and t. A shielded, balanced-loop antenna loaded with ferrite material was analyzed, showing that resonance of the loop could be maintained over a broad range of frequency. Radiation patterns from a ferrite-filled waveguide were evaluated on the computer, showing that with the use of ferrite loading the size of a waveguide radiator can be reduced by the factor 1r without substantial change in radiation pattern. The coaxial cavity equipment used to measure complex permeability and permittivity was improved to an accuracy of about 10% in' E, A' and about 20% in e", p". PURPOSE This report summarizes the work done on Contract No. AF 33(616)-7180 during this period from April 1, 1961, to July 1, 1961. The purpose of this task is to investigate the use of solid-state devices such as ferrites and dielectrics in their application to UHF-VHF antennas. More specifically, these materials are to be considered as loading devices or actual elements in the search for improvement of the following properties: (1) radiation resistance, (2) power ~gain and directivity, (3) broadbanding, (4) physical size, and (5) efficiency. Geometries now under consideration include dipoles, rods, slots, biconical dipoles, spirals, and yagis. v

1. REPORTS, TRAVEL, AND VISITORS During this period, no reports were issued, project personnel did not travel and no one visited the project. 2. FACTUAL DATA 2.1 THE PROBLEM OF A PLANE WAVE INCIDENT ON A MATERAL SPHERE The problem of a plane wave incident on a sphere of arbitrary permeability and permittivity was formulated in Quarterly Report No. 4. The interior fields were formally solved, and numerical results obtained for the power density at the center. A factor P was defined as the ratio of this power density to that of the incident wave. The factor P, when plotted against the radius of the sphere in material wavelengths, exhibits sharp resonant peaks where the concentration of power is very high. This study has since been continued and extended to (1) evaluate the effects of higher modes throughout the volume, which gives information on the effect of the materials on the prominence of the various modes; (2) map the lines of power flow, which provides a basis for a physical explanation of the field distortion phenomena; and (3) treat the case of an enclosed, perfectly conducting sphere, which extends the problem to more antenna-like characteristics. 2.1.1 Higher Modes.-The basic formulas will be repeated for conven1

Ei = Eoe-t j 2n+l -n - el n=l n(ni Loin - Ne (1) E jot. n 2n+l () 21) Hi = - - Eoe- j n+) eln + j Noln n=l n(n+l) The interior fields are represented by a linear combination of the above functions, where the coefficients are at and bn: Et = Eoe-J(t Z an 2n M+l (1 t bn(1 n=i n(n+l)- j b Nel (2) -- e - je t f n 2n+l Kt -(1) t -(1) Ht = ~,....... L J -T +J Ht=e n=l n(n+l) n Mln + an Nol t t The coefficients an and bn are expressed by: _t jP~K KS'(k R ka) - ka)Rl)(ka) S a)R )(koa) (53) bt jPK n. (.) (1) iS' (ka)Rn (koa) - KSn(kla)R( )(koa) Here, Ir = l1/o, Er = El/eO, and K = kl/ko = v rf r, where k1 is the propagation constant in the material. Plots of the coefficients vs. radius of the sphere in material wavelengths are shown in Figs. 1 and 2 for various value of Pr and Er. Inspection of Eqs. (1) and (2) shows that the plane-wave functions can be thought of as having the coefficients at = bt = 1. The curves of Fig. 1 show that there are critical radii where the coefficients take on very high values. For example, for yr = Er = 10 at a/Km =.65, it can be seen that the first mode is resonant, while the other modes have considerably smaller coefficientso 2

100 10.01 I / p.=e = I 0 w LL 0.5 1.0 1.5 2.0 0 n~l.001 --.0000 0.5 1.0 1.5 2.0 Fig. 1. Coefficients for ferrite sphere for ji = E = 10.

10 I O~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0 U) H 1.0 z a 0.1 0~~~~3.01 0.5 1.0 1.5 2,0 a/Xf Fig. 2. Coefficients for ferrite sphere for i = =.

Similar resonances appear at larger radii for the higher modes, but the predominance of these higher modes at resonance is not so striking. The resonant frequencies for a given radius can be found by minimizing the denominator. These are the frequencies that satisfy the transcendental equations: KSA(kla)Cn(koa) = 4rSn(kla)CA(koa) (4) IrSn(kla)Cn(koa) = KSn(ka)'Cn(koa) These are plotted in Fig. 3 as a function of mode number. 2.1.2 Power Flow.-Near the first resonance one can say that the field energy is predominantly in the first mode; even the cross-terms between modes are small. Thus the power flow distribution can be satisfactorily described considering only the first mode. The P-factor defined earlier can be represented by: =.Re(ExH*) E2./,t* ) -e() t1 1) (1) ~ 9/4 Re 1tbl Moll x MeJ + a1 b N ell x Noll = 9/4 Re (al b)i Ioll x Mell + ell x.0I (5) When broken into components, the expression in plane I is (where i = o,t) P = 9/4 Re(a b) *. 1 (k lrcos 3 ar 2Sl(klr) Si(klr) s sin E (6) (.klr)5 5

2.5 ---- ax 1.0 I E l J 0.5 0.0 I I I I 0 2 3 4 5 6 7 89 MODE NO. — Fig. 3. Resonance plot for p = C = 10.

This is shown schematically in Fig. 4. Several points are suggested by this equation. First, the shape of the field is not affected by changes in uLr and er as long as = kl/ko is left constant. Second, in the regions where the above assumptions hold (i. e., near the first resonance) the shape of the field depends on the value of klr, regardless of the value of kla, as long as klr < kla. This implies that the streamlines are not always perpendicular at the surface. In fact, they are perpendicular only when the tangential term Sl(klr)Si(klr) vanishes. Third, while the radial term must always have the sign of cos 0, the tangential term alternates in sign as klr is increased. Thus at 8 =:/2, where the radial term vanishes, the stremlines will be in the positive or negative z-direction, which means that some streamlines circulate, much like the turbulence in a high-velocity stream of fluid. 2,2 THE PROBLEM OF A PLANE WAVE INCIDENT UPON A COMPOSITE STRUCTURE CONSISTING OF A METAL SPHERE INCLOSED WITHIN, AND CONCENTRIC WITH, A MATERIAL SPHERE To resemble the problem of an antenna more closely, the problem of a plane wave scattered by a ferrite sphere can be modified by stipulating a spherical conducting boundary in the ferrite's interior (see Fig. 5). This allows one to evaluate the currents induced by the field on the surface. The added conditions required by this modification are two: (1) The tangential component of E vanishes at the surface of the metallic sphere. (2) Since the ferrite region does not now include the origin, the coefficient of the Neumann function is not zero. The most general formulation 7

14\ I\ \ 1 \ T. k \ I\' I~ co~~~~~~~~~~~~~~~~b Fig. 4. -power flO'v aiagram orf rieSh

y' E Ox az H / CONDUCTING Y SPHERE MATERIAL | l / SPHERE Fig. 5. Conducting sphere problem. includes both Bessel and Neumann functions, the latter of which becomes infinite at the origin. This is not physically permissible in the original problem, so the original coefficient must be zero. The expressions for the interior fields are now 00 Eiut 7 jn 2n+l t M(1) t -(2) t -(l) t -(2) Et+ = Ee n 2(n+l an ln + cn oln - bn Neln + dn eln Ht =- l Eoe z.n 2n+l t -(1) t -(2) t -(l) t -(2) Ht = - 1 Eoe it jn bn Meln + dn Meln + j an Noln + Cn Noln i= n(nl) +n eln n + J an oln n oln The boundary conditions are: ar x (Ei + Er) = ar x Et r = a ar x (Hi + H^.) = ar x Ht r. = (8) ar x Et = 0 9 r =b

These give rise to six simultaneous equations: anSn(kla) + cnCn(kla) - KanrRl)(koa) = KSn(koa) atSn(kla) + ctCn(kla) raR(1)(ka) = S(ka) aSn(klb) + tCn(klb) = 0 (9) t t t btSn(kla) + d Cn(kla) - br()(koa) = rSn(ka) bn nka) + dCn(ka) - KbnR((k) KSn(koa) = bnSn(klb) + nCnC(klb) = 0 The coefficients can be solved explicitly. The interior coefficients are: bt J rK n(kla)R1)(koa) - rSn(kla)R(1)(koa S (klb) rC (kla) - KCn(ka) R n(koa) A Lr nk) n n L~)Cnnc(klb) ( t JILrK C( kla)R(1) (ka) - PrCn(kla)Rn(l)(koa] C ( klb) BkR(kla)(kOa) KSn( l a )R(lR)( ak SC(kb)n t SJprK dn rC(kla)R(l)(koa) - KCn( klAa)(1)(ka Ckl) rS(ka)R)(kOa) - KSn(kla)R(1)(koa 10

It will be recalled that Sn, Cn, and l) are adaptations of spherical Bessel, Neumann, and Hankel functions; that is, Sn(z) = z jn(z), and similarly for -1 the others. As z approaches zero, Cn(z) is proportional to z so that for Sn(klb) Sn(klb) a small radius of the conducting sphere, the fractions, (k) and (kCnlb) (klb) are small. Thus it is evident from the above equations that, as the conducting t t sphere vanishes, an and bn approach the values which they had in the original problem, and ct and dt approach zero. This is intuitively reasonable, for as the metal sphere is shrunk, its effect on the fields vanishing in the limit should diminish. Curves of the coefficients are shown in Figs. 6 and 7 for ILr = Er = 10 with an inner sphere of 0.1 ferrite wavelength. The resonant peaks are not at the same radius for the Tm and TE coefficients. This separation between TM and TE coefficients decreases for the higher modes. 2.3 SCATTERING OF A NORMALLY INCIDENT PLANE WAVE BY A MAGNETIZED FERRITE CYLINDER The solution of the boundary-value problem for a normally incident plane wave on a dielectric or ferrite cylinder, was described in Quarterly Progress Report No. 4, is now being explored thoroughly by computer programs. To investigate the various possible uses of a ferrite rod as a director of energy, the electromagnetic field distribution in and around an axially magnetized ferrite rod is now being determined. It is expected that, with the biased ferrite rod, the radiating and impedance properties of solid-state cylindrical structures can be better con11

100 /J= E - 10 INNER SPHERE RADIUS: 0.1 Xm I0 z C) LL t b2.01 - - ^ —--—' —------- 0.5 1.0 a/ Xm Fig. 6. Coefficients of ferrite sphere with conducting inner sphere. Inner radius = 0.1 km. 12

loo, —-----------— i —------------- I 100 INNER SPHERE RADIUS: 0.50Xm I0 t z w W X ) 01.1.0l 0 a t 0 0.5 1.0 Fig 7 Coefficients of ferrite sphere with conducting inner sphere. Fig. 7. Coefficients of ferrite sphere with conducting inner sphere. Inner radius = 0.5.n13

trolled, One of the principal advantages would be a broadbanding of the resonant-power-gathering ability of the ferrite cylinder. The analysis shown below is an extension of the work of W. H. Eggiman, as presented in the July, 1960, issue of the Transactions of the PGMTT (pp. 440-445). Only the TM case (incident field having an electric field in the zdirection only) will give rise to nonreciprocal effects. For TE (Ex, Hz only), the time-varying magnetic field is in the direction of the applied 2 d-c magnetic field, and therefore no nonreciprocal interaction occurs. In the following, a time dependence, e, is to be understood. For the ferrite rod with d-c biasing, the permeability is a tensor quantity: L/ +j -jK with 4 and K given by 4 = 10 \1 + J oW (10) K = 2 ao0 -W where 7r.oMz = IM and WLoHo = wo. Ho is the effective internal magnetic field. For a thin rod, magnetized along its axis, Ho = Happ. For cylindrical rods with a length-to-width ratio not much over one, Ho = Happ - NzMz, where Happ = applied field in the z-direction, Nz = demagnetization factor in the z-direction, and Mz = demagnetization in the z-direction. Since our problem is two-dimensional, we can write (for a time de14

pendence e- ut): B 1 0 1- = 0 ) x E - jWi) -z O Ez ijW l o In air: H -i Q *j *VEZ _ -1y. (;~ ~ * z In ferrite: 1 H-1 ( 1( ) * zThe equation for the H field in ferrite becomes: i jK VE H = - 0$1 -- -j which gives in cylindrical coordinates: Hr (2_K2) -6r r as (11) H. = -- - JM — 1 K Ez_ H - (KL2_K2j ( - CTD (wQ -K2) 6r r 0 / To solve the problem completely, we need expressions for the field quantifiers inside and outside the cylinder. Hr and H. can be derived from Ez for a TM wave according to the equations given above. Inside the cylinder, Ez is given as the solution of the homogeneous wave equation in cylindrical coordinates; i.e., Ez = Z CnJn(Br)e-Jn. Outside the cylinder, Ez is given by the sum of the homogeneous wave solution (representing a wave traveling outward) and of the expansion of the incident travelingplane wave in cylindrical wave form; i.e., E = Scat + E inc 15

anl)(3ore +_)eZ _ jn Jn((or)e-j. Fields inside (r < a): Ez = bnJn(r)e- jn -00 ___ 700 00 Hr = L( 2 K2) 7, bnJa(Pr)e-j - r ~ bnnJn(pr)e ij -2-K2 ) oo r _ (12) Ho = -(2_K2) _ - bnJ (Dr)e jn + K -_ bnnJn(r)e-jn Fields outside (r > a): Ez = 0 anHn(por)e-n~ + Z jnJn(por)e-Jn n=-oo -00 Hr = V z an a ()(pr)n e- + jJn(or)n e- (13) Oi Lpro00 0 -00 22 2 P2- j JB' = Ox aHJ(or)e jnd + Z jn(or)e with: 2 = 22 1Ke2_ =.LPeff =03 The expansion coefficients an and bn are obtained by matching the tangential H(= H), and the normal E(= Ez) at r = a: 16

an= _(j)n Jn(poa)Dn(pa) + Jn(poa)Jn(pa) Hn(Poa)Dn(pa) + Hn(Poa)Jn(pa) bn = j -Hn(Poa)Jn(oa) + Jn(poa)Hn(poa) ( Dn(pa)Hn(poa) + Jn(Ba)HA(Poa).2 jn 1 j11- 1_ v_, - ____ Poa Dn(pa)Hn(loa) + Jn(Pa) x HA(,Poa) where the Dn is defined as Dn(Pa) = Aff FJnJ(na) + a- Jn(al 4eff Lo Ja + - J The an's and bn's have to be evaluated for different Pa, p., and K before any field quantities can be determined. A program now in preparation will provide the expansion coefficients for a range of different rod diameters and a range of different ferrite parameters 4 and K. Then the amount of power flow through the cylinder can be evaluated, which will allow comparison of the power-gathering ability of a ferrite rod with that of a d-c biasing magnetic field. A more detailed study of the fields inside and just outside the cylinder, involving some quite lengthy calculations, is planned to determine promising combinations of Pa, p, and K, i.e., for combinations where the energy densities inside the cylinder are considerably greater 1than what they would be in the absence of the cylinder. 17

2.4 THEORY OF LOOP ANTENNA 2.4.1 Analysis of the Shielded, Balanced-Loop Antenna.-The resonance condition for the shielded, balanced-loop antenna immersed in a ferrite medium has been analyzed. The method follows closely that given by Libby3 for a loop in air. The antenna, shown in Fig. 8, consists of a coaxial line bent into a loop. There is a small gap in the outer conductor at one point and a balanced feed directly across from the gap. As derived in Libby's paper, this configuration can be reduced to the equivalent circuit shown in Fig. 9. Basically, what has been done is that the outer shield has been transformed into the equivalent length of the two-wire transmission line shown in the left part of the figure. Assuming that the frequency is high enough, the fields inside the coaxial line are independent of the fields induced on the. outer legs of the shield. This allows us to treat the inner coaxial line separately as an additional length of line, as shown at the center of the figure. The terms shown on the figure are: Zoo = characteristic impedance of the equivalent two-wire line replacing the outer shield zoo = 276 log D d ~ro D = diameter of the outer shield d = diameter of the outer shield wire Zoi = characteristic impedance of the inner coaxial line 7 - 138 D' Zoi = 1 log D' = inside diameter of the coaxial line: out conductor d' = diameter of the coaxial line: inner conductor 18

/ \ \ /ID~~~~~~~~~~~ p I // P \\ I / // Fig. 8. Shielded balanced-loop antenna. 19

ro = relative permeability of the medium surrounding the antenna Ero = relative permeability of the medium surrounding the antenna ZAHZHD = the terminating impedances eri = relative permittivity of the medium in the coaxial line. SHORT z ^ ~r — V ~01 ( A I - — P/2 — P/2 Fig. 9. Equivalent circuit of shielded loop antenna. The shielded loop receives energy through the induction, by the propagated field, of electromotive forces on the outside surface of the shield, along its legs, causing current to flow and thus producing voltage VEG across shield gap. Letting 8O be the electrical length of the equivalent two-wire line and Si be the electrical length of the coaxial line, the total length (8t) of the transmission line can be found. ZAH and ZHD will be assumed open circuits for the following derivation. Were ZOo is equal to twice Zoi, ~t would be the sum of 60 and Oi. This is not true, so an equivalent electrical length Seq of the outside transmission line with target to the inner line must be found. This is done by equating the impedance to the left of BC (Fig. 9) in terms of Z to the same impedance in terms of twice Zoi. Then 20

j Zoo tan o0 = 2j Zoi tan eeq (15) Solving for eeqQ 9eq = arctan Coo tan e (16) 2 oi Then St = Oi + ~eq = ei + arctan 00 tan 80 (17) 2 Zoi The frequency at which this transmission line network goes through resonance is found by setting Et equal to 90~ and solving for the wavelength, 2. From Eq. (3), tan t = tan Gi + arctan (o0 tan 0 (18) 2 Zoi Using the identity tan A+tan B tan (A + B) = an A+tan B (19) 1-tan A tan B then Zoo tan Gi + 2 Z tan eo tan Ot = (20) zoo 1 - - tan 00 tan i. 27 oi tan Et - 8t t aet t2Z~ tan + tan tan + tan (21) 2 oi o2 Zi Dividing through by tan Et and letting Et be 90~, 1 - zo tan 0o tan i = 0 (22) 2 Zoi 21

or tan E0 tan i ='i (23) Zoo where Oi = Fi Pi is the propagation constant in the coaxial line 3 60 360f 3 60 iPi = -r- = -ri = -- riri ki c ~ = P/2, the length of coaxial line, the length of the twowire line = Po o is the propagation constant in the medium surrounding the antenna 5c~~ 360f Ad _360 __1_E_ = 560 - f r - =6o N 6roero lri = relative permeability of the medium in the coaxial line x = free space wavelength of antenna ki = wavelength in coaxial line 5o = wavelength in the two-wire line Equation (23) becomes tan l Ero tan ( 1 ) (24) \ak \ h. o00 Equation (24) is the design equation for resonance. An illustrative design has been calculated as follows: Assume: Zoi = 50 ohms Ero = 10 D = 4 in. 22

d =.142 in. P/2 = 6.28 in. Eri = 2.1 ~ri = 1 pro = frequency-dependent (to be determined) then, = 3275 9os 7150 o xo Zoo = ro 7 log 4 = r 26.5 J10.142 Equation (24) then becomes tan 10 tan327 = 1790 (25) %715o Jl\o /%o As can be seen from the equation, the resonant wavelength depends on the value of kpro. This transcendental equation was solved graphically for ro vs. X. The wavelength is converted to frequency and plotted in Fig. 10, which shows, for a particular loop antenna, the value of pro needed to resonate at any frequency in the range 1 Me to 200 Mc. It also reveals that a broadband antenna can be realized if the permeability varies with frequency according to the curve. In the given frequency range, the ferrite materials exhibit a dispersion characteristic similar to the curve. The dotted line in the figure exemplifies the 4 frequency characteristic for an experimental ferrite. The major problem in constructing a model of this antenna is the high loss presently associated 23

10,000 x 8 6 U-Lro NEEDED FOR 5 4 RESONANCE OF / LOOP ANTENNA 2 1,000 86 0 X FLro OF EXPERIMENTAL 1 00o - FERRITE o 4 6 _ / X > 2 < 10 a, / 3_ / / - / OCI i. 8 x 24 Xx 3 2L.I 8 6543 2 8 6 5 4 3 2 8 6 5 4 3 2 2 - 0 0 0 -- FREQUENCY (MC) Fig. 10. Ikro as a function of frequency needed to resonate the shielded-loop antenna of Fig. 8. 24

with ferrites of this character. Derivations of this type indicate the need for improved materials. For the design given above, a reasonable bandwidth would be from 5 Me to 100 Me (20 to 1 bandwidth), since values of pro greater than 500 and less than.9 are unlikely in this frequency range, A shielded loop similar to the one described above has been constructed. It will be tested, insofar as possible with available material, and the results will be compared with the theory. 2.4.2 Broadbanding Discussion.-The method of broadbanding described in Section 2.4.2 can also be applied to other antenna structures. The basis of the theory is that the wavelength in the medium either (1) remains constant over a given frequency range, or (2) changes more slowly than the frequency variation according to some calculated curve. For (1), the wavelength is given by: = v = c- (26) f'Er where: v = velocity of propagation in the medium f = frequency of operation c = velocity of light in free space r = relative permeability, frequency-dependent cr = relative permittivity For constant wavelength, we then need f If/-r = constant (27) 25

Among the antennas that could use this type of broadbanding are horns, slots, dipoles, and simple arrays. An example of an antenna utilizing the second type of permeability characteristic is given in Section 2.4.1 on the shielded loop. Although materials are not now available to test the theory properly, we will continue our efforts along this line to increase the bandwidth of antennas. 2.5 WAVEGUIDE RADIATORS 2.5.1 General Discussion. —Derivations of the characteristics of material-filled waveguide radiators have been undertaken. The same type of antenna filled with air, has high efficiency, is easy to construct, and has been built in a number of forms, some of which might benefit by using solidstate materials in their construction. It is expected that a practical antenna will evolve from these derivations. One disadvantage of waveguide radiators at the frequencies of interest (around 150 Me) is their large size. Filling the waveguide with a high pt, e material will reduce the wavelgnth considerably and thus reduce the cutoff frequency and over-all size of the waveguide. As an example, consider the rectangular waveguide shown in Fig. 11. For the dominant TE10 mode, the cutoff wavelength is given by \c = 2a. For a cutoff frequency of 100 Me, the dimension "a" must be 59 in. If, however, the waveguide is filled with material of |t = e 7 10, the wavelength is reduced by a factor of 10 and thus "a" is reduced to 5.9 in. 26

z (a) z P 0 I/ x (b) Fig. 11. (a) Open-end rectangular waveguide radiator. (b) Coordinate system for the representation of the far fields. 27

While the size advantage is readily apparent, changes in antenna characteristic such as gain, efficiency, bandwidth, etc., must be investigated using a detailed analysis. Of several derivations now in progress, one has been completed, and is presented in the next section. 2.5.2 Theoretical Results. —The antenna to be discussed in this section is the open-ended waveguide radiator shown in Fig. 11. The waveguide is assumed filled with a material of relative permeability pr and relative permittivity Er. The derivation for the radiated fields is similar to that of Silver5 for an air-filled waveguide. Huygens principle is used to replace the source by the fields in the aperture. To simplify the solution, higherorder modes and the current distribution over the exterior surface of the waveguide are neglected. As shown by Silver, the radiated fields from an aperture are given by: ER = 0 jke-3kR +4rR i cosi (Nxcos +Nsin) jke= n cos X X (Nxsin O - Nycos O) where.. s +p jk(x sin ~ cos ( + y sin 8 sin 0) aperture (29) and Et = resultant electric field of the dominant mode over the aperture 28

(Et)i = incident electric field of the dominant mode over the aperture F = reflection coefficient of the open-end waveguide k = oI - = 2-, X = free space wavelength. ko Only TE modes in the waveguide are considered in the above equations. For TE modes, the expressions for the incident fields at the aperture are: (Et)i = j'I mLY sin m cos n 7 K~a a b (30) j wlt nTr mrrx nary (.)i = 7 2b cos - sin y Y7 KIb a b where a) )2 2 = (T)2 + ()2 From Eq. (29), Nx and N~ are computed jnn (l+F) r mTx (jkx sin 3 cos ). n (jky sin 8 sin ) Os = 2 co_ dx sin Osin e dy X IKb o a b (31) jmT(l+r) sin mKXe(jkx sin 8 cos <) dnry (jky sin 9 sin ) =y - sa "e dx os b dy Performing the integration, we obtain n2 It (lt+r) T ej(kasin 8 cos 0 + m)r N = -5- -- k sin ~ cos _) x K2b ksncoALsin28 cos2 - (D 2 [ ej(kbsin 8 sin 0 + njt _ K2sin2 sin2~ - (t Ny = - m22(l+2)k sin sin F eJ(kasin 8 cos + mj (52) Y ~ Ka _ K2sin28 cos2 _ -' ) 1 - O j(kbsln sin +-n 2 _ 9sin2~ Sin2 - (n)2 29

By substituting into Eq. (29), we get for the far fields 1F r j(7iab)2 =sin mn 0 osP [lo0 ^E = 1'J 22R sin cos a + r - cos + ( E0 = o r an (aab) si sin cos 5 (34) Cos 8+ + r O - - -3]mn(8,)) where mn(si) = ( c 2 - (2 sin s )2 - (+ 2 -j[kR - 7o sin Q(a cos 0 + b sin 0) - (m + n + 1)+ ] Equations (33), (34), and (35) can be simplified when only the TEo mode propagating in the waveguide. Letting m = 1, n = 0 we obtain =- ~ r tioO ca2b P1lO l-O- ) eE3 ~ 1lr-g 2 sin + + r.......... eo 2XoR cuir`coWr N (ita sin ~ 7 7 Ttb sin (356) cos ( sin cos ) sin(7 sin sin sin cos sinsin cos ) ()j -j[kR - - sin 9 (a cos < + b sin $>) ] e )'3 50

EO = 1- r r2b cos N cos ~4 + lo + r cos - o o Co 2AoR W otr ro CO -cos (sa sin a cos ) 1 sin ( sin sin O ^~_______ --- % (37) sin cos )2 2 sin sin 0 I -j[kR - - sin 8 (a cos + b sin ))] The phase factor, kR - T sin e(a cos $ + b sin 0), can be simplified for the I %o far field by shifting the origin to the center of the aperture. The phase factor then becomes kR where R is now measured from the center of the aperture. Since the electric field is polarized in the y-direction in the waveguide, the yz-plane is the E-plane of the system and the xz-plane is the H-plane. The patterns are: A. E-plane, $ = i/2 E = 0 0o 2a2b + lo P.. E = + 1r +_ a I + O cos 9 + r - lo cos e Ve2 = GO +!r YjoRo Cor ^lo~0 ml(38) -sin )-b sin 8) -jkR 2* sin 3 h-Ao 31

B. H-plane, 0 = 0 Ee = 0 E = -t 7^ cos 9 + lO + (cos - _0 7 ^o 2Xo R W oo r Kr r G JO (39) cos (". sin ) 0) t: sin 0)2 - (2 kR The radiation patterns were calculated from Eqs. (38) and (39) using the IBM 704 computer. For this calculation r was assumed to be zero. Referring to Fig. 11, the plot was made for the following conditions: a/b = 2 a/\o =.625/ r4r b/o, =.312/ Vr r f/fc = 1.25 where: fc is the cutoff frequency in the waveguide, f is the frequency of operation, and \o is the free-space wavelength of operation. The pattern is shown in Fig. 12 for several combinations of or, Er values. As can be seen from the graph, there is a small broadening of the pattern compared to the same antenna filled with air for or equal to 3, Er equal to 3, and for or = 10, Er = 10. The patterns are changed more radically for or different from Er. For or ~ er, the H-plane pattern is similar to the air case for 0 < ~ < 90~ and exhibits radiation in the reverse direction. For the E32

1.o A 0.9 -~ H - PLANE x'r = I\0 0.8-'r:\ 0 20 40 60 80 1\00 1 0 10 160'9 " 0.6 \A \ r 3 160.5\ \ xr X 01 0 0.2 \ / 0.3 I I I r i~-3 0 20 40 60 80 100 120 140 160 180 I.0 o A \A E -PLANE 0.9 \EEr 0.8 0 4 A A A 00 X 0.7 \3 0.6 Er 0 0 20 40 60 80 100 120 A0 160 180 N 3

plane, the pattern is practically omni-directional. For the case of er ~>> r the situation is reversed with a narrow beam in the E-plane and a broad beam in the H-plane. An open-ended waveguide antenna is being constructed and will soon be tested. 2.6 MATERIALS 2.6.1 Powdered Ferrite.-Date were received for the powdered ferrite characteristics from the manufacturer. The measurements were taken for a sample in the solid form. A large difference characteristics exists between the material ordered and that received. Reproduction of the original material is a problem requiring additional time and funds. Data on the original sample and the new sample as measured by the manufacturer are given in Table I. TABLE I MANUFACTURER'S DATA ON POWDERED FERRITE 100 Me 200 Me [ I' TI II H Original Sample 7.1 0.028 6.1 <0.01 New Sample 10.5 2 1 8.0 3,6 The high losses associated with this material make use in experimental testing of the antennas of doubtful value. Tests have been made in our laboratory of the properties of this ferrite in the powdered and in the solid form. Results are shown in Table II. 34

TABLE II RESULTS OF LABORATORY TESTS Measurement,, It Sample Frequency' " e' ~ Method Solid Resonant Cavity 260Mc 8.06 3.34 8.2 0.53 Solid VSWR 260Mc 7.6 3.4 7.0 0.4 Powder Resonant Cavity 260Mc 3.27.55 As was expected, the permeability (a') of the powder is roughly half of the permeability of the solid, while the magnetic Q("'/p") of the powder is greater than the Q of the solid ferrite. 2.6.2 Experimental Results on Material Measurements. —Measurements of permeability and permittivity have been made using the Perturbation method described in the second Quarterly Progress Report. Results of measurements made on several materials are given in Table III. 35

TABLE III MEASURED VALUES OF PERMEABILITY AND PERMITTIVITY Material ___ E_ c Qe Ceramag 22 5A 14.45 2.01 Ceramag 22 5A 12.83 2.16 Ceramag 22 5A 7.9 Ceramag 22 5A 6.77 M072 7.06 7.12 M112 9.0 M112 8.9 M469 8.02 M469 8.06 2.41 M469 8.04 19.21 M469 8.21 15.29 Powder 5.27 5.95 Stycast Hi-K-4 4.09 Stycast Hi-K-4 3.7 Frequency: 260Mc 3. ACTIVITIES FOR THE NEXT PERIOD (1) Experimental work on the ferrite-loaded biconical antenna, the shielded-loop antenna, and the waveguide radiator will be completed. (2) The theoretical studies of plane-wave diffraction by a ferrite sphere and a ferrite cylinder will be extended to analyze the power flow near resonance. (3) A theoretical study of plane-wave diffraction by a ferrite spheroid will be initiated. (4) Theoretical results of radiation from sectoral horns will be analyzed on the computer. (5) Experimental work on the ferrite-loaded spiral will be initiated. 36

4. SUMMARY The theoretical study of plane-wave diffraction by a ferrite sphere has been extended to (1) evaluate the effect of higher modes, (2) map the lines of power flow, and (3) treat the case of an enclosed, perfectly conducting sphere. The theoretical study of plane-wave diffraction by a ferrite cylinder has been extended to treat the longitudinally magnetized case. An analysis of the resonance condition for the shielded, balanced-loop antenna immersed in a ferrite medium has been made. Conditions for maintenance of resonance over a broad frequency range have been obtained and found to be fairly consistent with the published properties of known ferrite materials. The analysis suggests the possibility of tailoring ferrite properties for broadband use in microwave components and antennas. Radiation from a ferrite-filled rectangular waveguide has been analyzed. The results show that, for pt = e, the radiator size can be decreased with very little change in beam pattern. Experimental results of the measurement of ferrite materials are given. 37

5. REFERENCES 1. J. A. Stratton, Electromagnetic Theory, New York: McGraw-Hill Book Co., Inc., 1941. 2. W. H. Eggiman, "Scattering of a Plane Wave on a Ferrite Cylinder at Normal Incidence," Trans. IRE, PGMTT, pp. 440-445, 1960. 3. L. L. Libby, "Special Aspects of Balanced Shielded Loops," Proc. IRE, 34, 641-646 (1946). 4. NBS Report No. 6063, A Summary of the Investigation of Ferromagnetic Materials-Ferrites, Fig. 77. 5. S. Silver, Microwave Antenna Theory and Design, Radiation Laboratory Series, Vol. 12, New York: McGraw-Hill Book Co., Inc., 1959. 38

BIBLIOGRAPHY I. PERIODICALS - ANTENNAS a. General Theory 1. "The Measurement of TV Field Strength in the VHF/UHF Bands," H. T. Head and 0. L. Prestholdt, Proc. IRE, Vol. 48, No. 6, June 1960, p. 1000. 2. "The Archimedean Two-Wire Spiral Antenna," J. A. Kaiser, IRE Trans. A & P, Iay 1960, p. 312. 3. "Spiral Antennas," W. L. Curtis, IRE Trans. A & P, Vol. AP-8 No. 3, May 1960, p. 298. 4. "A Broad-band Spherical Satellite Antenna," H. B. Riblet, Proc. IRE, Vol. 48, No. 4, April 1960, p. 631. 5. "The Spiral Antenna," R. Bower and J. J. Wolfe, NRC, Part I, 1960, p. 84. 6. "Parasitic Spiral Arrays," R. M. Brown and R. C. Dodson, NRC, Part I, 1960, p. 51. 7. "A New Method of Near Field Analysis," R. C. Hansen and L. L. Bailin, Trans. IRE, PGAP, December 1959, p. 458. 8. "The Finite Conical Antenna," S. Adachi, R. G. Kouyounijian and R. G. Van Sickle, Trans. IRE, PGAP, December 1959, p. 406. 9. "The Numerical Solution of Antenna and Scattering Problems," George Sinclair, Trans. IRE, PGAP, December 1959, p. 402. 10. "Numerical Integration Methods for Antenna Pattern Calculations," C. A. Allen, Trans. IRE, PGAP, December 1959, P. 387. 11. "The Bandwidth of Helical Antennas," T. S. M. Maclean and R. G. Kouyounijian, Trans. IRE, PGAP, December 1959, p. 379. 12. "The Equiangular Spiral Antenna," J. D. Dyson, Trans. IRE A & P, Vol. AP-7, April 1959, p. 181. 13. "A Variational Expression for the Terminal Admittance of a Semi-Infinite Dielectric Rod," Angulo and Chang, IRE Trans. A & P, July 1959, p. 207. 14. "Calculated Radiation Resistance of an Elliptical Loop Antenna with Constant Current," J. Y.Wong, J. of Brit. IRE, Vol. 19, No. 2, March 1959, p. 117. 59

Ia 15. "The Rectangular Loop Antenna as a Dipole," R. King, IRE Trans., January 1959, p. 53. 16. "Radiation Field of an Elliptical Helical Antenna," Wong and Loh,. IRE Trans., January 1959, p. 46. 17. "A Theoretical Study of the Equiangular Spiral Antenna," P. E. Mast, Electrical Engineering Research Lab., University of Illinois, Urbana, Illinois, Tech. Report No. 35, Sept. 12, 1958. 18. "Evaluating the Impedance Broadbanding Potential of Antennas," A Vassiliadis and R. L. Tanner, Trans. IRE, PGAP, July 1958, p. 226. 19. "Surface Current Induced by Short Wavelength Radiation," J. A. Cullen, Physical Review, Vol. 109, No. 6, 1958, p. 1863. 20. "Characteristic Impedance of Two Infinite Cones of Arbitrary Crosssection," R. L. Carrel, Trans. IRE, PGAP, April 1958, p. 197. 21. "Determination of a Current Distribution Over a Cone Surface Which Will Produce a Prescribed Radiation Pattern," H. Vuz, Trans. IRE, PGAP, April 1958, p. 182. 22. "Back Scattering Cross-section of a Center Loaded Cylindrical Antenna," Yueh-Ying Hu, Trans. IRE, PGAP, January 1958) p. 140. 23. "The Prolate Spheroidal Antenna: Current and Impedance," C. P. Wells, Trans. IRE, PGAP, January 1958, p. 125. 24. "The Current Distribution and Input Impedance of Cylindrical Antennas," E. V. Bohn, Trans. IRE, PGAP, October 1957, p. 343. 25. "An Experimental Investigation and Application of the Spiral Antennas," Temco Aircraft Corp., Dallas, Texas, Final Engineering Report, July 1957. 26. "The Prolate Spheroidal Monopole Antenna," C. Flammer, Stanford Res. Inst., Menlo Park, California, Tech. Report No. 22, June 1957. 27. "A Simple Solution to the Problem of the Cylindrical Antenna," Gesse G. Chaney, Trans. IRE, PGAP, April 1957, p. 217. 28. "Frequency Independent Antennas," V. H. Rumsey, 1957 IRE National Conv. Rec., Vol. 5, Part I, p. 114. 29. "Spherical Surface Wave Antennas," R. S. Elliott, Trans. IRE, PGAP, July 1956, p. 422. 30. "Theory of the Corner Driven Square Loop Antenna, R. King, Trans. IRE, PGAP, July 1956, p. 393. 31. "Solution of Problems in Electromagnetic Theory on a High Speed Digital Calculating Machine," E. K. Ritter, Trans. IRE, PGAP, July 1956, p. 276. 40

a 32. "A Method of Analyzing Antennas of Unequal Size," C. A. Lewis and C. T. Tai, Trans. IRE, PGAP, April 1956, p. 128. 33. "Antenna Pattern Distortion by Dielectric Sheets," J. H. Richmond, Trans. IRE, PGAP, April 1956, p. 139. 34. "Variational Principles for Electromagnetic Resonators and Waveguides," A. D. Berk, Trans. IRE, PGAP, April 1956, p. 104. 35. "A New Interpretation of the Integral Equation Formulation of Cylindrical Antennas," C. T. Tai, IRE Trans. A & P, July 1955, p. 125. 36. "Spiral Slot Antenna," E. M. Turner, Wright Patterson AFB, Ohio, Tech. Note WCLR-55-8, WADC, June 1955. 37. "The Spiral Antenna," B. H. Burdine, Res. Lab. of Electronics, MIT, Cambridge, Massachusetts, Report Nos. 1 and 2, March 15, 1955 and April 15, 1955. 38. "Radiation Characteristics of a Conical Helix of Low Pitch Angle," J. S. Chatterjie, J. of App. Phys., Vol. 26, March 1955, p. 331. 39. "The Study on Flush-Mounted Circularly Polarized Antennas and Polarization Modulation," J. C. Pullara and H. H. Hibbs, Melpar, Inc., Falls Church, Va., P. 0. 569838, Prime Contractor —Sperry Gyroscope Co., March 1955. 40. "A Comparison of Antenna Problems at VHF and VHF TV," L. O. Krause, NCR, Part I, 1954, p. 126. 41. "Radiation Field of a Conical Helix," J. S. Chatterjie, J. of App. Phys., Vol. 24, May 1953, p. 550. 42. "Cylindrical Aerials —Now Solution of Hallew's Integral Equation for Current," B. Storm, WE, Vol. 29, No. 346, July 1952, p. 74. 43. "Radiation Characteristics of Helical Antennas of Few Turns," O. C. Haycock and J. S. Ajioka, Proc. IRE. Vol. 40, No. 8, Aug. 1952, p. 989. 44. "General Theory of Electromagnetic Horns," A. F. Stevenson, J. of App. Phys., Vol. 22, No. 12, December 1951, p. 1447. 45. "General Theory of Symmetric Biconical Antennas," S. A. Schelkunoff, J. of App. Phys., Vol. 22, No. 11, November 1951, p. 1330. 46. "Radiation Field of Helical Antennas With Sinusoidal Current," E. T. Kornhauser, J. of App. Phys., Vol. 22, No. 7, July 1951, p. 887. 47. "Current Distribution on Helical Antennas," J. A. Marsh, Proc. IRE, Vol. 39, No. 6, June 1951, p. 668. 48. "Separation of Variables in Electromagnetic Theory," D. E. Spencer, J. of App. Phys., Vol. 22, No. 4, April 1951, p. 386. 41

Ia 49. "Radiation from Wide-Angle Conical Antennas Fed by a Coaxial Line," C. H. Papas and R. King, Proc. IRE, Vol. 39, No. 1, Jan. 1951, p. 49. 50. "Input Impedance of Wide-Angle Conical Antennas Fed by a Coaxial Line," C. H. Papas and R. King, Proc. IRE, Vol. 37, No. 11, 1949, p. 1269. 51. "The Helical Antenna," J. D. Kraus, Proc. IRE, Vol. 37, No. 3, March 1949, p. 263. 52. "On the Theory of Biconical Antennas," C. T. Tai, J. of App. Phys., Vol. 19, December 1948. 53. "Input Impedance of Wide-Angle Conical Antennas," C. H. Papas and R. King, Cruft Lab. Tech. Report, December 1, 1948. 54. "Center-fed Half-wave Radiating Slot," J. L. Putman, B. Russell and W. Walkinshaw, J. B. IEE, Vol. 95, Part III, No. 36, July 1948, p. 282. 55. "Admittance Diagrams for Antennas and the Relation Between Antenna Theories," E. Hallen, Cruft Lab. Tech. Report, Harvard University, June 1, 1948. 56. "The Measurement of Antenna Impedance Using a Receiving Antenna," D. G. Wilson and R. King, Cruft Iab. Tech. Report, Harvard University, May 15, 1948. 57. "Measured Impedances of Helical Beam Antennas," Glasser and Kraus, J. of App. Phys., Vol. 19, No. 2, February 1948, p. 127. 58. "Characteristics of Helical Antennas Radiating in the Axial Mode," Kraus and Williamson, J. of App. Phys., Vol. 19, No. 1, January 1948, p. 87. 59. "The Conical Dipole of Wide Angle," P. D. P. Smith, J. of App. Phys. Vol. 19, No. 1, January 1948, p. 11. 60. "The Influence of the Width of the Gap Upon the Theory of Antennas," L. Infeld, Quart. Appl. Math., Vol. 5, July 1947, pp. 113-132. 61. "The Impedance Measurements of Antennas Involving Loop and Linear Elements," Tung Chang, Cruft Lab. Tech. Report, Harvard Univ., 1947. 62. "Low-Frequency Aircraft Antennas," J. V. N. Granger, Cruft Lab. Tech. Report, Harvard University, 1947. 63. "Relation to Complementary Wire Aerials (Babinet's Principle)," J. IEE, Vol. 93, Part IIIA, 1946, p. 620. 64. "The Radiation Field of an Unbalanced Dipole," W. Kelow, Proc. IRE, Vol. 34, No. 7, 1946, p. 444. 65. "The Cylindrical Antenna: Current and Impedances," R. King and D. Middleton, Quart, Appl. Math., Part III, 1946, p. 302. 42

[a 66. "Principal and Complementary Waves in Antennas," S. A. Schelkunoff, Proc. IRE, Vol. 34, No. 1, January 1946, p. 23. 67. "A Helical Antenna For Circular Polarization," H. Wheeler, Proc. IRE, Vol. 33, No. 12, 1945, p. 1484. 68. "Loop Antennas With Uniform Current," D. Foster, Proc. IRE, Vol. 32, No. 10, October 1944, p. 603. 69. "Circular Loop Antennas at UHF," J. B. Sherman, Proc. IRE, Vol. 32, No. 9, November 1944, p. 534. 70. "The Principle of Reciprocity in Antenna Theory," M. S. Newman, Proc. IRE, Vol. 31, No. 12, December 1943, p. 666. 71. "Radiation Energy and Earth Absorption with Dipole Aerials," A. Sommerfeld, F. Renner, Ann. d. Phys., 1942, p. 41. 72. "On Radiation from Antennas," S. A. Schelkunoff and C. B. Feldman, Proc. IRE, November 1942, p. 511. 73. "Theory of Antennas of Arbitrary Size and Shape," S. A. Schelkunoff, Proc. IRE, Vol. 29, September 1941, pp. 493-521. 74. "Theoretical Investigation into the Transmitting and Receiving Qualities of Antennas," E. Hallen, Nova Acta Regial Soc. Sci. Upsaliensis, Ser. 4, Vol. 11, November 1938, pp. 1-44. 75. "Biconical Electromagnetic Horns," W. L. Barrow, L. J. Chu, and J. J. Jansen, Proc. IRE, XXVII, December 1939, pp. 769-779. 76. G. Sinclair, "The Patterns of Slated-Cylinder Antennas," Proc. IRE, Dec. 48, pp. 1487-1492. 77. A. F. Stevenson, "Theory of Slots in Rectangular Waveguides," JAP, Vol. 19, 1948, pp. 24-38. 78. D. G. Froad and J. R. Wait, Inst. Elec. Engrs. Proc., V 105, pt B (Radio and Electronics Eng) NO. 7, Jan. 56, pp. 103-109. 79. J. R. Wait and S. H. Kahana, "Calculated Patterns of Circumferential Slots on a Circular Conducting Cylinder," Can. J. Tech., Vol. 33, Jan. 55, PP. 79-97. 80. R. J. Stegan, "Slot Radiators and Arrays," Radio-Electronics Engr., Jan. 52. 81. H. Gruenberg, "Second Order Beams of Slotted Waveguide Arrays," Cam. J. Phys., Vol. 31, pp. 55-59. 82. S. Silver, "The External Field Produced by a Slot in an Infinite Circular Cylinder," JAP, Feb. 1950. 43

a 83. "Fields Produced by a Slot on a Large Circular Cylinder," IRE Trans., Ap. 3, July 55, pp. 128-137. 84. K. Franz, P. A. Mann, and J. Vocalides, "Der Wirkleitniert Von Dipolen Andlicher Large und Dicke," Ar chir der Elektrischen Ubertrayungen, Vol. 12, No. 2, Feb. 1958, pp. 49-53. 85. Uda Mushiyake, "Yagi-Uda Antenna," Sasaki Publishing Co., Sendai, Tohoku, Japan, 1955. 86. P. Brundell, "Current Potential Distribution on a Circular Loop Antenna," Transactions of the Royal Institute of Technology, Stockholm, Sweden, Monograph No. 154, 1960. 44

I. PERIODICALS - ANTENNAS b. Utilizing Dissipative Media 1. "Resonance and Supergain Effects in Small Ferromagnetically or Dielectrically Loaded Biconical Antennas," C. Polk, Trans. IRE, PGAP December 1959, p. 414. 2. "Radiation Properties of a Thin Wire Loop Antenna Embedded in a Spherical Medium," O. R. Cruzan, IRE Trans. A & P, Oct. 1959, pp. 345-352. 3. "The Radiansphere Around a Small Antenna," H. W. Wheeler, Proc. IRE, Vol. 47, No. 8, Aug. 1959, p. 1325. 4. "Impedance Characteristics of a Uniform Current Loop Having a Spherical Core," Saburo Adachi, The Ohio State Univ. Res. Foundation Report 66226, April 15, 1959. 5. "Miniaturized Resonant Antenna Using Ferrites," D. M. Grimes, J. of App. Phys., Vol. 29, No. 3, March 1958, p. 401. 6. "Immittance of Thin Biconical Antennas Containing Material of Arbitrary Permeability and Permittivity," RCA Lab, Digital Computer Problem No. 619, January 1958. 7. "Closely Spaced High Dielectric Constant Polyrod Arrays," L. W. Michey and G. G. Chadwick, NCR, Part I, 1958, p. 213. 8. "Radiation from a Radial Dipole Through a Thin Dielectric Spherical Shell," M. G. Andreasen, Trans. IRE, PGAP, Oct. 1957, p. 337. 9. "A Method of Estimating the Power Radiated Directly at the Feed of Dielectric-Rod Aerials," R. H. Clarke, IEE Proc., Vol. 104, Part B, No. 17, September 1957, P. 511. 10. "VHF Ferrite Antenna': Radiation Properties," O. R. Cruzan, Diamond Ord. Fuze Lab., Washington 25, D. C., Tech. Report No. TR-516, August 15, 1957. 11. "Research in Magnetic Antennas," J. L. Stewart, California Inst. of Tech., Pasadena, ASTIA AD 140500, July 1957. 12. "A Technique for Controlling the Radiation from Dielectric Rod Waveguides," J. W. Duncan and R. H. Duhamel, Trans. IRE, PGAP, July 1957, p. 284. 13. "Thin Wire Loop and Thin Biconical Antennas in Finite Media," J. Herman, Diamond Ord, Fuze Lab., Washington 25, D. C., Tech. Report No. TR-462, May 1, 1957. (General size spherical core) 45

Ib 14. "On the Estimation of Ferrite Loop Antenna Impedance," W. L. Weeks, Elect. Eng. Res. Lab. Tech. Report No. 17, Univ. of Ill., Urbana, Ill., April 10, 1957. (Electrically small antennas) 15. "Fenod Radiating System," Reggia, Spencer, Hatcher and Tompkins, Proc. IRE, Vol. 45, No. 3, March 1957, p. 344. 16. "On Ferrite Loop Antenna Measurements," J. L. Stewart, IRE Conv. Rec., 1957, p. 46. 17. "VHF Ferrite Antenna: I. Radiation Properties," O. R. Cruzan, 1957 PGMIL Conv. Rec., pp. 169-175. (Mainly electrically small spherical core) 18. "VHF Ferrite Antenna: II. Radiation Measurements," H. A. Dropkin and E. Metzger and J. C. Cacheris, 1957 PGMIL Conv. Rec., pp. 175-182. (Ferrite rod cores) 19. "Impedance of Ferrite Loop Antennas," V. H. Rumsey and W. L. Weeks, Elect. Eng. Res. Lab. Tech. Report No. 13, Univ. of Ill., Urbana, Ill,, Oct. 15, 1956. 20. "Radiation Properties of Spherical Ferrite Antenna," 0. R. Cruzan, Diamond Ordnance Fuze Lab., Washington 25, D. C., Tech. Report TR-387, Oct. 15, 1956. 21. "Radiation From Ferrite-Filled Apertures," P. J. Angelakos and M. M. Korman, Prbc. IRE, Vol. 44, No. 10, October 1956, p. 1463. 22. "Electrically Small Ferrite Loaded Loop Antennas," V. H. Rumsey and W. L. Weeks, NCR, Part I, 1956, p. 165. 23. "Ferrod Radiator Systems," F. Reggia, E. G. Spencer, R. D. Hatcher and J. E. Tompkins, NCR, Part I, 1956, p. 213. 24. "IRE Standards on Radio Receivers: Method of Testing Receivers Employing Ferrite Core Loop Antennas," Proc. IRE, Vol. 43, No. 9, September 1955, p. 1086. 25. "Input Impedance of a Spherical Ferrite Antenna with a Latitudinal Current," W. L. Weeks, Elect. Eng. Res. Lab. Tech. Report No. 6, Univ. of Ill., Urbana, Ill., Aug. 20, 1955. 26. "The Radiation of a Hertzian Dipole Over a Coated Conductor," IEE Proc., Vol. 102, No. 1, Part C, March 1955, p. 104. 27. "Surface Matching of Dielectric Lenses," E. M. T. Jones and S. Cohn, NCR, Part I, 1954, p. 46. 28. "The Receiving Loop With a Hollow Prolate Spheroidal Core," J. R. Wait, Canad. J. Tech., Vol. 31, June 1953, pp. 132-137. 29. "The Magnetic Dipole Antenna Immersed in a Conducting Medium," J. R. Wait, Proc. IRE, Vol. 40, No. 10, Oct. 1952, p. 1244. 46

Ib 30. "A Broadside Dielectric Antenna," G. E. Mueller, Proc. IRE, Vol. 40, No. 1, 1952, p. 71. 31. "Radiation From a Uniform Circular Lop Antenna in the Presence of a Sphere," C. T. Tai, Stanford Res. Inst., Tech. Report No. 32, 1952. 32. "Dielectric-lens Aerial —for Marine Navigational Radar," D. G. Kiely, WE, Vol. 28, No. 337, October 1951, p. 299. 33. "Dielectric Aerials with Shaped Radiation Patterns," D. G. Kiely, WE, Vol. 28, No. 338, June 1951, p. 177. 34. "On the Directional Patterns of Polystyrene Rod Antennas," R. B. Watson, J. of App. Phys., Vol. 22, No. 2, Feb. 1951, p. 154. 35. "Electric Dipoles in the Presence of Elliptic and Circular Cylinders," W. S. Lucke, J. of App. Phys., Vol. 22, No. 1, Jan. 1951, p. 14. 36. "On Radiation and Radiating Systems in the Presence of a Dissipative Medium," C. T. Tai, Cruft Lab. Tech. Report No. 77, Harvard University May 10, 1949. 37. "Reflection and Refraction of a Plance Electromagnetic Wave at a Periodic Surface," C. T. Tai, Cruft Lab. Tech. Report No. 28, Harvard Univ., 1948. 38. "Surface Currents on a Conducting Sphere Excited by a Dipole," C. H. Papas and R. W. P. King, J. of App. Phys., September 1948. 39. "Small Aerial in Dielectric Media," R. H. Barfield and R. E. Burgess, WE, Vol. 25, No. 8, August 1948, p. 246. 40. "Radiation Patterns of Dielectric Rods —Experiment and Theory," R. B. Watson and Horton, J. of App. Phys., Vol. 19, No. 7, July 1948, p. 661. 41. "Polyrod Antennas," G. E. Mueller and W. A. Tyrrell, Bell System Tech. Journal, Vol. 26, No. 4, October 1947, pp. 837-851. 42. "Dielectric-Rod Aerials," D. F. Halliday and D. G. Kiely, J. of Brit. IEE, Vol. 94, Part IIIA, No. 14, 1947, p. 610. 43. "Propagation of Electromagnetic Waves from a Dissipative Medium to a Perfect Dielectric," C. T. Tai, Cruft Lab. Tech. Report No. 18, Harvard University, 1947. 44. "Radiation of a Hertzian Dipole Immersed in a Dissipative Medium," Cruft Lab. Tech. Report, No. 21, Harvard University, 1947. 45. "The Magnetic Antenna," L. Page, Phys. Rev., Vol. 69, June 1946, pp. 645-648. 47

Ib 46. "Iron-cored Loop Receiving Aerial," R. E. Burgess, WE, Vol. 23, No. 6, June 1946, p. 172. 47. "The Radiation Field of a Symmetrical Center-Driven Antenna of Ferrite Cross-Section," C. W. Harrison and R. King, Proc. IRE, Vol. 31, No. 12, 1943, p. 693. 48. "Radiation from a Point Dipole Antenna in a Ferrite Sphere," D. M. Lipkin, Amer. Elec. Lab., September 1957. 49. D. Hondrus, P. Debye, and Ann Phipik, "Elektromagnetische Wellen an Dielektischen Drahten," 32, 1910, pp. 465-476. 50. H. E. Shanks and V. Galindo, "Ferrite Excited Slots with Controllable Amplitude and Phase," 1959 IRE Nat. Conv., Rec. U7 pt. 1, Antennas and Propagations, pp. 88-92. 51. H. Subl and L. R. Walker, "Tropies in Guided Wave Propagation Through Gyromagnetic Media," pt. 1 pp. 579-654, May 54, pt. II pp. 939-986, July 1954, pt. III, pp. 1133-1194, Sept. 1954. 52. P. S. Epstein, "Theory of Wave Propagation in a Gyromagnetic Medium," Rev. Mvs. Phy. Vol. 28, Jan. 1956, pp. 3-17. 53. H. Gamo, "The Fareday Rotation of Waves in a Circular Waveguide," J. Phy, Soc. of Jap., Vol. 8, No. 2, p. 3-4, 1953. 54. C. L. Hozan, "The Ferromagnetic Farndey Effect at Microwave Frequencies," BSTJ 31, Jan. 52, pp. 1-31. 55. M. L. Kales, "Modes in- Waveguides That Contains Ferrites," NRL Report 4027, Aug. 8, 1952. 48

II, PERIODICALS - MATERIALS a. Ferrites 1. "Survey of Ferromagnetic Resonance in Small Ferri Magnetic Ellipsoids," F. R. Morgenthaler, J. of App. Phys., 5th Annual Symposium, Vol. 31, No. 5, Supplement to May I960, p. 955. 2. "Determination of Molecular Field Co-efficients in Ferri Magnets," G. T. Rado and V. J. Folen, J. of App. Phys., Vol. 31, No. 1, Jan. 1960, p. 62. 3. "Experimental Results on the Magnets —Crystalline Anisotropy of the Hexagonal Oxides," V. Enz, J. F. Fast and H. P. J. Wijn, Le Journal de Physique et le Radium, Vol. 20, 1959, p. 360. 4. "Hexagonal Magnetic Compounds," Third Quarterly Progress Report, Sept. 15, 1959 to Dec. 14, 1949, (DA Project No. 3-99-15-108, U. S. Army Signal Engineering laboratories, Fort Monmouth, New Jersey), David Sarnoff Research Center, RCA Labs., Princeton, New Jersey. 5. "Dipolar Magnetodynamic Ferrite Modes," W. H. Stein and P. D. Coleman, J. of App. Phys., Vol. 30, No. 9, September 1959, p. 1454. 6. "Ferromagnetic Resonance Modes in Spheres," Fletcher and Bell, J. of App. Phys., Vol. 30, No. 5, May 1959, p. 687. 7. "A Technique for Minimizing Hysteresis in a 35 db Ferrite Variable Alternator," H. I. Gloss, Trans. IRE, PGMTT, April 1959, p. 295. 8. "Domain Wall Motion and Ferrimagnetic Resonance in a Manganese Ferrite," J. F. Dillon and H. E. Earl, J. of App. Phys., Vol. 30, No. 2, February 1959, P. 202. 9. "Ferrite HP Effects in Waveguide," E. Stern and R. S. Mangiaracina, Trans. IRE, GM1T, January 1959, p. 11. 10. "Temperature Effects in Microwave Ferrite Devices," J. L. Melchor and P. H. Vartanian, Trans. IRE, PGMTT, January 1959, p. 15. 11. "Propagation Constants of Circular Cylindrical Waveguides Containing Ferrites," H. K. F. Swerin, Trans. IRE, PGMTT, July 1959, p. 337. 12. "Electromagnetic Wave Propagation in Cylindrical Waveguides Containing Gyromagnetic Media (Ferrite)," R. A. Waldron, Part I, IEE Proc., Vol. 18, No. 10, October 1958, p. 597; Part II, IEE Proc., Vol. 18, No. 11, Nov. 1958, p. 677; Part III, IEE Proc., Vol. 18, No. 12, December 1958, p. 733. 13. "Radiation From a Rectangular Waveguide Filled With Ferrite," G. Tyros and G. Held, Trans. IRE, PGMTT, July 1958, p. 268. 49

IIa 14. "Propagation in Ferrite-Filled Microstrip," M. E. Brodwin, Trans. IRE, PGMTT, April 1958, p. 150. 15. "Effect of Hydrostatic Pressure and Temperature on the Magnetic Properties of a Nickel-Zinc Ferrite," C. Q. Adams and C. M. Daws, J. of App. Phys., Vol. 29, No. 3, March 1958, p. 372. 16. "Nature of Electrical Resistivity of the Feno-Magnetic Metals at Low Temperatures," Kondorsky, Galkina, Tchernikova, J. of App. Phys., Vol. 29, No. 3, March 1958, p. 243. 17. "Theory of Magnetostriction and g Factor in Ferrites," Nobom Tsuya, J. of App. Phys., Vol. 29, No. 3, March 1958, p. 449. 18. "On the Propagation of Surface Waves Over an Infinite Grounded Ferrite Slab," R. L. Pease, Trans. IRE, PGAP, January 1958, p. 13. 19. "A Ferrite Boundary Value Problem in a Rectangular Waveguide," C. B. Sharpe and D. S. Heim, Trans. IRE, PGMTT, January 1958, p. 42. 20. "Viewpoints on Resonance in Ideal Ferrite-Slab-Loaded Rectangular Waveguides," H. Seidel, IRE Wescon Rec., Part I, 1957, P. 58. 21. "Dispersion Relations for Tensor Media and Their Application to Ferfites," B. S. Gourary, J. of App. Phys., Vol. 28, No. 3, March 1957, p. 283. 22. "Effects of Annealing on the Saturation Induction of Ferrites Containing Nickel and/or Copper," L. G. Van Vitert, J. of App. Phys., Vol. 28, No. 4, April 1957, p. 478. 23. "Magnesium-Copper-Manganese-Aluminum Ferrites for Microwave Application," L. G. Van Vitert, J. of App. Phys., Vol. 28, No. 3, March 1957, P. 320. 24. "Effects of Size on.the Microwave Properties of Ferrite Rods, Disks, and Spheres," J. 0. Artman, J. of App. Phys., Vol. 28, No. 1, January 1957, p. 92. 25. "Progress in Ferrite Materials," Electronics and Radio Engineers, Vol. 34, No. 2, February 1957, P. 56. 26. "Ferroxplana, Hexagonal Ferromagnetic Iron Oxide Compounds for VHF," G. H. Jonker, H. P. J. Wijn and P. B. Braun, Philips Tech. Rev., Vol. 18, 1956-57, p. 145. 27. "On the Minimum of Magnetization Reversal Time," R. Kikuchi, J. of App. Phys., Vol. 27, No. 11, November 1956, p. 1352. 28. "Miethod for Forming Large Ferrite Parts for Microwave Applications," L. G. Van Vitert, F. VW. Swanekamp and F. R. Monforte, J. of App. Phys., Vol. 27, No. 11, November 1956, p. 1376. 50

IIa 29. "Multiple Ferromagnetic Resonance in Ferrite Spheres," R. L. White and I. H. Solt, Jr., Phys. Rev., Vol. 104, No. 1, October 1, 1956, p. 56. 30. "Dielectric Properties of and Conductivity in Ferrites," L. G. Van Vitert, Proc. IRE, October 1956, p. 1294. 31. "Intrinsic Tensor Permeabilities on Ferrite Rods, Spheres, and Disks," E. G. Spencer, L. A. Ault, and R. C. LeCraw, Proc. IRE, Vol. 44, No. 10, October 1956, p. 1311. 32. "Resonance Loss Properties of Ferrites in AKMC Region," S. Sensiper, Proc. IRE, Vol. 44, No. 10, October 1956, p. 1323. 33. "Molecular Ringing," Stanley Bloom, J. of App. Phys., Vol. 27, No. 7, July 1956, p. 785. 34. "Nickel Copper Ferrites for Microwave Applications," L. G. Van Vitert, J. of App. Phys., Vol. 27, No. 7, July 1956, p. 723. 35. "Measurement of Microwave Dielectric Constants and Tensor Permeabilities of Ferrite Spheres," E. G. Spencer, R. C. LeCraw and F. Reggia, Proc. IRE, Vol. 44, No. 6, June 1956, p. 790. 36. "Nonlinearity of Microwave Ferrite Media," N. G. Sakiotis, H. N. Chait and M. L. Kales, Trans. IRE, PGAP, April 1956, p. 111. 37. "Temperature Behavior of Ferrimagnetic Resonance in Ferrites Located in Wave Guide," B. J. Duncan and L. Swern, J. of App. Phys. Vol. 27, No. 3, March 1956, p. 87. 38. "Nonlinearity of Propagation in Ferrite Media," A. Clavin, Proc. IRE, Vol. 44, No. 2, February 1956, p. 259. 39. "Frequency Doubling in Ferrites," W. P. Ayres, P. H. Vartanian, J. L. Melchor, J. of App. Phys., Vol. 27, No. 2, February 1956, p. 188. 40. "Energy Concentration Effects in Ferrite Loaded Wave Guides," J. L. Melchor, J. of App. Phys., Vol. 27, No. 1, January 1956, p. 72. 41. "Some Properties of Ferrites in Connection with Their Chemistry," E. W. Gorter, IRE Proc., Vol. 43, No. 12, December 1955, pp. 1945-1973. 42. "Nonlinearity of Propagation in Ferrite Media," Sakutis, Clait, Kabs, IRE Proc., Vol. 43, No. 8, August 1955, p. 1011. 43. "Isotropic Variable Index Media," W. O. Puro and K. S. Kelleher, Nat. Conv. Rec., Part I, 1954, p. 76. 44. "Developments in Sintered Magnetic Materials," J. L. Salpeter, Proc. IRE, Vol. 42, No. 3, March 1954; p. 514. 45. "Magnetic Resonance Phenomena in Ferrites," F. Brown and D. Park, Phys. Rev., Vol. 93, No. 3, February 1, 1954, p. 381. 51

IIa 46. "Magnetic Resonance in Ferromagnetics," R. K. Wangsner, Phys. Rev., Vol. 93, No. 1, January 1, 1954, p. 68. 47. "Properties of Ferrites in Waveguides," N. G. Sakiotis and H. N. Chait, Trans. IRE, PGIITT, Nov. 53, P. 11. 48. "Complex Magnetic Permeability of Spherical Particles," J. R. Wait, Proc. IRE, Vol. 41, No. 11, November 1953, p. 1664. 49. "Ferrites and Their Properties at Radio Frequencies," R. L. Harvey, Proc. NEC, Vol. 9, September 1953, p. 287. 50. "Analysis of Measurements on Magnetic Ferrites," C. D. Owens, Proc. IRE, Vol. 41, No. 3, March 1953, P. 359. 51. "Ferrites at Microwaves," Sakiotis and Chait, Proc. IRE, Vol. 41, No. 1, January 1953, p. 87. 52. "H. F. Magnetization of Ferromagnetic Laminae," 0. I. Butler and H. R. Chabliani, WE, Vol. 28, No. 330, March 1951, p. 92. 53. "Ferromagnetic Materials and Ferrites: Properties and Application," M. J. 0. Strutt, WE, Vol. 27, No. 327, December 1950, p. 277. 54. "High Frequency Permeability of Ferromagnetic Materials," G. Eichholz and G. F. Hodsman, Nature, Vol. 160, No. 4061, August 30, 1947, p. 302. 55. "Gyromagnetic Resonance in Ferrites," J. L. Snoek, Nature, Vol. 160, No. 4055, July 19. 1947, P. 90. 56. "The Permeability of Ferromagnetic Materials at Frequency Between 105 and 1010 c/s," J. T. Allanson, J. Inst. Elect. Eng., Part III, Vol. 92, No. 20, December 1945, pp. 247-255. 57. "The Problem of a Metallic Sphere in a Uniform Alternating Magnetic Field," M. Divilkovsky, USSR J. Phys., Vol. 1, 1939, pp. 471-478. 58. "Magnetic Materials at Radio Frequency," F. M. Colebrook, Radio Research Board Special Report No. 14, HMSO, 1934. 59. "A Summary of the Investigation of Ferromagnetic Materials —Ferrites," A. L. Rasmussen, R. D. Harrington, R. C. Powell, and J. L. Dalke, NBS Report 6063. 52

II. PERIODICALS - MATERIALS b. Ferroelectrics 1. "Ferroelectric and Ferrimagnetic Properties of (Ba6.2xR2x)(Nbg-x Fel+) 030" P. H. Fand and R. S. Roth, J. of App. Phys., 5th Annual Symposium, Vol. 31, No. 5, Supplement to May 1960, p. 2785. 2. "Dynamic Properties of the Polarizability in Ba TiO3 Crystal," K. Husinu, J. of App. Phys., Vol. 30, No. 7, July 1959, p. 978. 3. "Transition to the Ferroelectric State in Ba TiO," D. Meyerhofer, Phys. Rev., Vol. 112, No. 2, Nov. 1958, p. 413. j 4. "Phenomenological Theory of Polarization in Ba TiO3 Single Crystals," C. F. Pulvari and W. Kuebler, J. of App. Phys., Vol. 29, No. 9, September 1958, p. 1315. 5. "Dielectric Properties of Single Domain Crystals of Ba TiO3 at Microwave Frequency," T. S. Benedict and J. L. Durand, Phys. Rev., Vol. 109, No. 4, February 15, 1958, p. 1091. 6. "Radiation Resulting From an Impulsive Current in a Vertical Antenna Placed on a Dielectric Ground," C. L. Perkeris and Z. Alterman, J. of App. Phys., Vol. 28, No. 1, November 1957, P. 1317. 7. "Domain Effects in Polycrystalline Barium Titanate," E. C. Subbarao, M. C. McQuarrie and W. R. Buessem, J. of App. Phys., Vol. 28, No. 10, October 1957, p. 1194. 8. "Intrinsic Electrical Conductivity in Silicon Carbide," J. H. Racette, Phys. Rev., Vol. 107, No. 6, August 1957, P. 1542. 9. "Extension of Babinet's Principle to Absorbing and Transparent Materials and Approximate Theory of Backscattering by Plane, Absorbing Disks," H. E. J. Neugebauer, J. of App. Phys., Vol. 28, No. 3, March 1957, p. 308. 10. "Electromagnetic Transmission Characteristics of a Lattice of Infinitely Long Conducting Cylinders," Z. A. Kaprielian, J. of App. Phys., Vol. 27, No. 12, December 1956, p. 1491. 11. "Extension of the'Thin-Sample Method' for the Measurement of Initial Complex Permeability and Permittivity," E. E. Conrad, C. S. Porter, N. J. Doctor and P. J. Franklin, J. of App. Phys., Vol. 27, No. 4, April 1956, p. 346. 12. "Retarded Polarization Phenomenon in Ba TiO Crystals," H. H. Wieder, J. of App. Phys., Vol. 27, No. 4, April 1956, p. 413. 53

IIb 13. "Variational Method for the Calculation of the Distribution of Energy Reflected from a Periodic Surface I," W. C. Meecham, J. of App. Phys., Vol. 27, No. 4, April 1956, p. 361. 14. "Some Aspects of Ferroelectricity," G. Shirane, F. Jona and R. Pepinsky, IRE Proc., Vol. 43, No. 12, December 1955, PP. 1738-1792. 15. "A New Point of View on Magnetic Losses in Anisotropic Bars of Ferrite at Ultra-High Frequencies," Beljers, Van de Lindt and Went, J. of App. Phys., Vol. 22, No. 12, December 1951, p. 1506. 16. "High Permittivity Crystalline Aggregates," W. Jackson and W. Reddish, Nature, Vol. 156, No. 3972, December 15, 1945, p. 717. 54

II. PERIODICALS - MATERIALS c. Dielectrics 1. "The Matching of Parallel Dielectric Plates to Free Space," G. C. McCormick, Trans. IRE, PGAP, Dec. 1959, p. 288. 2. "Experimental Determination of Wavelength in Dielectric Filled Periodic Structures," E. Weissberg, Trans. IRE, PGMTT, October 1959, p. 480. 3. "The Efficiency of Excitation of a Surface Wave on a Dielectric Cylinder," J. W. Duncan, Trans. IRE, PGMTT, April 1959, p. 257. 4. "Anomalous Dispersion in Artificial Dielectrics," A. F. Wickersham, Jr., J. of App. Phys., Vol. 29, No. 11, Nov. 1958, p. 1537. 5. "The Excitation of a Dielectric Rod by a Cylindrical Waveguide," C. M. Angulo and W. S. C. Chang, Trans. IRE, PGTT, October 1958, p. 389. 6. "Field Displacement Effects in Dielectric and Ferrite Loaded Waveguides," T. M. Strauss, IRE Wescon Rec., Part I, 1958, p. 135. 7. "A New Class of Artificial Dielectrics," Ming-Kuei Hu and D. K. Chang, IRE Wescon Rec., Part I, 1958, p. 21. 8. "Launching Efficiency of Wires and Slots for a Dielectric Rod Waveguide," R. H. Duhamel and J. W. Duncan, Trans. IRE, PGMTT, July 1958, p. 277. 9. "A Simple Artificial Anisotropic Dielectric Medium," R. E. Collin, Trans. IRE, PGMTT, April 1958, p. 206. 10. "Propagation in Dielectric Slab-Loaded Rectangular Waveguide," P. H. Vartanian, W. P. Ayres, A. L. Helgesson, Trans. IRE, PGMTT, April 1958. 11. "Electron Interaction in Solids: Collective Approach to the Dielectric Constant," P. Nozieres, J. D. Pines, Phys. Rev., Vol. 109, No. 3, February 1958, p. 762. 12. "Use of a Complex Conductivity in the Representation of Dielectric Phenomena," F. A. Grant, J. of App. Phys., Vol. 29, No. 1, Jan. 1958, p. 76. 13. "Electromagnetic Diffraction by Dielectric Strips," D. C. Stickler, Trans. IRE, PGAP, Jan. 1958, p. 148. 14. "The Status of Microwave Applications of Ferrites and Semiconductors," B. Lax, Trans. IRE, PGMTT, Jan. 1958, p. 5. 15. "Application of Rayleigh-Ritz Method to Dielectric Steps in Waveguide," C. M. Angulo, Trans. IRE, PGMTT, October 1957, p. 268. 55

16. "Diffraction of Surface Waves by a Semi-Infinite Dielectric Slab," Carlos M. Angulo, Trans. IRE, PGAP, Jan. 1957, p. 100. 17. "Reflectionless Transmission Through Dielectrics and Scattering Potentials," I. Kay and H. E. Moses, J. of App. Phys., Vol. 27, No. 12, December 1956, p. 1503. 18. "Limit-Periodic Dielectric Media," R. Redheffer, J. of App. Phys., Vol. 27, No. 11, November 1956, p. 1328. 19. "Rapid Measurement of Dielectric Constant and Loss Tangent," D. M. Bowie and K. S. Kelleher, Trans. IRE,,PGMTT, July 1956, p. 137. 20. "Influence of Magnetic Fields Upon the Propagation of Electromagnetic Waves in Artificial Dielectrics," E. R. Wicher, J. of App. Phys., Vol. 22, No. 11, November 1951, p. 1327. 21. "Complex Dielectric-Constant Measurements in the 100 to 1000 Megacycle Range," A. G. Holtum, Proc. IRE, Vol. 38, No. 8, August 1950, p. 883. 22. "An Investigation of Dielectric Rod as a Waveguide," C. H. Chandler, J. of App. Phys., Vol. 20, No. 12, December 1949, pp. 1188-1192. 23. "Attenuation in a Dielectric Circular Rod," W. M. Elsasser, J. of App. hys., Vol. 20, No. 12, December 1949, p. 1193. 24. "Remarks on Slow Waves in Cylindrical Guides," A. Oliner, J. of App. Phys,, Vol. 19, No. 1, Jan. 1948, p. 109. 56

III. BOOKS 1. Elliptical Cylinder and Spherical Wave Functions, Stratton, Morse Chee and Hunter, The Technology Press, MIT ((in conjunction with Wiley and Sons, 1941). 2. Tables of Functions, E. Jahnke and F. Enide, Dover Publications, 1945. 3. Applied Mathematics for Engineers and Scientists, S. A. Schelkunoff, D. VanNostrand Co,, Inc., 1948. 4. Mathematics of Physics and Chemistry H. rgenau and G. M. Murphy, D. VanNostrand Co., Inc., 1956 5. I. S. Sokolnikoff and R. M. Redheffer, McGraw-Hill Book Co., Inc., 1958. 6. Applied Mathematics for Engineers and Physicists, L. A. Pipes, McGrawHill Book Co., Inc., 195. 7. R. F. Soohoo, Theory and Applications of Ferrite, Prentice Hall. 8. J. Smit and H. P. J. Wijn, Ferrite, Prentice Hall. 57

III. b 1. Electromagnetic Theory, J. A. Stratton, McGraw-Hill, 1941. 2. Rhombic Antenna Design, A. E. Harper, D. VanNostrand, 1941. 3. Electromagnetic Waves, S. A. Schelkunoff, D. VanNostrand, 1943. 4. Fields and Waves in Modern Radio, Ramo and 4Whinnery, Wiley and Sons, Inc., 1944. 5. Antennae —An Introduction to Their Theory, J. A. Abaroni, Clarendon Press, Oxford, 1946. 6. Microwave Antenna Theory and Design (Vol. 12, Radiation Lab. Series), McGraw-Hill, 1949. 7. Antennas, J. D. Kraus, McGraw-Hill, 1950. 8. Electromagnetic Waves and Radiating Systems, E. C. Jordan, PrenticeHall, 1950. 9. Mathematical Theory of Haygens Principle, Baker and Copoon, Oxford University Press, 1950. 10. The Theory of Electromagnetic Waves, A Symposium Interscience Publishers, Inc., 1951. 11. Advanced Antenna Theory, S. A. Schelkunoff, Wiley and Sons, 1952. 12. Antenna: Theory and Practice, S. A. Schelkunoff and H. T. Friis, Wiley and Sons, 1952. 13. Radio Antenna Engineering, E. A. Laport, McGraw-Hill, 1952. 14. Dielectric Aerials, D. G. Kiely, Methuen and Co., Ltd., 1953. 15. Electromagnetic Theory, V. C. A. Ferraro, Athlone Press, London, 1954. 16. Classical Electricity and Magnetism, W. K. H. Panofsky and M. Phillips, Addison-Wesley, 1955. 17. The Theory of Linear Antennas, R. W. P. King, Harvard University Press, 1956. 58

III. c 1. Advances in Electronics and Electron Physics, Vol. VI, Academic Press, Inc., 1954. 2. Introduction to Solid State Physics, John Wiley and Sons, Inc., 1956. 3. Solid State Physics, A. J. Dekker, Prentice-Hall, Inc., 1957. 4. Solid State Physics, Ed. by F. Seitz and D. Turnbull, Academic Press, Inc., 1957. 5. Light Scattering by Small Particles, H. S. Van DeHulst, Wiley and Sons, 1957. 6. Methods of Theoretical Physics, Morse and Feshbach, McGraw —Hill. 59

III. d 1. W.Franz, "On the Green's Functions of the Cylinder and the Sphere." 2. W. Magnus and F. Oberhettinger, "Formulas and Theorems for the Functions of Mathematical Physics," Chelser Publishing Co., N. Y., 1954. 3. A. D. Wheelon, "On the Summations of Infinite Series in Closed Form," JAP, Vol. 25, No. 1, Jan. 54. 4. Watson, "Treaties on Bessel Functions," Cambridge Press. 60

DISTRIBUTION LIST Copy No. Copy No. 1-10 ASTIA (TIP-DR), Arlington Hall 29 Commander, U. S. Naval Air Test Station, Arlington 12, Virginia Center, Attn: WST-54, Antenna Section, Patuxent River, Maryland 11-13 ASD (WWRNRE-4), Wright-Patterson AFB, Ohio 30 Material Laboratory, Code 932 New York Naval Shipyard, 14 ASD (WWDSED, Mr. Mulligan), Brooklyn 1, New York Wright-Patterson AFB, Ohio 31 Commanding Officer, Diamond 15 ASD (WWDBEG), Wright-Patterson Ordnance Fuze Laboratories, AFB, Ohio Attn: 240, Washington 25, D. C. 16 AFCRL (CRRD), Laurence G. Hanscom 32 Director, U. S. Navy Electronics Field, Bedford, Mass. Laboratory, Attn: Library, San Diego 52, California 17 AOGC (PGTRI, Technical Library), Eglin AFB, Florida 33 National Bureau of Standards, Department of Commerce, Attn: 18 AFMTC (Technical Library), Patrick Dr. A. G. McNish, Washington AFB, Florida 25, D. C. 19 AFMC (Technical Library), Hollo- 34 Adams-Russell Company, 200 man AFB, New Mexico Sixth Street, Attn: Library (Antenna Section), Cambridge, 20 AFBMD (Technical Library), Air Mass. Force Unit Post Office, Los Angeles 45, California 35 Airborne Instruments Labs., Inc., Attn: Librarian (Antenna Section) 21 Director, Ballistics Research Walt Whitman Rd., Melville, L. I., Laboratory, Attn: Ballistics N. Y. Measurement Lab., Aberdeen Proving Ground, Maryland 36 American Systems Inc., Attn: Technical Library (Antenna 22 National Aeronautics and Space Section), 3412 Century Blvd., Adm., Attn: Librarian, Langley Inglewood, Calif. Field, Virginia 37 Bell Telephone Labs., Inc.. Attn: 23 RADC (RCLTM), Griffiss AFB, New Librarian (Antenna Section), York Whippany, New Jersey 24 Research and Development Command, 38 Bendix Radio Division of Bendix Hq USAF (AFDRD-RE), Washington Aviation Corp., Attn: Technical 25, D. C. Library (For Dept. 462-4), Baltimore 4, Maryland 25 Office of Chief Signal Officer, Engineering and Technical Di- 39 Boeing Airplane Company, Aero vision, Attn: SIGNET-5, Wash- Space Division, Attn: Technical ington 25, D. C. Library, M/F Antenna aid Radomes Unit, Seattle, Washington 26 Commander, U. S. Army White Sands Signal Agency, Attn: 40 Chance Vought Aircraft Inc., SIGWS-FC-02, White Sands, New THRU: BU AER Representative, Mexico Attn: Technical Library, M/F Antenna Section, P.O. Box 5907, 27 801 Air Div (ICTTD), Lockbourne Dallas 22, Texas Air Force Base, Ohio 41 Collins Radio Company, Attn: 28 Director, Surveillance Depart- Technical Library (Antenna Secment, Evans Area, Attn: Tech- tion), Cedar Rapids, Iowa nical Document Center, Belmar, New Jersey 42 Convair, Attn: Technical Library (Antenna Section), Pomona, Calif. 61

DISTRIBUTION LIST (Cont.) Copy No. Copy No. 43 Convair, Attn: Technical Library 56 Hughes Aircraft Corp., Attn: (Antenna Section), P.O. Box 1950, Technical Library (Antenna San Diego 12, Calif. Section), Florence and Teal St., Culver City, Calif. 44 Dalmo Victor Company, Attn: Technical Library (Antenna Section), 57 University of Illinois, Attn: 1515 Industrial Way, Belmont, Technical Library (Dept. of Calif. Electrical Engineering), Urbana, Illinois 45 Dome and Margolin, Inc., Attn: Technical Library (Antenna Sec- 58 1TT Laboratories, Attn: Technition), 30 Sylvester Street, West- cal Library (Antenna Section), bury, L.I., N. Y. 500 Washington Ave., Nutley 10, N. J. 46 Douglas Aircraft Co. Inc., Attn: Technical Library (Antenna Sec- 59 Lincoln Laboratories, Massachution), 3000 Ocean Park Blvd., setts Institute of Technology, Santa Monica, Calif. Attn:. Document Room, P.O. Box 73, Lexington 73, Massachusetts 47 Electronic Communications, Inc., Research Division, Attn: Tech- 60 Litton Industries, Attn: Technical Library, 1830 York Rd., nical Library (Antenna Section), Timonium, Maryland 4900 Calvert Rd., College Park, Md. 48 Georgia Institute of Technology, Engineering Experi- 61 Lockheed Missile and Space Diviment Station, Attn: Technical sion, Attn: Technical Library Library (M/F Electronics Di- (M/F Dept. 58-40, Plant 1, Bldg. vision), Atlanta 13, Georgia 130), Sunnyvale, Calif. 49 General Electric Company, 62 The Martin Company, Attn: TechElectronics Laboratory, Attn: nical Library (Antenna Section), Technical Library, Electron- P.O. Box 179, Denver 1, Colorado ics Park, Syracuse, N. Y. 63 W. L. Maxson Corp., Attn: Tech50 General Precision Lab., Di- nical Library (Antenna Section), vision of General Precision 460 W. 34th St., New York 1, N.Y. Inc., Attn: Technical Library (Antenna Section), 63 Bedford 64 McDonnell Aircraft Corp., Attn: Rd., Pleasantville, N. Y. Technical Library (Antenna Section), Box 516, St. Louis 66, 51 Goodyear Aircraft Corp., Attn: Missouri Technical Library M/F Dept. 474, 1210 Massilon Rd., Akron 65 Melpar, Inc., Attn: Technical 15, Ohio Library (Antenna Section), 3000 Arlington Blvd., Falls Church, Va. 52 Granger Associates, Attn: Technical Library (Antenna 66 University of Michigan, Cooley Section), 974 Commercial St., Electronics Laboratory, Attn: Palo Alto, Calif. Technical Library (M/F Dept of Electrical Engineering), Ann 53 The Hallicrafters Company, Arbor, Michigan Attn: Technical Library (Antenna Section), 4401 W. 5th 67 University of Michigan, Radiation Ave., Chicago 24, Illinois Laboratory, 201 Catherine St. Ann Arbor, Michigan 54 Hoffman Labs Inc., Attn: Technical Library (Antenna Sec- 68 University of Michigan, Aeronaution), Los Angeles 7, Calif. tical Research Lab., Willow Run, Ypsilanti, Michigan 55 John Hopkins University, Applied Physics Laboratory, 69 Mitre Corp., Attn: Technical 8621 Georgia Ave., Silver Library (M/F Electronic WarSpring, Maryland fare Dept. D-21), Middlesex Turnpike, Bedford, Mass. 62

DISTRIBUTION LIST (Cont.) Copy No. Copy No. 70 New Mexico State University, 83 Southwest Research Institute, Attn: Technical Library Attn: Librarian (Antenna Lab), (M/F Antenna Dept.), Univer- 8500 Culebra Rd., San Antonio, sity Park, New Mexico Texas 71 North American Aviation Inc., 84 H. R. B. Singer Corp., Attn: Attn: Technical Library Librarian (Antenna Lab), State (M/F Dept 56), International College, Pennsylvania Airport, Los Angeles, Calif. 85 Space Technology Laboratory, 72 Autonetics, Division of North Inc., Attn: Librarian (Antenna American Aviation, Inc., Lab), P.O. Box 95001, Los AnAttn: Technical Library (M/F geles 45, Calif. Antenna Dept.), 9150 E. Imperial Way, Downey, Calif. 86 Sperry Gyroscop Company, Attn: Librarian (Antenna Lab), Great 73 Ohio State University Research Neck, L.I., N. Y. Foundation, Attn: Technical Library (M/F Antenna Labora- 87 Stanford Research Institute, tory), 1314 Kinnear Rd., Attn: Librarian (Antenna Lab), Columbus 12, Ohio Menlo Park, Calif. 74 Philco Corp., Government and 88 Sylvania Electronic System, Attn: Industrial Division, Attn: Librarian (M/F Antenna and MiTechnical Library (M/F An- crowave Lab), 100 First St., tenna Section), 4700 Waltham 54, Massachusetts Wissachickon Ave., Philadelphia 44, Penn. 89 Sylvania Electronic System, Attn: Librarian (Antenna Lab), P.O. 75 Radio Corporation of America, Box 188, Mountain View, Calif. RCA Labs Division, Attn: Technical Library (M/F Antenna 90 Technical Research Group, Attn: Section), Princeton, N.J. Librarian (Antenna Section), 2 Aerial Way, Syosset, New York 76 Radiation Inc., Attn: Technical Library (M/F Antenna Sec- 91 Ling Temco Aircraft Corp., tion), Drawer 37, Melbourne, Temco Aircraft Div., Attn: Florida Librarian (Antenna Lab), Garland, Texas 77 Ramo-Wooldridge Corp., Attn: Librarian (Antenna Lab), 92 Texas Instruments Inc. Attn: Conoga Park, Calif. Librarian (Antenna Lab), 6000 Lemmon Ave., Dallas 9, Texas 78 Rand Corp., Attn: Librarian (Antenna Lab), 1700 Main St., 93 A. S. Thomas Inc., Attn: LiSanta Monica, Calif. brarian (Antenna Lab), 355 Providence Highway, Westwood, 79 Rantec Corp. Attn: Librarian Massachusetts (Antenna Labj, 23999 Ventura Blvd., Calabasas, Calif. 94 Wheeler Labs., Attn: Librarisan (Antenna Lab), Box 561 80 Raytheon Electronics Corp., Smithtown, New York Attn: Librarian (Antenna Lab), 1089 Washington Street, Newton, 95 NASA, Goddard Space Flight Mass. Center, Antenna Section, Code 523, Greenbelt, Maryland 81 Republic Aviation Corp., Guided Missiles Division, Attn: Librar- 96 U. S. Naval Ordnance Lab., ian (Antenna Lab), 223 Jericho Attn: Technical Library, CoTurnpike, Mineola, L. I., N.Y. rona, Calif. 82 Sanders Associates, Attn: Li- 97 U. S. Naval Research Lab., brarian (Antenna Lab), 95 Canal Attn: Dr. A. E. Marston, Code St., Nashua, N. H. 5250, Washington 25, D. C. 63

DISTRIBUTION LIST (Cont.) Copy No. Copy No. 98 RCA, Missile and Surface Ra- 100-109 Cooley Electronics Laboratory dio Division, Attn: H. J. Project File, The. University Schrader, Moorestown, N. J. of Michigan, Ann Arbor, Mich. 99 Dr. B, F. Barton, Director, 110 Project File, The University Cooley Electronics Laboratory, of Michigan Office of ReThe University of Michigan, search Administration, Ann Ann Arbor, Michigan Arbor, Michigan 64

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