THE UNIVERSITY OF MICHIGAN OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR STUDY AND INVESTIGATION OF A UHF-VHF ANTENNA QUARTERLY PROGRESS REPORT NO. 4 Period Covering January 1, 1961 to April 1, 1961 3667-2-P Cooley Electronics Laboratory Department of Electrical Engineering Prepared by: A. T. Adams Approved by: R. M. Kalafus John A. M. Lyon J. C. Palais A. I. Simanyi Project 3667 Contract No. AF 33(616)-7180 Air Research and Development Command United States Air Force June 1961

TABIE OF CONTENTS Page LIST OF ILLUSTRATIONS iv SCOPE OF CONTRACT v ABSTRACT vi 1. PURPOSE 1 2. REPORTS, TRAVEL, AND VISITORS 1 3. FACTUAL DATA 1 3.1 The Problem of a Plane Wave Incident on a Material Sphere 1 3.2 Scattering of a Plane Wave by an Infinitely Long Dielectric or Ferrite Cylinder 9 3.2.1 Basic Problem 9 3.2.2 Theoretical Analysis 10 3.3 Comparison of Solid-State and Conventional Antennas 17 3.4 Measurements on Loop Antenna 27 3.5 Materials 32 3.6 Biconical Antenna Fabrication 32 4. ACTIVITIES FOR THE NEXT PERIOD 34 5. SUMMARY 35 REFERENCES 36 BIBLIOGRAPHY 38 DISTRIBUTION LIST 60 iii

LIST OF FIGURES Page Figure 1. Power density factor as a function of radius in material wavelengths. 8 Figure 2. Plane wave incident on cylinder, electric field parallel to cylinder axis. 11 Figure 3. Plane wave incident on cylinder, electric field perpendicular of cylinder axis. 12 Figure 4. Equivalent circuits of a transmitting antenna. 20 Figure 5. Equivalent circuits of a receiving antenna. 21 Figure 6. Measurement of total radiated power with elliptical polari zation. 22 Figure 7.0 Measurement of total radiated power. 24 Figure 8. Constant current and constant voltage measurement techniques. 26 Figure 9. Loop antenna. 28 Figure 10. Impedance measurement circuit. 28 Figure 11. Ferrite core loop antenna. 30 Figure 12. Impedance of loop antenna. 31 Figure 13. Ferrite enclosed monopole. 33 Figure 14. Monopole terminal connections. 33 iv

SCOPE OF CONTRACT For the period 1 April 1960 through 1 April 1961, the Contractor shall make available and employ its research and development facilities and personnel and provide necessary materials and services to perform research and development, study, and investigation directed to the design of an experimental UHF-VHF antenna for defensive electronic countermeasures used on advanced air vehicles, both manned and unmanned. The objective of this procurement is to advance the state-of-the-art of airborne UHF-VHF antennas wherein use is made of nonconventional radiating devices or techniques. In the past UHF-VHF designs have been largely limited to whips (monopole), isolated sections of the aircraft structure, and dielectric and/or resistive loaded slots. It is the intent of this procurement to exploit new techniques, such as, but not limited to, application of new solid-state advances to antenna design and the incorporation of the radiating element as a part of the power tube itself. This work shall include development and construction of specialized instrumentation required for any tests, together with working drawings, specifications, and operating instructions (which the Contractor prepares or has prepared).

ABSTRACT The effort during this period was devoted to the theoretical study of plane waves incident on a spherical and cylindrical material body, formulation of a basis for comparison of antennas, tests on a ferrite loop antenna, and construction of a biconical antenna. vi

STUDY AND INVESTIGATION OF A UHF-VHF ANTENNA QUARTERLY PROGRESS REPORT NO. 4 Period Covering January 1, 1961 to April 1, 1961 1. PURPOSE This report summarizes the work done on Contract No. AF 33(616)7180 during the period from January 1, 1961 to April 1, 1961. The purpose of this task is to investigate the use of solidstate 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. 2. REPORTS, TRAVEL, AND VISITORS Nd reports were issued during this period. No travel was made during this period. No persons visited the project during this period. 3. FACTUAL DATA 3.1 The Problem of a Plane Wave Incident on a Material Sphere In determining the effect of materials on antenna characteristics, one significant indication would be the effect of the material above on

the radio waves, If the permeability and permittivity are at all different from that of the medium in which the material is immersed, the field distribution will be altered; the geometry of the material also affects the field distribution. Diffraction theory deals with the fields external to the material, and a great deal of work has been done in the evaluation of these fields (Refs. 1, 2, 3). Thus it would be of interest to evaluate the interior fields. Using orthogonal vector functions, the case of a spherical medium has been rigorously solved in diffraction theory. An extension is made of this to treat the fields inside the sphere. Consider a plane wave propagating in the z-direction with its electric field polarized in the x-direction; then the incident fields are E. = aX E ejok jz t (1) Hi = a E e t H = a E 0 ejkoZDt i y o,u Following Stratton (Ref. 1) the orthogonal spherical vector functions are -(1) p 1 ( 1 )cos n sn 8 jn (kor) Pn (os 0) sin a (2) ap1 (kr) n (os e) sin - Cos e eln k r (kor) n (cos 8) p ar 0O 2p n (cos 0) sin - k_ [kor jn(kor)]' n cs a n sin n 0 ~

where: a. = unit vector in "i" direction E = rms electric field magnitude 0 E. = incident electric field H. = incident magnetic field (4) C 0= permittivity of free space o = permeability of free space k~ = propagation constant in free space W = radian frequency of fields jn(kor) = spherical Bessel function, defined by jn(X) = _. J Pl(cos e) = associated legendre function of the first kind The incident plane wave can be represented by: E - E e-jt z n 2n+l [M(1) i E0 e n(n+ [oln j ln n=i Hi. = — ~ E e z 2n-t1 [Min + j n.', n n(nWTT eln oln Maxwell's equations are satisfied by linear combinations of the orthogonal spherical functions. It remains now to find proper coefficients matching the boundary conditions. In order to satisfy the condition at infinity, the scattered wave must be in terms of Hankel functions. The external fields may be written: -- E e-t ~.n 2n+l [as (3b co (3~l (3) (3) s 0o e n ) n Moln - 3bn Neln] (6) H = _~ E e-~t n. n 2n+l [b ) s (3) 0 (n+l) n eln n oln

where the superscript (3) indicates Hankel functions of the first kind rather than Bessel functions. The interior waves may be written E'-jWt Z jn 2n+l at F(1).bt N(1)] Et o e n n(n+l) [ n oln bn eln n=1 (7) Eo e jwt j n 2n+l bt -(1)) t (1 H -= E e- Z n- Me ln + ja N t [L0 n=1 n+l) n eln n oln where the Bessel function argument is k r rather than k r; [k1 =ko 1Kko] Let the radius of the sphere be a, and subject Eqs. 5, 6, and 7 to the following boundary conditions at r = a: ar x (Ei + = x E r s r t (8) a x(Hi + H a x Ht r i s r t Two pairs of inhomogeneous equations result: at jn(Kp) - a hl)(p) = J(p) n n n n n (9) an[K jn(KP)]' - [ph()() = [ (p)] 0 o n t1 b h(l) (1) = j Kb Jn(KP) -— h (P K nin(KP) n (p) n (p10) bt [Kpj(Kp)' - Kb [ph(l)(p)]' = K[pjn(p)]' n n where: p = ka, Kp = kla. At this point the Ricatti Bessel functions will be introduced for convenience:

n(z) = zj (z) Cn(z) = znn(z) (11) R()(z) = zh(l)(z) = S (z)+ JCn(z) Solving (10) for the coefficients at and bt, and defining n n = Al/.o and e = el/E, S'(p) R(l)(p) - Sn(P) R! (p) at n n n t SKS'(KPP) 1K)(p) ( S()R p) (12) S (P) R(l)(p) - S (p) RI (p) = a K n n KAs(Kp) Rn (p) - ISn(KP) RA (p) The numerator reduces: (1') A (p) RA'(p) - Sn(p) - SR (p) R (p) the center of the sphere. As the argument approaches zero, z <<. j (z) - (22)n. R [Pin(z)' -, (2z)n ( + n) From (2), (3), and (13) it can be seen that at the center of (1) the sphere the higher modes are not sustained, and that only the o terms contribute to the fields; the orthogonal functions are: th cntr f hespee.Asth aguen apoahe zro z<<1

e1k 1 cos 1 sin oil 3 s'in ae 3 Cos cp (14) Nll = sine c ar + C6 c cp ae oil 5 cos r s e 3 o (15) 2 cos - 3 sin aq) since aPI(cos e) P'(cos e) = sin e and- s) - cos e (16) Thus at the center the fields are: -jwt t Et 1 bl[sin e cos q: ar + cos e cos cp ae - sin cp ae] (17) t = /L1 Eo e-Jct t Ht = -E et at[sin e sin cp ar + cos e sin cp a + cos cp a] which, when put in terms of x, y, z coordinates, become: - -jWt tHt =~1u Eo x Ht = l E ej at a The incident wave has a Poynting vector of Re {Ei = E2 a (19) The interior wave has the Poynting vector at the center of 1 a. t_ R {Et x H} Eo t b a (20) The Poynting vector at the center differs from the original wave by the factor

K t* t(21) al bl (21) Note that in the case of 1= o 1 = C, the expression reduces to unity, as would be expected. Thus the power density factor P is a function of the material parameters and the argument ka, which is 2r times the radius a in material wavelengths. For Ai = c = K = 10, the curve of P versus a/m is shown in Fig. 1. The resonant peaks occur at a/km =.64, 1.10, 1.56 and approach the half-wavelength points 2.0, 2.5, 3.0, and so on. These resonant points coincide with the natural oscillations of a sphere (Ref. 1, p. 556-7). Thus it appears that the plane wave is feeding energy to a spherical cavity such that the power flow near the center is a plane wave of increased power density. As a/km is increased, the peaks and dips smooth out, and the curve approaches the straight line P = >e = K2; i.e., as K >> 1 (22) at = bt Kip(K-l) 1 1-,Ke In the limiting case Kp <<, at t 3 (23) -1 b K2 (23) and P _....9 (K + 2)2 The restriction involved in the problem in using the center of the sphere as the point of investigation is fairly good as an approximation over a circular area around the center up to about a/km = 0.2; that is, an area interal will yield approximately (power density) x (area) as the power flow across the area.

2000 500 - 200 - 100 - 50 20 10.05.0 2 I L 2 w w 0.2.50 0.20.10.05.02.0 I.2 F;.50.7 5 1.00 L2.5 1.50 a/X M Fig. 1, Power density factor as a function of radius in material wavelengths.

The problem can be extended to deal with lossy materials by allowing,u and e to be complex. Then (21) becomes: (KSat * P b (24) Subsequently, the cases of arbitrary g and e and lossy materials will be treated, and a more complete discussion and interpretation of the results will be given. 3.2 Scattering of a Plane Wave by an Infinitely Long Dielectric or Ferrite Cylinder 3.2.1 Basic Problem. In order to further the understanding of the various phenomena which solid-state materials can give rise to in improving the performance of antennas, a study is now under way to evaluate the fields obtainable both inside and outside a right circular cylinder with an electric and magnetic susceptibility different from that of free space. The choice of a two-dimensional problem recommended itself for several reasons. One of the main advantages is that the amount of computation is not extremely laborious. Another is that the numerical evaluation on the computer study will not exceed the capacity of the IBM 704 computer. This study considers the following two cases: There is an infinitely long cylinder (with both p and e possibly different from that of free space) upon which a plane wave is incident. Since an arbitrarily polarized wave can always be made up of two waves which are polarized in perpendicular planes, for the purposes of this study there is considered the case of the E field parallel to the axis of the cylinder and that of

the E field perpendicular to the axis of the cylinder (see Figs. 2 and 3). The first case gives rise to TM modes and the second to TE modes. The chief interest in this problem centers on the "collecting" power of the cylinder. If this configuration is to be made part of a useful antenna system there must exist at some points in space, either inside the cylinder or close to-it on the outside, concentrations of power which exceed the power level before the scatterer was immersed in the field. At the present time a computer program is progressing for evaluating the real and imaginary power flow inside and outside the cylinder. This program will explore a range of values of the material parameters,u and e. It will also include a study of the power flow dependence on frequency and cylinder dimensions. 3.2.2 Theoretical Analysis. (a) Incident Electric Field Parallel to the Cylinder Axis. For this case the incident field for a plane wave is given by = A ei(ky-wot) Z O in rectangular coordinates (Fig. 1). Expanding in cylindrical coordinates, an infinite set of TM modes is obtained for the fields inside and outside the cylinder (Ref. 1) as follows: (E parallel to the cylinder axis) inside the cylinder (r < a): O10

z — z INFINITELY LONG CYLINDER 1LIEC /lo,Eo Sy P(r,0) Hi X Fig. 2. Plane wave incident on cylinder, electric field parallel to cylinder axis. 11

INFINITELY LONG CYLINDER Hz / | P(r,&) Fig. 3. Plane wave incident on cylinder, electric field perpendicular to cylinder axis. 12

2 minc E = k2 Zb e J(kr) z00 k2 in8 Hr = kr Z b ne Jn(kr) ik3 m inJ He F, b n e j'(kr) outside the cylinder (r > a): W 00 ~~~00. E = k2 a' ein H(kr) + A J(k r) ein z 0 n fn 0~ k 2 iO ine H = sr 2 nane e e Hn(kor) ein 0 in8, ine H a e Hn(kor) - A sin Jn(kor) e o P Ow 0 nk) The continuity of the tangential E and H fields (Ez and H0) at the cylinderfree-space boundary (r = a) yields explicit expressions for the coefficients a and b: n n cAO J n(koa) Hn(koa) - Jn(koa) Hn(koa) n k2 aJn(ka) H'(k a) - J" (ka) H (k a) k n n o n n o A J (ka) Jn(ko a) - J) (ka) J (ka) o n. n a = k n no n no 0 where: r, 8 are cylindrical coordinates. r = radial distance from axis of cylinder. e = angular distance, with incident wave normal in direction e = ir/2. A~ = amplitude of incident electric field. = permeability of cylinder. 13

= dielectric constant of cylinder. TM = permeability of surrounding medium. c0 = dielectric constant of surrounding medium. k = co T = wave number inside cylinder. k0= a Ioe = wave number outside cylinder. H n (x) (x)= Hankel function of the first kind. J'(x), H'(x) = derivatives of Bessel and Hankel functions wi h respect to the argument. a - I= In the evaluation of the convergence properties of the infinite series for the field components, the behavior of the coefficients a and b has to be determined. For the TM case, for n >> (ka)2, the formulas obtained are: Coefficients inside cylinder: 2Ak 0 P. ko)n n k2, +.O k Coefficients outside cylinder: iA0 P - O ( koa 2n a =n 2 + 1o 2 k2n! (n-l) o Several interesting observations can now be made regarding the coefficients of the higher-order modes: For terms outside the cylinder there is a definite difference in the frequency dependence of different modes. The expansion coefficients will ultimately converge due to the factor (n!)2 in the denominator. As a matter of fact, since n ~ 1(ka)2 the an's will have to be small before the above formula will hold. In the limit an = (w)2n-2/(n!)2 = (n- 1/n )2; so no matter how high a 14

frequency of operation we choose the series of coefficients will ultimately converge. In the final analysis we are interested in the value of the infinite series of modes making up the field components. Then, at any point of observation we encounter terms of the following nature, expressing the scattered fields as S PnerBSine s Ez zEn e H ne n n For n >> ~ (ka)2 A ~ LIo (koa) r > a E = o 1 (ko) n (n' + o 2 (k rn+ 02 o 2n H = 6o /:'. -Lo 1 (koa)2n mrn 2kr A40 A + o n-l (2kor)n r < a zn = F +,;i:1 (kr)n (ko n zn = nA 2.'' Hn = iAo ( k' ) ( T ( 2' 2Ao ko n 1 kkrn rn kr + o k (n-l) 2' Because of the n' in the denominator of all these terms, all the field components are obtained as bounded sums of the modes. (b) Incident Electric Field Perpendicular to the Cylinder Axis. For this case the incident field for a plane wave is given by 15

E A ei(ky't) X 0 in rectangular coordinates (Fig. 2). Expanding as before, an infinite set of TE modes is obtained as follows: 00 W-0 co, inc r< a E nb e Jn(kr) r r n _00 E = kip b e kJ (kr) a E -IL S nn n -00 2b in8 Hz = ko bn e Jn(kr) Z n n r> a E 2Tna em6in Hkor) A Cosa Jk ina r > ~f4-AEr Hnr C+ Ao nos + n(kor) e n i co Zn ein k kn(kr) - Jn(kr) ein 00 n o n 00 n Z 0a- in n0 then TheO n weo0 The expansion coefficients are given as-A0 c0 H (koa) J'(koa) + Hn(koa) %(koa) n 2 =Ll k(.k a) Jo(ka) - Hn(k a) Jn(ka) k o n o n n o n -A ~o Hn(koa) JA(koa) + H'(koa) J (koa) an 2 =.- L aB (k a) J'-(ka) - H'(k a) J (ka) k0 o n o n n o n Again expressing the field, components as: s =ein E = e E e en Then we have:

2Ao (koa) 2 r > a Esn (n-l) (2krn+ Ao o (koa)2n rn (2krn i< a / ~o _A kon kr)n-l E0: (n.!)'-l). Eo+,' n 0 H = -2Ae ( n 1 kr n B =r a(' the series is convergent. 3.3 Comparison of Solid-State and Conventional Antennas In attempting to evaluate solid-state antennas, it is important over antennas of conventional design. Comparison can be made for a number of characteristics such as: (1) Size (2) Directivity (3) Efficiency (4) Bandwidth 17

(5) Impedance (6) Power Capacity (7) Weight (8) Cost In the lower portion of the frequency range of interest for the contract, antenna sizes become large and size reduction becomes of primary importance, so that a reasonable method of comparison in this range would be to compare (2) through (8) for antennas of equal size. The natural inclination is to compare antennas of similar design, dipoles with loaded dipoles, etc.. However, there are a number of circumstances under which a comparison of this sort would be invalid. First, if the antenna with solid-state material were considerably larger than the conventional antenna, the comparison would be invalid. Second, if the conventional antenna and the solid-state antenna did not represent optimum designs, or if the characteristics which had been optimized in the designs of the two antennas were not the same characteristic, then a good comparison would be difficult. In general, the characteristics of a given solid state antenna must be compared with all conventional antennas. The question then becomes, "Can the characteristics of this solid-state antenna be duplicated or bettered by a conventional design of equal size?" Some of the special methods required for a good comparison of characteristics (1) through (8) are discussed below. (1) Size A strict comparison of antennas would be limited to those of approximately equal dimensions. The special space requirements of a particular application may allow comparison on a basis of equal volume, 18

equal maximum cross-sectional area, or some such other geometric factor. (2) Directivity and Gain G = gain over isotropic (Ref. 4) 0 D = directivity k = efficiency factor G = kD In a solid-state antenna with appreciable losses, gain will differ from directivity. (3) Efficiency In general the equivalent circuit of a transmitter and antenna or of a receiver and antenna can be represented as in Figs. 4 and 5. The efficiency of the antenna in all cases may be represented by Rr/(Rr + RL) or by total radiated power net input power to antenna Total Radiated Power The measurement of total radiated power may be made in several ways, one of which would be the use of the WADD beam pattern equipment, which integrates the radiated power over a sphere and integrates over the polarization pattern at each point. A method applicable to the equipment installed at CEL would be to take two complete measurements of the beam pattern (using the test antenna as the receiving antenna), one with vertical and one with horizontal polarization from the transmitting antenna. It can be shown (Fig. 6) that at any point the sum of the two measurements of radiated power per unit area is equal to the total radiated power per unit area at that point. Then the test antenna (in a specified orientation) would be used as a transmitter, and a field 19

RTI nl:I RL (a) Z T2 T RX r Xo * GENERATOR TRANSMISSION. MATCHING DEVICE ANTENNA LINE (DOUBLE-STUB TUNER) RTI n:1 1INT (b) Zo 0RT2'XT X Rr RL / 0' ANTENNA R = internal resistance of generator int Z~ = characteristic impedance of transmission line Rql, RT2 = transformer losses XT = variable reactance RL = antenna losses Rr = radiation resistance Za = antenna input impedance = (Rr + RL) + jXa a; r R' = Rr R'= r RL (RL +Rr)2 + (Xa)2 a X a Rr RL Efficiency = r r itr For conjugate match: If Z = Rint n = I XT = - Xa Fig. 4. EQuivalent circuits of transmitting antenna. 20

Rr MATCHING (a) GZ RL DEVICE T Xa ANTENNA TRANSMISSION REC LINE MATCHING ZL V Rr RL X. DEVICE (b) zo In figures 5(a) and 5(b) V is the voltage induced in the antenna by a passing wave. V is therefore dependent on' the antenna parameters as well as the incident wave intensity. A receiving antenna could also be represented by the circuit in Fig. 5(c), where V is dependent only on the incident wave intensity. GENERAL Rin =377z TWO-PORT (C) z OV ~NETWORK' TRANSMISSIO REC k,, J, ~/ TRANSMISSION REC ANTENNA LINE [Zal] = impedance matrix of antenna Za (in general). Zal] is difficult to measure. Fig. 5. Equivalent circuits of receiving antenna. 21

X (HOR I ZONTAL) fields may be represented as: E1 = a sin Hsin T H E42 = b cos ut H - - sin T Hrl o average power/area over one cycle 2 [E, + E,2 1 x [H,1 + H,2 d(IeT) = where: 1r x t2 = z Consider:measurements taken in vertical (y) + horizontal (x) planes. x = a cos 8 sin ot - b sin 8 cos WT E = a sln 8 sin oTy + b cos 8 cos (oT y.H. a a- a sin p sin oe - b cos cos r] / o average power/area over one cyclec 2 f [ExX + Ey ] x [Hx + Hy ]d(T) = o f 2{[A 2v {[(a cos e sin WT - b sin e cos T) x + (a sin e sin T + b cos e cos r) y] U- [(-a sin 8 sin ur - b cos e cos ouT) x + A = a2 b2A (a cos e sin wT - b sin e cos cw) y (cT) o o Fig. 6. Measurement of total radiated power with elliptical polarization. 22

intensity measurement would be taken at a given distance R (in the far field) from the test antenna. The field intensity measurement would be converted to watts/meter2 and would provide a reference level on the beam patterns for the total radiated power density at the orientation (Co eo0). The total radiated power is then determined by integrating the two beam patterns over a sphere of radius R. This procedure is outlined in Fig. 7. Net Input Power to Antenna: (See Fig. 4) Method 1 If we assume: 1. INT = Zo (generator matched to transmission line) 2. RT = RT2 = (lossless transformer) then, if the double-stub tuner is adjusted for conjugate match to the antenna, the net input power to antenna = available power of generator = V2/4RNT, which can be measured. Method 2 If we eliminate the double-stub tuner and assume: 1. RNT = Zo then, r = reflection coefficient = (Za - Zo)/(Za + Zo) Z = input impedance of antenna a Net input power to antenna = [1 - I rl2] x Available Power. If RINT f Zo0 then the formulas still hold if sufficient padding is added to the transmission line and available power measured after the padding. 23

TEST ANT REC XMTR (a) Beam pattern No. 1 (horizontal) 9, p specify orientation of test antenna REC XMTR (b) Beam pattern No. 2 (vertical) R NET INPUT POWER XMTR REC (c) Field intensity measurement No. 1 (vertical) XMTR REC (d) Field intensity measurement No. 2 (horizontal) It is necessary to have one comparison of XMTR power for horizontal + vertical measurements, either in the beam pattern or in the field intensity measurements. At o'o 60~ the ratio of vertical field intensity to horizontal field intensity should equal the ratio of'vertical beam pattern level to horizontal beam pattern level. Fig. 7. Measurement of total radiated power. 24

(4) Impedance The impedance criterion depends very much on the particular application. Some of the considerations in the comparison of impedances are: (a) If RINT = Z, which impedance is more closely matched to Z? (b) If a tuning device is available, which impedance maximizes Rr/(Rr + RL) (max efficiency)? In special applications, it may be desirable to combine the impedance and efficiency characteristics and to compare radiated power when each of the two antennas is connected to a fixed transmitter system or to compare the receiver indication when each antenna is connected to a fixed receiver system. Such a comparison would make sense only if the usefulness of the antennas could be considered to be restricted to a limited class of systems (or if the interest of the investigator were limited to a particular system). Occasionally, in the literature, antennas have been compared on the basis of equal input current or equal input voltage. This type of comparison results from a combination of the efficiency and impedance characteristics and applies only to a particular class of systems. Figur 8 shows several examples of this type. A general characteristic of these systems is that there is no possibility of matching generator to antenna or antenna to receiver. If it were possible to provide a conjugate match in the system, then a comparison would be valid only on a basis of equal input power. Moreover, if it were possible to reduce the mismatch in the system so that the inequality conditions of Fig. 8 no longer held, then a comparison on the basis of equal input current or voltage would

(a) RL RI NT Rr V Xa Case No. 1 Rintl >> IRL + Rr + JXal V current -- - regardless of antenna impedance. This leads to int equal input current method of comparison. Case No. 2 Rint << RL + Rr + JXal Voltage across antenna - V regardless of antenna impedance. This leads to constant voltage method of comparison. (b) RT I n::INT DOUBLE STUB TUNER OR ANTENNA OTHER MATCHING DEVICE If (r) XT = - X and (2) n2 (R +R)<< RT and (3) n2r >> R R +R' I Tl Then Case No. 1: 2 / RL \current to n ~ +RL) ~ antenna n~ + WRY; V F x n INT Case No. R' R \ voltage at anOn U ) S ~TU U tenna terminals \r L/ INTj R Fig. 8. Constant current and constant voltage measurement techniques. 26

be invalid. Figure 8(a) represents a simple antenna system in which a high degree of mismatch occurs between the internal impedance and antenna input impedance. Figure 8(b) is a somewhat more complicated system, in which transformer losses (sum of lead resistance losses, core losses, and radiation losses) are important. The antenna is represented as in Fig. 4(b). In this case, a comparison may be made on the basis of current or voltage if the transformation ratio (n:l) is taken into account, provided that the transformer losses vary with n in such a way that the stated inequalities of Fig. 8(b) hold. There are, of course, many other complex circuits which might provide, under certain conditions, other bases of comparison; however, in each case, the equal input power basis would still be valid and, in general, it is simpler to compare antennas on this basis. The other points of comparison can be made directly and need no special interpretation. 3.4 Measurements on Loop Antenna A loop antenna was designed and constructed (Fig. 9). The impedance of the loop was measured using the circuit shown in Fig. 10. The GR 874-UB balun used is a balanced-to-unbalanced coaxial transformer. It is tunable to any one frequency from 54 to 1000 Mc. The impedance transformation is 4 to 1, providing an output impedance of 200 ohms. The balanced two-wire air line was designed and built in the laboratory and consists of two 1/8" diameter brass rods spaced 0.354" apart, center to center. This line is about 88 cm long and has a characteristic impedance of 200 ohms. 27

, MATERIAL: SILVER SOLDER 45 % SILVER 30 % COPPER 25% ZINC II;.100 - 1.0625" Fig. 9. Loop, antenna. HP68A H1P803A GR874-UB LOO IGNAL VHF BALUN ANTENNA GENEATOR BRIOGE 200 OHM BALANCED TWO-WIRE AIR LINE. HP417A VHF DETECTOR Fig. 10. Impedance measurement circuit. 28

Using the standard method of placing a short at the antenna terminals, measuring the impedance, and then removing the short and measuring the impedance, the actual impedance of the loop by itself was determined. Using this measurement technique and the Smith Chart, errors due to losses in the balanced two-wire line were eliminated. The loss of the two-wire line was found to be approximately 0.1 db in the range'175 Mc to 275 Mc. The impedance and voltage reflection coefficient of the loop is shown in Table I. The impedance and reflection of a ferrite-core loop antenna are also shown in Table I. The metal antenna is exactly the same as shown in Fig. 9. A spherical core of ferrite powder is placed within the loop as shown in Fig. 11. The ferrite powder is enclosed by a thin balsa-wood shell, as also shown in the figure. Air-Core Loop Ferrite-Core Loop Frequency Impedance Reflection Impedance Reflection (Mc) (Ohms) Coefficient (Ohms) Coefficient 175 j188 1.0 21.2 + j347.5 0.955 200 11.3 + j260 o.96 46.0 + j477 0.925 225 17.8 + j339 0o.96 12.2 + j700 0.99 250 14.8 + j424 0.98 j680 1.0 275 j472 1.0 j608 1.0 Table I. Impedance and reflection coefficient of air-core and ferrite-core loop antenna. The ferrite used in the test is discussed in the section on materials. 29

SPHERICAL FERRITE CORE, 2.7" DIAMETER i E~3'4 9 I|~ |LOOP ANTENNA,2.82" DIAMETER BALSA WOOD (SAME LOOP AS IN FIG.9) I -I SHELL I:: II Fig. 11. Ferrite core loop antenna. A graph of the data from Table I is shown in Fig. 12. There is an appreciable increase in the resistance of the ferrite antenna close to 200 Mc, indicating an improvement in the radiation properties of the antenna. The only way to determine whether this increase in resistance is caused by increased radiation or by increased losses in the antenna is to measure the radiated power from the two antennas. There are two reasons that make it highly probable that the peak in resistance represents an increase in radiated power. The first reason is that the loss of the ferrite in the solid form does not increase until about 250 Mc. The second reason is that a peak in radiation resistance is expected due to a resonance in the core. This resonance is probably similar to that found in the calculations of the radiation resistance for the infinitesimal 30

70 - ANTENNA: LOOP,2.82" DIAMETER 700 65 -FERRITE: CORE SPHERE, 2.7"DIAMETER 60 - 3, 6 3 Z.RRITE CORE 600 REACTANCE 55 50 500 45 U3 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~U E 40 4 - 4 00 z o2 0 z 30 300 Z - \ FAIR CORE o (0 25 10 sr\ RESISTANCE w~ ~ ~ 1 220 20 15 -1 5 RES.CITANCE 10 1 00 z 5 0~~~~~~~~~~~~~~~~~~~~~~~~~ 175 200 225 250 275 FREQUENCY (MC) Fig. 12. Impedance of loop antenna.

dipole which were presented in an earlier report. According to Foster's Reactance Theorem, dx > 0 i.e., for a lossless netowrk, the slope of the reactance vs. frequency plot is always positive. Therefore, the negative slope of the reactance indicates the onset of losses due to the ferrite material. Several tests were made to measure the radiated power. Because of the generally poor radiation efficiency of the small loop, the power radiated from the balanced two-wire line was of the same order as that radiated by the loop, so the latter power could not be determined. A design is presently being worked on which makes use of a shielded twowire line between the loop and the balun. 3.5 Materials The ferrite powder used for the ferrite-core loop antenna has a permeability at 200 Mc of 6.45 in the solid form. In the powdered form, the permeability is reduced to about 3. Similarly, the dielectric constant is reduced to about 3. In the solid form, the magnetic Q of the material is greater than 600. Methods are being investigated to measure the properties of the ferrite directly in the powdered form. 3.6 Biconical Antenna Fabrication The equipment necessary for the construction of some biconical antennas is now being fabricated. The form will be a monopole over a conducting sheet of aluminum. This sheet, with the appropriate connecting devices, will be readily adaptable to biconical monopoles of arbitrary length and flare angle. A styrofoam shell will be hollowed out to allow 32

ALUMINUM CORE E R RTE POWDER | \STYROFOAM SHELL "I AL UMINUM < CONNECTORS SHEET Fig. 13. Ferrite enclosed monopole. ALUMINUM COROE TYPE "N" PIN f,ALUMINUM _ 000 SHEET B ASS_. BOLTS,-.LL E. D BR~~ASS~ / SET SCREW COLLAR. *; _~ "N MALE-TO-MALE IL=SS- ~ FITTING Fig. 14. Monopole- terminal connections.

the powdered ferrite to take the form of a hemisphere surrounding the pole (see Fig. 13). The styrofoam has the advantages of strength, machinability, lightness of weight, and extreme transparency to radio waves. The terminal connections, which are highly important to significant measurements, are shown in Fig. 14. The plane is a 1/8" thick aluminum sheet; the collar is brass. A male-to-male type "N" fitting is machined on one end to allow for the collar. A wooden hemisphere will be provided for strength at the base if necessary. A type "N" pin is pressed on the aluminum core to provide a continuous geometric transition from the connector to the core. Thus a coaxial cable will feed the antenna, eliminating the need for a balun. 4. ACTIVITIES FOR THE NEXT PERIOD (1) For the spring and summer the project has been realigned in order to have additional help in the fields of RF measurement as well as analytical computations. (2) With the coming of good weather, it is planned to fully utilize the experimental installation to obtain satisfactory data on elementary antennas as well as more sophisticated antennas utilizing ferrite materials. Antennas selected will include those which have practical radiation properties, including a high directivity, as well as a relatively high efficiency even without the use of ferrite materials. The ferrite materials will then be applied in order to determine what enhancement of characteristics, if any, is to be achieved. (3) The computational effort, including the use of computers, has appeared to be a very fertile aspect of the over-all research program. 34.

It has been found necessary to utilize more mathematical analysis in the preparation of the problems for the computer. For this reason additional assistance in this specialty has been acquired in terms of one added person for the project. (4) It is contemplated that the "scimitar" antenna will be analyzed, with the possibility of adapting such to the use of ferrites. (5) Multifeeding with appropriate phasing to simple antenna elements is one of the projected studies for this research effort. It is quite possible that slow-wave devices will be utilized in this part of the work. 5. SUMMARY A solution to the problem of scattering of plane waves from a material sphere has been derived. Results to date indicate regions of high energy density within the sphere that may make possible the design of small antennas with large effective apertures. The results of this study will be more completely analyzed and presented in later reports. Substantial progress has been made in the solution of scattering of plane waves from a material cylinder. Computer solutions are now in progress. Measurements on ferrite antennas have begun and problems of RF technique have been encountered and partially solved. It is apparent that all test antennas should be as efficient as possible and all equipment be adequately shielded. The study on a comparison of solid-state and conventional antennas indicates several techniques for determining the usefulness of any given antenna. The method used will depend on the type of antenna 35

being tested, degree of precision needed, and available equipment. REFERENCES 1. J. A. Stratton, "Electro Magnetic Theory," McGraw-Hill, 1941, p. 565. 2. H. C. Van DeHulst, "Light Scattering by Small Particles," Wiley and Sons, 1957, p. 123. 3. Morse and Feshbach, "Methods of Theoretical Physics," McGraw-Hill, 4. J. D. Kraus, "Antennas," McGraw-Hill, p. 27.

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, IMay 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. oIRE, 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. 1), No. 2, March 1959, p. 117. 38

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. 39

Ia 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. Iab. 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,t' 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. 40

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, AMrch 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 Iab. 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 Iab. Tech. Report, Harvard University, June 1, 1948. 56. "'The Measurement of Antenna Impedance Using a Receiving Antenna," D. G. Wilson and R. King, Cruft Lab. 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 19t8, 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 Iab. 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. 41

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. 42

Ia 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 wud 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. 43

I. PERIODICALS - ANTENNAS b. Utilizing Dissipative Media 1. "Resonance and Supergain Effects in Small Ferromagnetically or Dielectrically Loaded Biconical Antennas," C. Polk, Trans. IREt PGAP, December 1959, p. 414. 2. "Radiation Properties of a Thin Wire Loop Antenna Eibedded in a Spherical Medium," 0. 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, Septembelr 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) 44

14. "On the Estimation of Ferrite Loop Antenna Impedance," W. L. Weeks, Elect. Eng. Res. Iab. 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'. "VEF Ferrite Antenna: I. Radiation Properties," 0. 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," O. 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, Proc. 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, CR, 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. Iab. 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.,,!,, ~~4

30. "A Broadside Dielectric Antenna," G. E. Mueller, Proc. IRE, Vol. 40, No. 1, 1952, p. 71. 31. "Radiation From a Uniform Circular Loop 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. Tail 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, Cruf t 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. 46

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 DipQle 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. 47

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 1960, 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 Iaboratories, 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, PGMT, 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 PGMT, January 1959, p. 11. 10. "Teemperature 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, PGT, 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, LEE 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.

IIa 14. "Propagation in Ferrite-Filled NMicrostrip," M. E. Brodwin, Trans. IRE, PGMT, 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, PMTT 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. 47.8. 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. O. 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. "ethod for Forming Large Ferrite Parts for Microwave Applications," L. G. Van Vitert, F. W. Swanekamp and F. R. Monforte, J. of App. Phys., Vol. 27, No. 11, November 1956, p. 1376. 49

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. IeCraw, 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. 1ll. 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. 0. 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. o50

IIa 46. "Magnetic Resonance in Ferromagneticsj" 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, PGITT, 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. "Ferrormagnetic 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.

II. PERIODICALS - MATERIALS b. Ferroelectrics 1. "Ferroelectric and Ferrimagnetic Properties of (Ba6 2xR2x)(Nbg-x Fel+x) 030Q" 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. 3 4. "Phenomenological Theory of Polarization in Ba TiO3 Single Crystals," C. F. Pulvari and W. Kuebler, J. of AP. 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. 52

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.

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, PGMT, 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 Semiconcuctors," 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. 54

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. Phys., 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.

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. Margenau 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., 1958. 7. R. F. Soohoo, Theory and Applications of Ferrite, Prentice Hall. 8. J. Smit and H. P. J. Wijn, Ferrite, Prentice Hall. 56

III. b 1i. Electromagnetic Theory, J. A. Stratton, McGraw-Iill, 1941. 2. Rhombic Antenna Design, A. E. Haxper, D. VanNostrand, 1941. 3. Electromagnetic Waves, S. A. Schelkunoff, D. VanNostrand, 1943. 4. Fields and Waves in Modern Radio,.Riamo and Whinnery, 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 Haygen's 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. 57

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. 58

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. Wheelone, "On the Summations of Infinite Series in Closed Form," JAP, Vol. 25, No. 1, Jan. 54. 4. Watson, "Treaties on Bessel Functions," Cambridge Press. 59

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