THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING Department of Electrical Engineering Cooley Electronics Laboratory This project was undertaken in collaboration with the Countermeasures Department of the Institute of Science and Technology, The University of Michigan. The experimental work of this project has been done in the Countermeasures Laboratories facility. Interim Technical Report No. 2 4957-2-P Period Covering May 1, 1962 to August 1, 1962 DERIVATION OF AEROSPACE ANTENNA COUPLING FACTOR INTERFERENCE PREDICTION TECHNIQUES * D. W. R. K. R. B. Adams DeHart Harris Y. K. Kwon R. E. Kovac A. I. Simanyi Approved b /John A. M. Lyon Under Contract With United States Air Force AIR FORCE SYSTIdS COMMAND AERONAUTICAL SYSTEMS DIVISION Contract No. AF 33(657)-8178 Wright-Patterson Air Force Base, Ohio Administered Through Office of Research Administration Ann Arbor 4957-2-P = RL-2120 September 1962

01' OOEKJI' LIS?' OF L~TI~ t lo NPCtS~ TAVYILp AND V3S2S 3. AOTlYTI3 XBTN UOD2 I4* romZ KR5ULM 5 4.10 A5RLYSIS AND no0N, 5 4*ol 1. N A&L AR.LYSIS OF SLM ODTWLIN 5 4i. 1.2 I4)N13SIM COUPLING 15 4 01.3 SPIRAL A fRA15 4*2* KKRDDTL STD~23,2,SLOT COUPLING iKWURIS 23 i4.2.2. 1AV3GUYID11S.T40E1WOIZ IRAIS CNARACTIERL3T 50 APflNDIX 55 62 ii

LIST OF ILLwTATIOl Fiue Title P 1 Wavepide Coupled to Nalf-tace 6 2 Slot Coordinate 11 3 Slot Gomtry 14 4 Comparison of Theoretical and Experimental Slot Coupling Results 16 5 Comparison of Theoretieal and Experimental Slot Coupling Results 17 6 Coaxial Balun for Out-of-Phase Excitation 20 7 avity and Spiral Feed 22 8 Ground Plane Used for Measurement of Edge Effects 25 9 Absorbent Shield 26 10 Two Arbitrarily Oriented Slots 28 11 Slot Layout for Preliminary Coupling Measurements 28 12 New Ground Plane with Rotatable Slot 30 13 Mechanical Detail of Rotatable Slot 31 14 VSWR of Rotary Joints versus Frequency 34 15 Rotary Joint Connecting Arms 34 16 Methods of Klystron Amplitude Modulation 36 17 Modified Microwave Bridge 38 18 Final Layout of Revised Microwave Bridge 46 19 Slot Coupling Phase Relationships 47 20 Slot Waveguide Assembly with Tuned Screws 47 21 Smith Diagram for Slot Waveguide Assembly 49 22 VSWR of Slot Waveguide Assembly versus Phase Shift of Short Section 51 iii

LIS T OF' U. MI V (continued) 23 VSVR of Wev**dd*-to*-Xbwpo1* Trans fo~rmer L~oad wi th NkM-1e(rOsMt at 2.81 kaes. * 53 24 ~ Optimm frejuency versus Monopole Ibight 5 25 RangI of Integration for ~L and x 58 26 ange of Integration for y and. a 58 iv

1. REPORTS TRAVEL, AND VISIORS On May 3, 1962, proJect personnel visited Wright-Patterson Air Force Base, Ohioo Details of this visit are included in the previous Interim Technical Report Number 1 dated June 1962. 2, StI'Q4RY The analytical work previously reported in the first quarterly report has been continued. The power coupling between slots in a broadside-tobroadside arrangement was determined to be about 20 db below unity coupling for a spacing of one wavelength between the centers of the slots and to decrease at a rate of about 6 db per octave for spacings greater than one wavelength. For the edge-to-edge slot arrangement, the power coupling between slots was about 31.5 db below unity coupling at a spacing of one wavelength and decreased at a rate of about 12 db per octave for spacings greater than one wavelength. These coupling factors were determined both theoretically and experimentally with very good agreement. This type of simplified analysis has been extended to angular arrangements of rectangular slots. The analysis has been sufficiently developed so that it is now possible to predict within one db the power interference coupling between two rectangular slots at any orientation. Experimental procedures were followed in determining the power interference coupling between two slots at any angular orientation. Details of the physical arrangements as well as the modified bridge for measurement are described in Section 4.2.1. The experimental determination of the phase associated with the power interference coupling between two rectangular slots has been somewhat "-1

troublesome. The reliability of such measurements has not been good. For this reason substantial time has been devoted to the improvement of the phase measurement procedures. Since the improved measurement network has just been finished, complete information on phase is not available at this writing. However, it now appears that the phase angular measurements can bt made with a reliability of plus or minus five electrical degrees. Preliminary monopole impedance studies were continued. A monopole together with a ridge transformer has now been completely designed and tested, The impedance of the monopole at the Junction with the ridge is 33.83 ohms. Two of these monopole units have now been fabricated and are available for coupling measurements. 3. ACTIVITIES FOR THE NEXT PERIOD Within the first half of the next quarterly period slot coupling measurements of both amplitude and phase shall have been made for all arrangements of rectangular slots in a flat plate. This is on the basis that extended arrangements of slots can be predicted by either two-slot analysis or two-slot measurements. Currently analytical studies for slots in a conducting plane are being successfully concluded. Not much more time on this aspect of the project is now contemplated. A cavity-backed Archimedean spiral together with a balun transformer feed has now been fabricated. Input characteristics are being measured. Initially it appears that a minimum of three spirals will be needed. Two spirals will have the same rotation of circular polarization. Then one of these spirals will be paired with a second spiral which has an opposing -2 -

rotation of polarization. Measurements will be made at first on these two combinations. For reference purposes it is considered desirable to study the air coupling between two spirals without any conducting ground plane. However, it is recognized that terminal considerations may drastically influence the results obtained for this air coupling. Even though the reliability of such data may be poor it is anticipated that attempts will be made to get some data of this type. In general, two spirals will be studied with conducting ground plane coupling present. This means that the ground plane will have circular openings sufficient to accomodate the cavity-backed spirals. It is anticipated that power interference coupling in the far zone will be independent of the angular orientation of a spiral0 However, when two spirals are in close proximity this may not be the situation. It may be desirable to study two spirals set in a dielectric plane. This could be considered an intermediate case of the two previously described and might indicate the relative importance of dielectric and conducting materials in the coupling phenomenao A further possible arrangement of large numbers of spirals would be to have an orderly arrangement of spirals printed by photo-etching process on a sheet of dielectric material0 Such a sheet could then be backed by a large conducting ground plane. The sheet itself would be between the metal deposited spiral elements and the conducting ground plane. If necessary an additional sheet of dielectric material could be inserted between the printed sheet and the conducting ground plane. This does not place the spirals in the ground plane, but somewhat in front of the ground plane. The measurements on spiral elements can be made at the same time as the measurements on slot couplings. This means that the measuring equipment -3 -

used on one of these will not be needed for the measurements on the other. However, in going to monopole coupling measurements it is anticipated that substantial equipment which was used for slot coupling will now be used for monopole coupling. For this reason measurements on monopoles have been deferred until all slot coupling measurements in a conducting ground plane have been accomplished. Theoretical analysis of the coupling of two spirals is now underway. In a preliminary fashion in this analysis, various simplified representations of the spiral are being considered. However, it is hoped to make a reasonably rigorous study of the spiral antenna and the power interference coupling of one such antenna to another. Like and opposite rotations of polarization are being considered. Imnediately after coupling measurements on monopoles have been concluded it is anticipated that slot coupling measurements with slots mounted in cylindrical surfaces will be considered. It is proposed that the arrangements of slots in the cylindrical surface will be limited to either the axial orientation or circumferential orientation. In other words, it is not contemplated at this time to use all angles of orientation of two slots on the cylindrical surface. It is believed that this restricted testing program will supply much needed information not hitherto available. Furthermore, such experimental results would have some chance of being proved out by analysis. Theoretical analysis of slots in cylindrical conducting surfaces will be made. This type of analysis will commence as soon as substantial analysis has been established for the spiral coupling cases. No substantial analysis on monopole coupling is being contemplated. On this research project, use has been made of previous analysis and design

data in order to establish monopoles for use as antenna elements offering the theoretical driving point impedance. The whole purpose of the study of monopole coupling in this program is to present a comparison of this series of power interference coupling studies with other such studies which have gone on before and which are being carried forward at the present time by various research groups. 4. DETAILED RESULTS 4.1. ANALYSIS AND DESIGN The coupling between two fundamental half-wave resonant slots was determined analytically by use of far field approximations for the magnetic coupling field componentso In this derivation, the coupling between slots can be determined for any orientation of one slot with respect to the other slot, except for end-to-end slot coupling. In this case near-field approximations for the coupling fields are required. A spiral antenna has been constructed to be used in making spiral antenna coupling measurements at L-band. 44.1.1 TEEORETICAL EVALUATION OF SLOT COUPLING. In the analysis of coupling of the waveguide-fed slot antennas in an infinite ground plane, the accurate field patterns of one slot antenna must be known. Consider a rectangular waveguide coupled to half-space as shown in Figure 1. Let the interior of the waveguide represent region 1 and the half-space represent region 2. Assume that (a) the waweguide walls and the ground plane are perfectly conducting and have negligible thickness, and (b) the ground plane is infinite so that no radiation field exists behind the ground plane or outside the guide. -5 -

slot aperture incident wave - ---- --- - - ---- - -—,- z (1) (2) input waveguide ground plane (z. 0) Figure 1. Waveguide Coupled to Half-Space The electromagnetic field can be represented everywhere by the Hertzian magnetic vector R* from which the electric and magnetic fields E and H are derived through the relations from Reference 1, -AV X a, (1) and 2. Va 2 (2).t -6 -

where e is the dielectric permittivity and, is the magnetic permeability. Assume hamonic time-variation exp(jcwt), where w is the angular frequency. Equations (1) and (2) beco, i. -sVx x*, (3) and - VV- * + k2 t*, (4) 2 2 where k2 o 2C. According to a fundamental existence theorem of electramgnetic field theory, an uniquely determined electrcnagnetic field exists provided the tangential component of either the electric field or the magnetic field is specified at each point (including discontinuity points) of the surface bounding the given region. For the present problem the tangential electric field 3 x n vanishes on the ground plane and along the infinite hemisphere centered about the origin (radiation condition), and it has the value M in the slot. The unit vector a normal to the bounding surfaces points into the half-space. The exciting field in the slot is equivalent to a magnetic surface current of density M on a conductor. By employing the duality of the electric current and magnetic current, the Hertaian magnetic vector is obtained in the form: slot Jl -s' where r denotes the field point, and r' denotes the position vector of the magnetic current element. -7 -

The factor of two results from the imaging effect (see Reference 3). Substituting Equation (5) into Equation (4), (r).: ( + '7). r() ~ ~i' ~rdS, (6) slot where I is the unit dyadic (therefore!. A - A. I X 5 for an arbitrary vector ). SinceM x n x z0, where 0 is the unit vector in the positive direction of the z-coordinate, then (?) P r (r, r ). [0 x ) d (7) 8slot where Yh ( ) Yh(rr 2) (I I - (8) Equation (7) gives the magnetic field in the half-space if the electric field E(r') in the slot is known. The slot field E(i') can be determined, at least in theory, by imposing the condition that all components of f and fi must be continuous in crossing from region 1 to region 2 (the determination of the field in the guide region is well known). However, this procedure leads to an integral equation which is not generally solvable. Therefore, assume that the slot field is the same as that of the TE10 mode of rectangular guide, namely:,)- 1, 0) -^E cos (9) b(r)o | O)*oE (9) a a b b for-l<x< and- <y<< 2 2 2 2

where a = smaller dimension of the waveguide, b = larger dimension of the waveguide, and x = unit vector in the positive direction of the x-coordinate o (see Figure 2). Substituting Equation (9) into Equation (7), co ' l dS' () = Eo Jh(r, ) Yo e b slot where y unit vector in the positive direction of the y-coordinate. (10) Hence and e, a b -a.- b 2 2 a b 2 2 y 2 dx' ' co2 s (-k+ a b 29 2.-Jkir - r /-rrTT (11) 3 2 dyv (12) After differentiation, the following assumptions are made in order to simplify * the integration:; -;'l o (x-x )2+(y- y')2 + r xx (13) where r \p2 + y2 z; and 1 1 | - O0 1; -; r r -9 -

These assumptions are valid as long as any linear dimension of the slot is much smaller than Ir - r' L The results of the integration of Equations (11) and (12), after taking into account the assumptions of Equations (13) and (14), are: - -2J b jkr Ix o2 - ')r IC sin..L * (- sin 0 cos 0) sin 0 con j - sin2 sin 0 cos 0 + 0 (-2) r Cos (- sin, sin. 0) 1 (kb)2 si2 0 sin2 o -Jkr sin Hy +2JEEo b - e'IC (15) (1 ( 1 - sin2 9 sin2 0) + 0 (~) r (16) where 0(12) means order of 1/r2 and is negligible. r The power across a unit area is calculated from the expression: P 1= 2 L ( x *) = JAI2 2 W\2 \J (17) The general form for the power per unit area for the slot problem is thus; 1 - 2 2b2E 2 sin (1-a sin 9 cos c ) cos (K 422r J sinrcos r - (i (sin2 9 sin 0 cos 0)2 + (l - sin2 9 sin2 0)2. 2- sin G sin 0) i)2 sin2 G sin2 0 IC -~ (18) -10 -

y b slot aperture -a Note: The z-axis positive direction is normal to the paper and toward the readers Figure 2. Slot Coordinates On the ground plane ( 6 ), the power per unit area can be written as 2e k2 2r2 ik r f sin2(. cos 0) eJ 2 cos ( s2 sin 0) 1 - (b)2 in2 1 (19) The power transmitted from a slot is given by: VW C[(;) x *()] o dS. s8 lot (20) -11 -

Substituting ((r) x E cos M and Equation (10) for f(r) into Equation (20), 0 0 b W - j h ' ) Yo. co Os dS E * co 4 ds. (21) slot lot _ Integration of Equation (21) is done by using a method outlined in Reference 4 and is detailed in the Appendix (section 5). Hence, W = ()2 Eo F (22) where F 1 - 0.374 (b)2 + 0.130 (b)- 0.154 (b)6 1.36.8 (b)2 + 0.160 ()4 + 0556 ()4 X X X The gain of an antenna is given by: g (23) where r - distance between the antenna and the point of observation, P radial power density, and r WT = transmitted power. For the problem at hand, P = P and WT 2W (since W is the power supplied by r z T the slot and an equal amont of power is supplied by its image. Thereforo the gain of the half-space slot in this problem is given by g (24) 2W -12 -

Substituting Equations (19) and (22) in Equation (24), the gain of the slot is kb cos (-sin0i) 2 1 2 a g sin2 ( a os 0) (25 ) g 2 7ra^ 2c' b 2 (25) 1 (-) sin $ The far-field coupling between one slot and another is defined by W C - (26) T where WR is the power received by the second slot, and is given by R WR = Pr A = Pr (27) where x = free-space wavelength, and gR = gain of the receiving slot. Substituting Equations (23) and (27) into Equation (26) gives the coupling as 2(28 C -( )gT gR(' (28) where gT is the gain of the transmitting slot. The gain of each slot is given by Equation (25). For a slot arrangement such as that shown in Figure 3, the far-field coupling is finally C K3-r 2 L sin (ka cos T) sin2 (2 cos 87T 3 FTFR 2 s T 2 cos (- sin T) cos ( sin R 2). kb. (29) ( —sin2 1- (- R )2 sin R) - in2R?T O 7r~ -13 -

9 where aT = smaller dimension of transmitting slot, aR = smaller dimension of receiving slot, bT = larger dimension of transmitting slot, bR = larger dimension of receiving slot, 0T = orientation angle for transmitting slot, =R = orientation angle for receiving slot, F = Ft T Ia aT b = bT and FR FaR bbR R la = aRj b - b. X' y t \ \ SLOT lEANSMITTING SLOT f-I Figure 3. Slot Geometry -14 -

For this problem, i.e., two slots of equal apertures, T aR a bT bR F b F^ R ^- F hence the coupling given by Equation (29) reduces to: C (_ 2 2 ka2 ka C sin s in2 ( Cos CR) cos (k sin T) cos (kb sin (R) 2 - 2 --- — (30) 1 ()2 sin2 - (r ) s in RJ) For a = 0.4".1 b = 0.9", and X = 1.283"' the far-field coupling given by Equation (30) for two situations are plotted in Figures 4 and 5. Experimental results are also shown for comparison. 4.1.2. EDGE-TO-ELGE SLOT COUPLING. Preliminary analytical derivation of the mathematical expressions for the coupling of slots oriented in an end-to-end configuration, which involves a near-field coupling phenomenon, has been made. However, improvement to the derivation is necessary before it can be reported. 4.1.3o SPIRAL ANIT t. 4o3.10o Resume of Spiral Antenna Characteristics. The basic properties of flat spiral antennas make them very useful in applications which require a broad-beamed, circularly polarized pattern that can be achieved across a wide frequency band (Reference 5>) Various approximating solutions toward explaining the radiation pattern of two-arm spiral antennas have been proposed. The -15 -

-26 -281 NA a C) P4) U >4~ 0 0 4.) 10 H) -301 Calculatod fruM p4Uation (3 0) - - - Experimental i' m 9.20 kmso X = 1. 283 in. d XFi gure i.. Comparison of' Theoretical and. RxperimentAl Slot Coupling Results.00 5,00p -1j6-, 600,

-052 i6T 0md~ for D0 (per1 1 iarl) 050 048 I I!4 -ON s3.361 1 10 IL # I*( Ikp —w arnt.! poluts -Ca3*"Uted vith Zq~at1on ( 30 ) f a 9.30 %M x a 1#.283 Iii. 0 0.5 1.00 I.$ two 3.00 3,,?isur* 5. C isrion of MMMortIto- & I ai. Z ui' Inu sl81ot Co4uplizi Rwi~ltA -17-M

so-called band theory provides a good method for understanding the operation of spirals (Reference 6). In short, this theory states that the chief contribution to the radiated energy for Archimedean spirals occurs from radiation bands which have a mean diameter of X/7r, 3X/w, etco, for an outof-phase excitation of the two spirals arms, and a mean diameter of 2/7T, 4X/7T, etco, for in-phase excitation of the armso Kaiser (Reference 7) has presented some very illuminating diagrams of the computed phase shift along the spiral armso From his presentation it is quite easy to see why radiation bands existo For the out-of-phase excitation the current elements on adjacent portions of the two arms of the spiral at its input are 180 degrees aparto Since their physical separation is small in terms of wavelengths, the radiated fields cancel almost entirely. Proceeding outward along the spiral, the phases of the current elements on the two different arms approach each other due to the different line lengths traversed. Finally, at diameter d = X/7, adjacent current elements are in phase Moreover, at diametrically opposite current elements, the 180-degree electrical phase shift plus the reversal of the direction of the current in space yield two radiating elements which are in phase and separated by a distance d. This condition, favorable for efficient radiation, will hold over diameters somewhat smaller and larger than do, so it is seen that the band around d is the important source far the o radiated fieldso Since the electrical phase change is 90 degrees per quarter turn along the spiral at diameter d, the resultant radiation is circularly polarized. The radiation mode which occurs at the smallest diameter do = X/t is most frequently used, and requires out-of-phase currents at the spiral input terminals. The radiation pattern for this mode is a broad beam symmetrical about the axis of the spiral. For in-phase current excitation, the pattern is characterized by a split beam with an on-axis null. -18 -

4,132o Impedance and atching. The input impedance to the spiral can be controlled by changing the ratio of arm spacing, b, to arm width, wo The most commonly used spirals are designed such that the arm width and the arm spacing are equal, ieo, b/w - 1. For this self-complementary antenna the impedance is 180 ohms. This impedance can be decreased by making b/w largerO Conversely, this impedance can be increased by using a smaller ratio, The spiral feed requires the use of a network with two outputs having a balanced capacitance to ground. In addition, the output currents must be out of phase to obtain the lowest mode of radiation from the two-arm spiral0 This can be achieved simply by means of the balun shown in Figure 6. The two outputs for the balun are created by the tee. Arm A is adjusted to provide 180 degrees greater phase shift than Arm B at a given frequency so that the required out-of-phase currents are generated. This balun also provides a 1:4 impedance transformation between input and output. The major inherent limitation of the balun described is the narrow-band characteristics, but this is not a serious disadvantage for the measurements intended, since the balun can be retuned at each frequency to provide a proper matcho Another type of balun was considered which could be used to cover a frequency range of one octave with the spiral operating in the basic mode. The balun would utilize two broadband 90-degree phase shifters similar to those described by Schiffman (Reference 8). An operational balun of this type was reported by Craven (Reference 9)o It would be convenient to construct this type of balun from simple stripline circuit elements. However, due to the high ratio (o) of even-mode to odd-mode impedance needed for Schiffman's original design, realizing these phase shifters in dielectric-loaded stripline would be extremely difficult. For example, the clearance slit between two quarter-wavelength coupled sections would be only 0.002" for 1/4-inch ground -19 -

adjustable pShae shifter (tron*) rll ----1 -1 --- -------- rF 60 CorM —l --- -— f- t-fb --- hoitati plane separation0 Fc, this reasc a nov design was daelo pe4 for the pbae original design. In -r to counteract this frequency sensitivity, a mare with opt.values of /01 anP for tb typ of a network, a + I.6-dearee pae shift deviation from l&) degrees results o a 2:1 banvidth for the bu Since the cortruction and testing of the stripline balun woAld require ~- - considerable time, i was deide tat the ial un wCd be used for aot least the initial spir cantea hmer yie fatrt. leat the initial spial antenn z-asreen *20 -

4.1.3.3 Construction of the Spiral An Archimedean two-arm spiral, each arm consisting of eight full turns, was photoetched on a thin fiberglass base. The spacing between the arms was made equal to the conductor width of 0.049 inch. The spiral is located at the mouth of a cylindrical metal cavity approximately three and one-half inches in diameter and two inches deep (see Figure 7). The largest diameter to which the spiral arms extend is 3o35 inches. Therefore, there is a clearance of Ool inch between the outermost arm of the spiral and the inside diameter of the cavityo As shown in Figure 7, a two-wire open line connects the spiral to the input terminals on the back of the cavityo The characteristic impedance of this transmission line is tapered from 200 ohms at the input terminalsto 180 ohms at the spiral to provide a matched feed from the coaxial balun. The cavity depth is one-quarter wavelength at 1.5 kiloaegacycles per second. This frequency will be close to the low-frequency limit of the spiral, the diameter of the radiation band for this frequency occurring at 2.52 inches. If radiation from the outermost diameter for one arm, 3.19 inches, would still give a useable pattern, the lowest operating frequency would be fixed at 1.2 kmcs. The high-frequency limit will be determined by the cavity depth, due to the gain reduction occurring as a result of the reflections from the cavity backo According to experimental evidence the gain will be reduced by 3 db when the cavity depth becomes equal to three-eighthswavelength, resulting a high-frequency limit of 2.25 kmcs. for the present spiral-cavity combination. Another possible highfrequency limitation would be the appearance of the first split-beam mode at 2.36 kmcs. The proper operating range for the spiral and balun combination will be determined by taking pattern measurements, which will indicate the lowfrequency and high-frequency limits of the spiial by a deterioration of the regular pattern. -21 -

apmetroia A4A ID OD d a a in a O0-63 o0.62 o.3J44 o.66 la's 1*. Ing in. spiral on disleotria shoot 3.o56 &iaVIte7 of tapez" lziss St #m4U eMA is O01e *07 ri,brass raity Flare 7.* Caiwtt aMSia 1d.22.'

4.2o EXPERIMENTAL STUDIES X-band slot coupling measurements, similar to those reported last period, were made to determine (1) the effects upon the magnitude of slot-to-slot coupling introduced by locating one of the slots near an edge of the ground plane, (2) the effects upon the magnitude of coupling due to slots oriented at various angles to each other, and (3) a method for measuring the phase of coupling between slots. S-band measurements were made to develop a waveguide-to-monopole transformer which matches the monopole impedance to the impedance of a waveguide through a tapered ridge and an adjustable short network. 42olo1 SLOT COUPLING MEASUREMENTSo More slots were added to the ground plane (used for previous coupling measurements) for the purpose of measuring and evaluating edge effects upon the two-slot coupling magnitude. A second ground plane was constructed with a rotatable slot so that the magnitude of coupling between two slots oriented at various relative angles could be measured. Phase measurements of the coupling associated with these magnitude measurements were attempted. However, the accuracy and repeatability of these measurements were very poor. Improvement in the phase measurements was obtained by making various modifications to the microwave bridge arrangement used for the coupling measurements0 These modifications consisted of replacing some of the microwave components with less phase-sensitive components, rearrangement of the bridge so that equal length arms existed in the bridge, and the utilization of a slotted line for measuring the phase instead of a phase shifter. -23 -

4,2.l1l. Edfe Effects. Two more slots have been added to the 24" x 36" brass ground plane, as shown in Figure 8, to experimentally determine the magnitude of edge effects upon measured slot coupling0 One of the new slots (No, 8) is spaced 7.67 wavelengths from slot No. 6 and 6.80 wavelengths' from the nearest edge of the ground plane. The second new slot (No. 9) is spaced 7.67 wavelengths from slot No. 3 and 0.727 wavelength from the nearest edge of the ground plane. Measured coupling between slot No. 6 and slot No0 8 is -38.6 db at 9,20 kmcs; measured coupling between slot No0 3 and slot No0 9 is -38,4 db. The small difference between these two measured values suggests that edge effects are negligible. Before concluding thus, the distance between one slot and the edge of the ground plane, as well as the slot attitude relative to the edge, should be varied and measurements repeated for these general cases0 4.201.20 Absorbent Shield0 The equipment used for the experimental measurement of X-band slot coupling factor is extremely sensitive to microwave scatterers in the vicinity of the ground plane containing the slots. For example, personnel within ten or fifteen feet of the slots can cause intolerable variations in the null detector signal0 To overcome this problem, a miniature microwave anechoic chamber (see Figure 9) was constructed to enclose the ground plane and slots, thus providing a shield from external objects and personnel0 The shield was constructed from plywood and four-inch "Hairflex" microwave absorber manufactured by B. F. Goodrich. Twine was used to "sew" the edges of the plywood together so that reflections would be minimized. With the microwave absorber shield in place, the null detector signal was sufficiently quiet to facilitate repeatable and accurate slot coupling

O I I L6 #9 #3j #8 new slots Figur 8. Groun dne lauod for40 Ierftost Mms tWmnt -25.

" —% Me-on.. "-Noma. 0 0 a &V a 10 '-GROUND PLANE "W- -... - -~ ABSORBENT MATERIAL - PLYWOOD FIGURE 9. ASRRV SHIRlD

measurements. The effect of the shield upon the waveguide-to-slot impedance match is barely detectable, even for the slot near one edge of the ground plane (slot No0 9 in Figure 8). The effect of the shield upon measured slotto-slot coupling is also negligible. 4o2.1o30 Coupling Between Two Slots of Arbitrary Orientation. Let two d slots, spaced - wavelengths apart, be oriented at arbitrary angles, defined as a and p, as shown in Figure 10. The magnitude of the coupling factor is d a function of A, a, and o To obtain a crude but quick experimental check for the theoretical predictions of this coupling factor, measurements of coupling were made using slot No0 1, No. 2, or No0 3 with slot Noo 4, No. 5, No. 6, or d No0 7 (see Figure ll)o With these seven slots, ten distinct combinations of, c, and p were possible, limited in variety because (a) one slot orientation was always ninety degrees from the second slot orientation, and (b) the vertical component of the separation between the two slots was always equal to two wavelengths at the operating frequencyo The results for the ten possible cases (refer to Figure 11) are given in Table Io The slot separation, d, and the angles a and p, were calculated from measured values of the variable horizontal component of the separation, D. Coupling (K) is given in decibels referred to unity coupling (0 db). 4o2olo4. New Ground Plane With Rotatable Sloto In order to obtain a more flexible means for comparing experimental values of slot-to-slot coupling with those predicted by theory, a new copper ground plane with four fixed slots and one rotatable slot was constructed, and is shown in Figure 12o The mechanical detail of the rotatable slot is shown in Figure 130 A dial on the back of the ground plane indicates the orientation angle of the rotatable slot, relative to an adjustable reference angleo -27 -

TMNSI1ER? aim Ba SITA 4 ffm,.I — I -k4 11.Arm m am Yiswe 10. Two Arbitrarily Or -iit( Slots O.a779X 7Th N WL #2 -1 F #7 F.1 1 #5 Ar i i i i t I i i.. i i - - - L~ I L IL -F IL -T I MO 2x IP ~0.390.j-11 pigawe U. oSlot layout for Pwizr olpi Nos~r Iinmta

TABLE I.... —, Slots Used D d XMTR RCVR x aB K I, Noo Noo No. Noo No. No. Noo No. No No. No. 7 5 1 6 5 2 6 1 7 5 3 Noo Noo No No. Noo No. No. No Noo Noo No. 3 1 4 1 2 4 3 7 1 3 4 0 000 0.221 0.611 0.779 1o000 10390 2o000 2.779 2.779 3o000 3.390 2000 2.015 2.092 2.146 20236 2.436 2.828 3.424 3.424 3.606 30936 +90.0~ +8307~ +163 0~ +11103~ + 63.4~ - 34.8~ + 45.0~ -125.7~ +144o3~ + 33 7~ - 59-.5 0.0~ - 6.3 +73~00 +21.30 -26.6~ +55 2~ -45.0~ -35.7~ +54.3~ -5603~ +30050 -72 -46o6 -39.4 -38.3 -3702 -36.0 -37.1 -38.8 -3809 -39o8 -41.4 db db db db db db db db db db db (approx.) f = 9.20 kmq X = 1.283 inch These data have been plotted in Figure 5o The coupling between fixed slots B and C and the rotatable slot, A, were measured for a = 0, - P2 e- in five-degree increments (refer to Figure 10). Measured coupling data, in decibels below unity coupling, have been shown in the curves of Figure 4o It was observed that the phase of the coupling, with respect to the variable, p, was essentially constant. Truly dependable -29 -

F IN -4' 7.I 4 i f ", I I I I 1. I I i i I c i I I i i i cii 3. 8~4 IQ"' 2.,566! 4 I B — I.F - -.. It - -- - 1. -. - I I. I i I i I I I -ow- 2-5662 —ol"o- 3,1%901 12' Figure 12...- - - -- - -.. 2 4 t raw Groutnd Plane with Rotatable Slot - 30 -

vo@ - - a oldazS4 bra.O wsrSPi6 VOIppw PlSn* 7iw:.)g..aa Dt1.O Ist~1 slot to 31.

phase measurements were impossible because of the poor phase stability (+ 150) of the coaxial cables which couple the slots to the microwave bridge. An effort was made to measure secondary coupling, which consists of coupling between two slots via a third slot (terminated with a matched load) with the two primary slots decoupled (a ~ 0~, JpJ - 900). Two such configurations were used: (1) slots A and B as primaries, slot C as the intermediate, and (2) slots A and C as primaries, slot B as the intermediate. Coupling should be approximately -70 db for these configurations. This coupling factor was not measurable because of reflections caused by the connecting cables and adaptors 4.2ol.5o Improved Connecting Cableso New coaxial cables with doublestub tuners were used in an effort to obtain the phase and low-level coupling measurements discussed above. The phase stability was improved somewhat (- 100), but the matching stubs could not be set so that reflections would be minimized for many cable positions. Obviously, some other means of coupling the slots to the microwave bridge was necessary in order to obtain sufficiently accurate coupling data. 4.2.1.6. Rotary Joint Connecting Arms. Two forms of rotary joints, in conjunction with waveguide bends and straight sections, were considered as means for improving measurement accuracy. The first form consisted of two waveguide-to-coax adaptors joined by a dual female N-type connector. Five of these joints were required to couple one fixed slot and one rotatable slot to the microwave bridge. In order to move the rotatable slot, or to change from one fixed slot to another, it was necessary to loosen the connector at each joint, move the "flexible" arms to the new position, and retighten each connector. -32 -

Although this method of coupling resulted in smaller reflections (VSWR < 1o05), the phase stability (or repeatability) was still not better than - 3. Five precision waveguide rotary joints were next considered. Operating at a frequency of 9.2 kmes. (that used for previous measurements), a phase stability better than - 1 was observed while moving these joints to all possible positions 4.2.1.7. Characteristics of Waveguide Rotary Joints. Because these rotary joints are relatively narrow-band devices, it was though best to determine the optimum frequency of operation. Figure 14 shows the VSWR obtained for each rotary joint as a function of frequencyo In order to minimize reflections, a frequency of 9.29 kmcs. was selected as optimum. Rotary joints No. 5, No. 2, and No. 4, because of their similar characteristics, were selected to couple the rotating slot to one terminal of the microwave bridge (see Figure 15). Likewise, rotary joints No0 3 and Noo 1 were selected to couple the fixed slot to the other bridge terminal. The phase and magnitude of the worst reflection, which is a function of the angular position of the rotary joints, were determined for each connecting arm. In order to minimize these reflections, a double-stub waveguide tuner was designed and constructed for each set of rotary jointso At this point, phase stability was rechecked and found to be better than + 1/2~. Since this stability is entirely adequate for the intended coupling measurements, all waveguide slots were retuned for a perfectly matched input at 9.39 kmcs. 4o2olo8. Performance of Microwave Bridge Employing Rotary Joints. The microwave bridge (shown in Figure 7 of Interim Technical Report No l1) was tested with a typical configuration of two-slot coupling, using the five waveguide rotary joints to connect the slot waveguides to the bridge terminals0 -33 -

is j14 11I2 it 10 1,08 'SWI I va 1 *#~ irme 1.00 to 9* fst, 0.*, 93 S5 W*9 aft, - - - -. lw- t0gu e froqiwncy (kime) Ike * 'W of Rotary Joitst versus Frequency dioublefstatu tunersa. to uicroaew bridge Figure. 15. Rotary Joint Connecting Arms

The best null obtainable, however, was only 20 db below the bridge input power level, which resulted in a rather broad null and poor repeatability. This phenomenon was explained by the presence of incidental frequency modulation of the klystron oscillator; since each bridge arm represents an electrical length of several wavelengths, the microwave signal undergoes considerable phase shift in propagating through each arm. This phase shift is directly related to the frequency for small frequency deviations, and increases with increasing electrical length of the bridge arm. Hence, a frequency.modulated signal applied to the input of each bridge arm results in a frequency- and phase-modulated signal at the output. If the two bridge arms are not of equal electrical lengths, then the difference in the phase modulation of the two microwave signals appears at the null detector. Since a perfect null can only be produced at the instant when the relative phase of the two signals is 1800, an amplitude modulation of the null signal results from the modulation of the relative phase of the two signals from the bridge arms. The null meter will thus respond to the average null signal which is considerably higher than the best instantaneous null signal, hence a broad null of large amplitude results. The incidental frequency modulation was partially attributable to ripple and/or noise present on the active side of the square-wave modulation signal (see Figure 16a) in the klystron power supplyo By raising the reflector voltage, the square wave was shifted as shown in Figure 16b. This placed the opposite side of the square wave in the active position on the klystron mode, and resulted in less frequency modulation. To reduce the sensitivity of the microwave bridge to frequency modulation and thereby improving the null still further, it was necessary to equalize the electrical lengths of each bridge arm. To facilitate this change, and to -35 -

I /10- active II I of osei anii I I T actAiv KlystraouL - - Voltas. (zmoptiv) K2iystron Ro f ~t~' YoI (ini. KXystrou Ref lecto Yolt4.(m~ptiw) I A4 ~btho mp3~to r USI~t~tIAMII IN-0 - (aY - WAlk a In Idatublo 1. - (b) d% 7

minimize insertion loss in the bridge arms (so as to maximize the null-signal to meter-noise level), the two 10-db directional couplers were replaced with waveguide tees. The resultant layout of the modified microwave bridge is shown in Figure 17. Note that the precision phase shifter has been moved from the "unknown" arm to the reference arm to help equalize their lengths. An additional attenuator was required in the "unknown" arm to offset the insertion loss of the phase shifter so that the bridge could be balanced, with no slots connected, for reference phase and attenuation. The accuracy of this bridge was tested by inserting various lengths of waveguide between the "unknown" terminals, where the slot waveguides would normally be connected. The attenuation of these waveguide sections is negligible; the phase shift of each was calculated from measurements of their physical dimensions. Table II shows the measured attentuation and phase shift versus the calculated phase shift for these sections. TABLE II Calculated Measured Measured Phase Shift Phase Shift Error Attenuation 0.0~ (reference) 0.0~ 0.0~ 0.00 db llo9~ 12.9~ +1.00 -0.13 db 53-0~ 58.5~ +5.5~ -o.41 db 238.9~ 240.3~ +1.40 +0.07 db 292.0~ 294.0~ +2.0~ +0.17 db 4.2.1.9. Replacement of Output Tee and Phase Shifter with Slotted Line. The errors indicated in Table II are at least partially attributable to interaction of the reflections from the phase shifter and reflections from other -37 -

input ----~ — 40 to osciLLoscope and spectrum amly.ar — lplane bond shunt too reference arm ---- ~~ 29 — cm. section.. arm_ Li erstsl d6tectAw to a lots

components of the microwave bridge, hence another revision to the bridge was made: The precision variable phase shifter was removed from the reference arm and the output tee was replaced with a slotted section for phase measurements. These two changes gave rise to a two-fold improvement: (1) reflections from the phase shifter were eliminated, and (2) the relative phase relationship among other reflections was held fixed. The further revised bridge was tested in two ways: First, the "tracking" of the precision variable attenuator in the reference arm with respect to the variable flap attenuator in the "unknown" arm was obtained by setting the variable flap attenuator to a given value and recording the setting of the precision variable attenuator required to rebalance the bridge. These data are listed in Table III. The gradual deviation of one attenuator from TABLE III Variable Flap Attenuator Setting (db) 0 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 MAX. Precision Variable Attenuator Setting (db) o.o4 1.17 2.23 3 30 4031 5.40 6.31 7 51 8.52 9066 10.74 12.66 14.71 16.67 18.77 20.73 26.95 the other is most likely due to calibration error of the variable flap attenuator, while the irregular deviations probably constitute actual measurement errors due to reflections within the microwave bridge. Second, the bridge was again tested -39 -

with several straight waveguide sections as "unknown" insertion networks. Table IV shows the measured attenuation and phase shift versus the calculated phase shift for each section. The calculated values of phase shift in the TABLE TV Calculated Phase Shift 0.00 (r4 13.2~ 52.7~ 235.1~ 402.8~ 637.9~ 769 3~ 1196.2~ 1407.2~ 1965 5~ 2018.2~ 3617.5~. eference) Measured Phase Shift 0.00 13.0~ 50.70 233.6~ 408 9~ 638.2~ 767 2~ 1192.5~ 1409.70 1965.90 2023.7~ 361 0 3616.5 Measured Attenuation -- --- ---- -- Error 0.00 -0.20 -2.0~ -1.50 +6.10 +0.3 -2.1~ -3.7~ +2.50 +0.4~ +5.5 -1.0O 0.00 -0.02 -o.04 +1.22 -0.05 +0o.14 -0.03 -0.11 +0.07 +0.01 +1.50 +0.o6 db db db db db db db db db db db db table above were obtained thus: Consider the phase shift of a given waveguide section as having two components, and expressable as 0 = nT 4 8@ radians, (31) where n represents the number of multiple half-wavelengths included in the total length of the section. The value of n was determined from an approximate measurement of the physical length of the waveguide section and a knowledge of the guide wavelength. The remaining phase shift, Q, was determined from a precise slotted line measurement. The slotted line was first terminated with a shorting -40 -

plate, and the positions of the voltage minima noted. Then the unknown waveguide section was inserted between the slotted line and the shorting plate, and the new positions of the voltage minima noted. The value of Q was then calculated from the direction and magnitude of the shift of the voltage minim using the equation 9- - s radians, (32) Xg where s = shift of the voltage minima toward the load, Xg = guide wavelength at the operating frequency. Errors presented in the data of Table IV indicate the presence of serious residual reflections within the microwave bridge, The only bridge component still remaining which could have caused these reflections was the input shunt tee. To reduce this problem, a hybrid tee was substituted for the shunt tee, The fourth port (series arm) was terminated with a matched load to help absorb unwanted reflections0 The measurements taken with the shunt tee were repeated and are shown in Table V. Some improvement is indicated, but errors are still excessiveo TABLE V Calculated Measured Measured Phase Shift Phase Shift Error Attenuation 0. 0 (reference) 0.00 000~ 0000 db 235o1~ 23705~ +2.4~ +4044 db 63709~ 63909~ +20~0 +0.41 db 1196o2~ 1191.7~ -4 5~ -0o 13 db 1965.50 196200~ -3 5~ -Oo04 db 2018.2~ 2018.6~ +0~4~ +0.30 db -41 -

4.2ol.10 Final Consideration of Bridge Inaccuracies. In order to maximize the accuracy of the microwave bridge, the following steps were considered: a. Measure and minimize all possible reflectionso b. Precisely equalize bridge arms, using a typical slot-to-slot separation, so that the null signal is most free from noise and effects of residual frequency modulation. ca Use ferrite isolators and/or padder attenuators in both bridge arms to minimize interaction. do Replace hybrid tee with matched hybrid tee to minimize interactiono e. Use less probe penetration in slotted line detectoro All components used in the microwave bridges described were tested for quality of performance at the selected frequency of 9290 megacycles per second. The rotary joints were tested in the exact form used for the microwave bridge, as described in Section 402.1.7. and shown in Figure 15, i.e., as connecting arms for the slotso Results of these measurements, taken while moving the rotary Joints to all possible orientations, are: Connecting arm for rotary slot Maximum VSWR = 1.043 Minimum VSWR = 1.022 Connecting arm for fixed slot Maximum VSWR = 1.033 Minimum VSWR = 1.021 Two ferrite isolators were also tested for further consideration of point (c) above. The data for these two components are:

Ferrite Isolator (Litton X-250) Input VSWR = 1.010 Insertion Loss = 0.4 db Output VSWR = 1.014 Isolation = 14.5 db Ferrite Isolator (Uniline H-86-96) Input VSWR = 1.051 Insertion Loss = 0.4 db Output VSWR = 1.044 Isolation = 10.3 db Several other components were tested, yielding the following data: Termination (Microline 150) VSWR = 1.013 used for VSWR measurements Termination (HP X910B) VSWR = 1.025 Precision Variable Phase Shifter (HP X885A) Maximum VSWR = 1105 Minimum VSWR = 1.004 Precision Variable Attenuator (HP X382A) Maximum VSWR = 1.041 Minimum VSWR = 1038 Variable Flap Attenuator (HP X375A) Maximum VSWR = 1.034 Minimum VSWR = 1.005 Shunt Tee (shop) VSWR of shunt arm = 3.00 VSWR of symmetrical arms = 156 Series Tee (HP X84QA) VSWR of series arm = 2.40 VSWR of symmetrical arms = 1.56 Hybrid Tee (DeMornay-Budd) VSWR of shunt arm = 3.00 VSWR of series arm = 1.95 VSWR of symmetrical arms 7 117 -43 -

Matched Hybrid Tee (Aircom 1092X- - matched at 9.0 kmcs.) VSWR of shunt arm = lo12 VSWR of series arm = 1.54 VSWR of symmetrical arms - 1.17 In order to test the merit of point (d) above, the hybrid tee and the matched hybrid tee were tested for isolation between symmetrical arms: An adjustable short was connected to one symmetrical arm, the short arm and the series were terminated with matched loads, and the second symmetrical arm was regarded as the input. While adjusting the short through more than one-half wavelength, the input VSWR (ideally 1,000) was measured; Hybrid Tee (DeMornay-Budd) Maximum *SWR 173 Minimum VSWR = 1018 Matched Hybrid Tee (Airco 109-X-l - matched at 9.0 kmcso) Maximum VSWR = l122 Minimum VSWR = 1o14 These data show that considerably better isolation can be obtained by using the matched hybrid teeo Hence, one final step in perfecting the microwave bridge will be to replace the hybrid tee with the matched unito Data on the precision phase shifter confirm the wisdom of its replacement with the slotted line for phase measurements. The two attenuators incorporated thus far, based on the above data, should cause no problem. The rotary joint connecting arms should likewise cause little troubles When the physical dimensions of the bridge arms were modified to accept the matched hybrid tee, the reference arm was carefully designed to balance the "unknown" arm thus satisfying point "b" aboveo Finally, it was concluded that less probe penetration would not affect the bridge accuracy (point "c" above) because at a null, the probe is at a point of near-zeto impedanceo -44 -

The final bridge design is shown in Figure 18, and incorporates all of the above considerations. Although no measurements have been made with this bridge at the time of this writing, slot coupling factors should be measurable within plus or minus one-half decibel in magnitude and within plus or minus three degrees in phase. 4.2.1l11o Measurement of Slot Coupling Phase, The phase of the twoslot coupling factor will be referred to the conducting ground plane and will include the two slot apertures propero From Figure 19, it can be seen that this phase angle, 0, cannot be directly measured due to the presence of the input waveguides and associated tuning screws. The phase angle 9 can be m measured readily, and is directly related to the unknown 8 by the equation: m 20- + 01 + 02 (33) where 0 = phase shift introduced by each set of tuning screws 01 = phase shift due to length I1 02 = phase shift due to length 12 The greatest problem in the measurement of the coupling phase angle 9 is to determine the value of 0 so that 8 may be calculated from 8. Since there is no analytical method available to calculate 0 with sufficient accuracy, a method for measuring this phase shift has been developed. Note that if the straightforward method of Section 4.2.1o9 were attempted, using a slotted line and a shorting plate, a serious error could result from the characteristic S-curve caused by the interaction of the reflections from the tuning screws and the shorting plate. The method devised for this measurement employs two slot input waveguides of any length connected back-to-back through a short section (see Figure 20). Before connecting these slot waveguides thus, each is tuned for a match while -45 -

4 -w tQ P rA —. s K i if -1 liur 18. i1 LAyot of Add B l a idg Fipure l8.?izml layout of Rers.d Miorcowve Bri&Ll I A I CM 8.46 -

I I I tuning serews o ) m -. slot Ipertur go~w&n ple FiPar 19. Slat CcMpliaf Phase Relationships B~*1 I I I I I I I ii i AlJ'D i I I I I I I-A rY I I2 I I ftArM 10. slot Wk~vpai4. *s ith Twme4 Seroes.47..

mounted on the ground plane. The two waveguides are then carefully removed from the ground plane and equippedLwith flanges. because each set of tuning screws is mounted a fixed distance from the ground plane for coupling measurements, and because the separation between the two screws is the same for all slot waveguides, it is assumed that all sets of tuning screws are adjusted to the same tuning. Hence, each of the two waveguides removed include a representative set of tuned screws. From the Smith diagram (Figure 21), it can be seen that if the assembly shown in Figure 20 is terminated with a matched load, then only a pure phase shift, 0, is required between the back-to-back slot waveguides to obtain a match at the input of the assembly. For the sake of clarity, stubs "A" and stubs "B" have been assumed to present normalized shunt susceptances of bA = + 1.0 and bB ' + 2.0 respectively. The diagram is obtained by assuming a perfect match at both input and output terminals, and plotting the admittance of each half of the assembly while moving toward the short section in the centero The short section then provides the required phase shift (03) to join the two end points on the diagram0 Note that it is not necessary to preserve lengths I1 and t2 after removing the slot waveguides from the ground plane; it is only necessary to preserve the tuning of the two sets of screws, A change in 21 and/or t2 may simply require a different value of 03 to produce a match, and 0 is independent of 03o To actually produce this condition in the laboratory, the assembly was terminated with a perfectly matched load consisting of a typical lossy termination plus a double-stub tuner adjusted to cancel the residual reflection at the frequency of operation. The straight section in the center of the assembly was progressively machined to smaller lengths and the input VSWR of the assembly was measured and plotted as a function of the electrical length of the straight -48 -

! — 4 - K- -11 II./ Ix,. "r Figure 21. Fn2ith Diagram for Slot Waveguide Assembly

section (see Figure 22). A second waveguide section was then machined to the optimum length and connected into the assembly. The phase shift through this assembly can now be measured with the microwave bridge. To obtain the phase shift introduced by two sets of tuning screws (2 0), it is only necessary to remove the screws after having obtained the previous measurement and a'in measure the phase shift through the assembly. The difference in the phase shift, introduced by the removal of the screws, is equal to minus 2 J. Returning to the original problems that of obtaining $ from 6m (Equation (33), it can be seen that the two remaining factors to be determined are 01 and 02. These phase shifts can be determined, with the slot waveguides involved mounted on the ground plane, by the method of Section 4o2.1.9o It is necessary to temporarily remove the tuning screws to make these measurements. 4o2.2o WAVEGUIDE-TO-MONOPOLE TRANSFORMER CHARACTERISTICSo Results of measurements on the monopole feed system are illustrated in Figures 23 and 24~, Two areas were explored: ao The input VSWR of the ridge transformer was determined across a frequency band, first with the short adjusted for the best match at 2.81 kmcs., and second with the short adusted for an optimum match at each frequency0 b. For various monopole lengths, that frequency was found which gave the best match while varying the short position. 4o22.1ol Input VSWR Across a Frequency Band0 All the monopoles used had hemispherical end caps. For frequencies lying between 2750 and 2870 mcs. the VSWR was measured for the ridge transformer loaded with a short and a monopole of length h = o9600 inch (2h/X =.4571 at 2810 mcs0, the calculated resonance). -50 -

voltage — a.IngwaeRatio H 0 Co 0 51:0 0 0r1 Ii I 01% I* AIk S 00S '8

Ptw.23 VJRofWa~tdtoMopo rzwor Lsdvith Nm pole (re soxsut at 2.~81 kmu.. A - no adjustmnt~ B rtuz abort I i i II i —. - i i t I I 0 'I 0 tpr 2.o75 2.76 2.77 2.78 2.79 2.80 2-.81 2.8e Ism-(km.) 2.83 2.,85 2.86 2.w87

4o 20' - ~ i 0.76 0.78 0.80 0.82 0.8 o0.6 OB6 0.92 o.S o.9 0.96 0.98 HMoapole x l*t, h (in.) Fior 2. Optlin Fr~quncy vArd McOle BRo iat 1.00

The ridge impedance at the junction point with the monopole is 33083 ohmso This ridge impedance corresponds to a clearance of.090 inch between the top of the ridge and the top wall of S-band waveguide (2.841" x 1.345" I.D.). Of the two curves shown in Figure 23, curve A was obtained by adjusting the short (terminating the ridge waveguide) for minimum VSWR at the resonant frequency of the monopole, i.e., at 2810 mcs., and then taking the remainder of the data by changing only the frequency. For curve B the position of the short was adjusted at each frequency to yield the minimum VSIR obtainable. The difference in broad-band operating characteristics is quite noticeable: For curve A, there is a 1.64-percent (46 mcso) bandwidth across which the VSWR is less than 1.2. By retuning the short for each frequency, a bandwidth of 3.12 percent (88 mcs.) is obtained for the same VSWR, as shown by curve B. One interesting point to be derived from the VSWR curves is this: Assuming a center frequency of 2o81 kmcso, a - 30 mcso drift in frequency can be tolerated before the radiated power will be down more 0.1 db due to mismatch. Of course this number will have to be doubled to account for a similar mismatch on the receiving end of the system. 4,2-2.2. Minimum VSWR vs. Frequency for Different Lengths of Monopoles. Antenna lengths between 07970 inch and.9760 inch were inserted as radiating elements into the ridge-transformer monopole mount. For each antenna a frequency was determined at which, by varying the position of the ridge-guide short, the VSWR could be minimizedo The radius of each monopole was o045 inch. Figure 24 shows the experimental curve of frequency versus monopole lengtho For each antenna the minimum VSWR obtained was less than 1l03o - 54 -

APPENDIX Calculation of Equation (21) The integral part o a b a 2 2 2 K = dx dy dxf a b a -2 2 2 f Equation (21) is b 2 il denoted by K, namely k2 Yo v b 2 e +Jklr j rI 1r - Fi cos by b since? and ri are on the same transmitting slot and z = z' = zero, hence; K -fjf IC -cs cos (1 1 k e+ jkR R d x dy dx' dy' _ I I I II I II I I[11 IIII I I....... where R x' )2 Since a - e ---- oy2 \ I - + (y - y)2 2" -ft - - Jkl' -? I, Ir - " t ' K -=ff, e+R d osb dx dy dx' dy' -2 J cos b cos a e+JkR b C-T — R dx dy dx' dy' The differentiation involved in the above formula can be removed by integration by parts, for instance in the integral, b b - 4 -I= dyP dy' cos- cos 5 ab a b b - - - - 2 2 -55 -

Consider only the integration with yt, and let u = Cos T and dv = T - dyj; b R dye; then b 2 I = dy cos 2Q b 2,s~) e+JkR y l b 7y R ' yI b 2 b = 2 b + I b - b 2 dy' (in at by +JkER R b 2 I= b 2 dy cos ME b b 2 b 2 -dy sin b e JkR b 8y b b I - dy sin dy eos a b b 2 2 Now consider the integration with respect to y and similarly perform the inteob gration by parts as that done for y'. Hence, b m 2 I= I b 2 cdy sin b +JkR y y b 2 b I " 2 b 2 + 7b dy isin U) R b 2 b b 2 2 I =(b d b b dy (sin -)Tin be R -56 -

Therefore K mj~ '(Os 20& os R dx dy dxVI dy'I I k2 il i&Vs2in ~ (b ff~snb\ b) +R dxdy dx ' dy' K = 1J f Cos 1 (y + y I) + Cos.a (y e+j kR -0 yl) R dx-. dy dx I dy I 1 1 2k2 2? (i) CTff s (y + y '). COB, ( Y ')] R dxL. dy dx I dy'I Now introduce new integration variables:, (y + y') = "'. (x + XI) - v 0-r(y - yt ) - X 7T ( x. xi) = C' T h e n dy dy' I J I-I, dpi dX - (b)2 IT d1L dX,9 where IL,p Xj b b b b b2 similarly dx dx' - 1 2 (-~) 2d der. 7T -057 -

The ranges of integration are shown in Figures 25 and 26. y -l ('it + ), - -0 (nir+ X) b/2..L =('7T-x ) x _ _ _ _ _ _ _ _ - (i - x ) /1 / I17t Figure 25. Range of Integration for ~~ and ). When xgoes from 0tolr i~ ranges from - (?T X) to (7ir- X) When X goes from - 'ir to 0, ~L ranges from - ('it + X) to (7r + X). V = al + a) -*b. alT V =; ('+ ) V (- - a ) a ar V - *I (~ - a ) air Figure 26. Range of Integration for v and a -58 -

When a goes from 0 to-, v ranges from - (- ) to ( - a). When a goes from - 7 to 0, v ranges from - (a + a) to ( + a). Let A =1> + a2, then let f(A) = A exp (jkbA/Tr); then K = () (OS + f(A) dc dX dv da + 2 s - cos x bf(A) d d dv da Due to the symmetry of the integrand, the integrations can be carried out for one quadrant in both Figure 25 and Figure 26. The final result is obtained by multiplying the quadruple integral by sixteeno a7T a7f T-X 7r b a b K= 2 () (dTP) r d. d dvf d cos + cos x f(A) o 0 0 0 7T-X T - Cy=2 2 (7b-) 12 x r dv rj da F1 - cos I ~(A) 0 0 0 o First integrate with respect to 4 and v: b K = 2 ()3 dao (d a - o) dX sin x + (7r-X) cos X f(A) o o0 a7r b T + (77)2 do (a a- o ) fdx Ein - (7r-X) cos X] f(A) 0 0 -59 -

Rearranging the terms, K =3 2b ( ) _ 1 k. 2 7 arT b 0 da a \ do b 7T) 7T d% (1 - X) cos X f(A) 0 a-r b 1 kb 2 7T T — J o 7 dX f(A) sin X o } Equation (21) then.states W = 2 Re 7r K 2 2rr 0 ekb 2k 1 aiT b I da 0 (a b - r 0 dx (1 - ) cos X sin( A) A + kb )2 + a7r b 0 d: (b 7T 0 sin X sin( A) trA I Now use the following approximation: skAkb sin 2 Sin - 2 + kb A /2. ()3 (X2 2) kb)5 22 22 6 + 120 kb )7 (x2 + 2) 3 - -. + Q 0 o 5040 -60 -

Substituting this approximation into the abovre formula, perform the straightf orwardi integration. W= ci 2 k (kb)2 kb) a (-) (-) 2411fj (,2 3LL'5 -m 8) bI)2 x 15 xj-. 4 r2 b14 22 2 (37r - 72r + 432) (-) + (T x 105 (7r6 -_607T4 + 10607tr2 - 5760) b1)6 (. a- 8) (akb) 2 2 + ~(a)4] F1 M. I 724 +2 ( 214qr2 + 144) ab2 2 (-0.-~) + S * 0 I +.. I -J or 8 (ab 2 f1 j.(,2 8) )' +1b274 Kl (-) 1 72n2 + 432)( G)4 K I 1 6. 6c4.w..a- (7T 105 + j0307~- 5 760) (b) 6 27a) 1 2 b2 1 4 2 b 24] I"8) (~) + O-247 + 144) (Qj 4 (24 +525 Kl + if 9

REFERENCES 1. J. A. Stratton, Electromagnetic Theory, McGraw Hill, New York, 1941, p. 29o 2. Jo A. Stratton, Electromagnetic Theory, McGraw Hill, New York, 1941, p. 431o 3. Lo Lewin, Advanced Theory of Wave Guides, Ilissee and Sons, London, 1951, p. 123 4. No Marcuvitz and Lo Bo Felsen, "Slot Coupling of Rectangular and Spherical Waveguides", Journal of Applied Physics, Volo 24, No. 2, June 1953, Po 755 -5o Eo Mo Turner, "Spiral Slot Antenna", Technical Note WCLR-55-8, Wright Air Development Center, Dayton, Ohio, June 1955. 6. Ro Bawer and JO JO Wolfe, "The Spiral Antenna", Institute of Radio Engineers, International Convention Record, Part 1, 1960. 7. JO A. Kaiser, "The Archimedean Two-Wire Spiral Antenna", Institute of Radio Engineers, Professional Group on Antennas and Propagation, May 1960o 80 Bo Mo Schiffman, "A New Class of Broad-Band Microwave 90-Degree Phase Shifters", Institute of Radio Engineers, Professional Group on Microwave Theory and Techniques, April 19580 9o Jo Ho Craven, "A Novel Broad-Band Balun", Institute of Radio Engineers, Professional Group on Microwave Theory and Techniques, November 1960. -62 -