Oct. 1, 1946.- w. P. MAsoN 2,408,435. ' I PIPE ‘ANTENNA AND PRISM Filed March 1', 1941 Jqiql 5.012 6. v .4 I.”?e il?xJib* 3T. $1 A‘ » 5 Sheets-Sheet 1 ‘ .. o M 4%! IIVV NTOR Y WI? ?-JASON >- ‘ AfrbRA/EV a l, 1946. 5 '~ i _ ' I N P_ MASON . PIPE ANTENNA AND PRISM ~ ‘ Filed March 1, 1941 .. _ 2,408,435 I __ I 5 Sheets-Sheet 2 . i' FIG. 6 GIANGLE OFARRIVAL OF WAVE WI!‘H RESPECT TO THE LONG/I'UHMIL AXISOFTHE P/PEANFE/VNA 0i020304050®706090100|l0l20l30l40£50l®l70l€0 0- AM9SoroonI/G0VnLA5w mNraRWoEISnP/0TcCsmH'1. 1 g 9=AUGLE OFARRIVAL 0F WAVE WITH RESFEC 1‘ TO THE LO'VGITUD/NAL AXIS OF THE PIPE'ANTE'NNA ‘IO 29 30 4O 5O 6O 7O 8O 90 I00 "0 12050140 I50 ‘ISOITO IE), I‘: ' - Y ' A/NVENTOR BYWRMASOA/ Oct. 1, 1946. ' 2,408,435 w. P. MASON PI‘PE ANTENNA AND PRISM Filed March 1,. 1941‘ 5 Sheets-Sheet 3 FREQUENCY M000“ T80 ///6 OSCILLATOR ' - INVENTOR » um MASON ATTORNAV‘V _w. P.»MASON Oct. 1, 1946. 2,408,435 PIPE ANTENNA AND PRISM Filed March 1, 1941 RECEIVING ‘ 5 Sheets-Sheet 4 . ANTENNA , ‘I82 [8/4 Maa __ LEE 486 . 5761/4 I R561.‘ 4 Il [Fa/6795C. zsq’géeégnsz $15255. -' RANGES 4? RECZ . \ . )90 ' 192 I94 Fl6‘. I5 12a ,2 ~ I30 4 ' /25 [40 - +1; ‘F’, 91 .L. 204 I'IIlov FIG: /7 . 2 I) / 6 44 /|L__ , ' ‘ ‘"19 - T @a ._L ' FIG. /8 ' iiii‘y“IIIIIIL/ y,lp";y>r?', ,7 4 lllllllll 1101111!!!" III III I //V VIZ-N TOR By W P MASON ~ ATTORNEY . 'p u I Oct. 1, 1946. '_ w. P, MASON 2,40,435 ' 2,468,435 Patented ‘Oct. 1, 19-46 STATES ‘PATENT QFFIQE 2,408,435 ' LIZ ]‘PIPE ANTENNA AND PRISM Orange, N. J ., assignor to Warren P. Mason, West Bell Telephone Laboratories, v‘Incorporated, New York, N. Y., a corporation of New York Application March 1, 1941, Serial No. 381,236 12 Claims. (Cl. 250-‘—.11) 1 This invention relates to new and improved methods and means for directionally radiating . and absorbing wave energy. More particularly, it relates to Wave energy radiating and absorbing methodsand means, the latter being generally 1 . designated hereinafter as “pipe antennas” and 'course'of the following description of preferred illustrativeembodiments and‘ in the appended claims. The-principles of-the', invention will be more 'readily'understood in connection with the accom panyings: in = which: “prisms”- wherein the total potentially useful energy is subdivided at the radiating or absorb ing means into a large number of components of particular predetermined relative phase. Di- > rective effectsare obtained by proportioning the parameters of the system, i. e., the mechanical . and/or electrical dimensions in particular man ners With respect to the frequency, or frequencies, of the energy to be employed. The recombining of the components produces the desired directive Fig. 1». shows, in longitudinal cross-section, a .7 directive antenna: comprising a- hollow pipe vor wave-guide having» a" row ~of ‘ regularly ~spaced ori?ces. along. the upper. side . thereof ; Fig. 2 shows in longitudinal cross-secticna .directiveantenna- comprising a coaxial conduc torpair having a .rowof regularly spaced ori?ces along the upper side thereof and. a short laterally projecting conductona?ixed to‘ the central con ductor and, promoting into the opening of each . phenomena. ‘ori?ce; Forms of particular interest for the invention ber of regularly-spaced ori?ces along them. In amore highly specialized form of the invention the pipe ortube is proportioned, and,.if neces erties of the pipe antennas of the invention; ‘Figs; 4A and 4B are employed in explaining the ‘directional characteristics of antennas of the invention; sary, modi?ed, to constitute a multisection Wave or band (if-frequencies. Provision is then made for radiating or absorbing a portion of the total useful energy at corresponding points of each section of the “?lter” and advantage is taken of the variation of the phaselof the ?lter through out its transmitting region to .afford directive properties which change with frequency. At ultra-high frequencies, energy may be con ducted through the pipe as a Wave-guide. . At lower frequencies conducting elements are placed within the pipe to permit appropriate transmis sion of energy therethrough and in a number of instances auxiliary conducting members having the functions of modifying the impedances and/or increasing the radiation or reception of venergy are also employed. . An object of the invention is therefore the pro vision of novel directive antennas, hereinafter esignated ‘fpipe antennas,” of extremely simple mechanical vconstruction. A further object. is to provide “pipe antennas” or “prisms” operable over a wide range of fre quencies and having highly directive properties which vary as the frequency of the energy em ployedis varied. . . Another object is the provision of highly. direc tive-antennas which include as enclosing. mem bers, simple perforated pipes. Additional ‘objects are the vprovision 'of sys tems for assisting‘in the navigation of mobile craft. ~ , v'Fig.£‘>_sl‘1ows,.in diagrammatic. form, an elec tricarcircuit employed inv explaining the prop usually include pipes or tubes with a large num filter passing a particular predetermined range ‘2 ’ ‘Otherdbjects will‘ become apparent during ‘the 2.13 I"ili'ig. 5 [illustrates a method'of modifying the ‘electrical characteristics and of providing more rigid mechanical support for the-center conduc ‘$01’ of ‘the antenna cfFig'. 2;_ illustrating re ‘*‘Fig.~ ‘6 I comprises three curves sponse versus angle of approach for several pipe antennas of the invention; ' ‘Fig. 7 comprises six curves illustrating re "sponge versus angle of approach for a number of pipe antennas of’ the ‘invention and for various ‘ percentages of 1 power radiated; ."'Fig. 8 shows‘ two pipe antennas of the inven tion arranged to :radiate a pair of lobes directed cat- slightly different vertical angles in a common 5 plane‘to provide an inclined median line of equal ' energies from the 'two antennas .for use in land "ingi ‘ai‘rgraft; -Fig.~ ihshowseight pairs of pipe. antennas, ar ranged radially from a common center, eachcpair ‘being/designed as for the-‘pair shown in Fig. 8, to provide inclined, guiding median energy lines for aircraft, approaching from any azimuth angle; _ Figs. 10 and 11 show hybrid antennas com bining features of the “pipe antenna” with fea 50 tures of prior art dipole antenna arrays; Fig. 12 illustrates a further use of pipe. antennas in a system for guiding aircraft; .> 'Fig.;13. shows in diagrammatic form an elec trical circuit employed in explaining certain fea 55 ‘ tures ofthe. antennasof 1 the (invention; 2,408,435 4 , Fig, 14 illustrates in diagrammatic form a re ceiving system which may be used in direction indicating systems of the invention; Figs. 15 to 17, inclusive, illustrate the elements of the structure will have pressure or voltage re sponse compared to the normal wave of and equivalent electrical circuit of an acoustic antenna designed to employ the principles of the invention; Fig. 18 shows in longitudinal cross-section a wave-guide, band-pass ?lter-type pipe antenna oi:r the invention; 'E'ig. 19 shows curves of attenuation andphase for a “section” of a “?lter-type” pipe antenna of the invention; and I . (1) where n is the number of tubes, 2 the incremental 10 length, and c the velocity of wave propagation. If we insert short electromagnetic waves in each of the tubes, it is obvious that the same form of device can be made to give a directive electro magnetic wave pattern, as in the acoustic case. Fig. 20 shows curves of frequency versus ampli— It is more feasible and economical, however, to tude of reception for beams impinging at differ~ 15 use the general type various forms of which are ent angles upon a pipe antenna. illustrated schematically in Figs. 1, 2, 5 and 18 of the accompanying drawings. Antennas of this In more detail, the illustrative embodiment of’ Fig. 1 comprises 'a directional ultra-high fre general type, characterized by the use of an outer quency radiator which can be constructed from 20 member in the form of a single pipe having a row a simple hollow pipe 0r wave-guide 39, with a row of ori?ces therein, will be referred to herein as. of regularly spaced holes 32, cut in it along a pipe antennas. For such structures, if we start a high frequency wave traveling down a concen straight line. The directivity attainable is 'ap tric conductor (or a wave-guide) 'which'has a row proximately the same as that for a correctly de signed electromagnetic horn of equal length, but 25 of small holes bored in the side, the holes being all considerably smaller in diameter than a wave since only pipe of uniform and relatively small length, then a small amount of energy is radi cross-section is required, the pipe-type radiators ated from each hole and the device radiates en are in general simpler, cheaper, and more con ergy directively' in a manner indicated by Figs. veniently constructed and installed. Also as will appear subsequently variable directive charac 30 4AA and 43, provided the amount of energy radi ated from each hole is approximately the same. teristics may be readily imparted to the pipe an tennas. , ' ' In many cases, it will be desirable to design the pipe antenna so that the direction of greatest propagation is along the longitudinal axis of the pipe or at a small angle with respect thereto; As A resistance termination substantially matching the impedance of the radiating structure is, pref erably, provided at the far end of the structure to absorb the energy which reaches the end of' thetube, so that reflections. of energy maybe disregarded. In order to prove the feasibility of will be demonstrated hereinafter, the angular this method of radiating energy, it is necessary range within which the major part of the radia to show that each hole will radiate the required tion is concentrated is, for a given spacing be amount and that the relative phases of the sev tween holes, inversely proportional to the square 40 eral amounts of this radiation will be correct. ' of the length used. By varying the sizes of the The radiation resistance of a concentric hole holes along the length of the pipe to more favor has been investigated by S. A. Schelkunoff, in an ably control the radiation therefrom, as will be article entitled “Some equivalence theorems of explained at greater length hereinunder, sec electromagnetics and their application to radia ondary lobes can be eliminated to substantially any desired degree. tion problems,” published in the Bell System Technical Journal, January 1936, page 92, who It will also be demonstrated that a concentric conductor, such as is illustrated in Fig. 2, com prising outer pipe 48 having a row of holes 48 ?nds it to be approximately therein and central conductor 42, terminating in resistance ?lm termination 44 and bearing radiating stubs £36 arranged concentrically in the holes 658, can be employed as a pipe antenna. It will be further be shown that by incorporating shunt sections of line short-circuited on the free ends for use with the concentric conductor type of pipe antenna or by using a wave-guide with the proper ratio of diameter to wave-length, pipe 1, 2 k2 log — ~ R=17ri,0(—TLl) ohms (2) where A is the wave-length in centimeters, b is the inside radius of the outer conductor, a the outside radius of the inner conductor, and S is the area of the opening, i. e., 1r(b2-a2). The reactance associated with the hole has not been determined precisely but at low frequencies it will obviously be the fringing capacity between The pipe antenna of this invention is in some respects analogous to the tubular directional the inner conductor and the outer conductor. As long as the diameter of the hole is considerably less than a wave-length this relation will still hold for higher frequencies. Hence for the conductor of Fig. 2, the e?‘ect of the hole will be to shunt the transmission line by a parallel capacitance microphone described in a paper by R. N. Mar and resistance as indicated in Fig. 3. > antennas can be made to radiate wave energy of a predetermined frequency at any particular desired angle with respect to the longitudinal axis. shall and applicant, published in the Journal of the Acoustical Society of America, vol. 10, pages 206 to 215 of January 1939. The microphone there described consists of a number of tubes of varying lengths, consecutive ones being an equal increment of length longer than the adjacent ones as shown in Fig. 2 of the paper. It is shown in the above-mentioned paper ‘that a plane Wave coming at an angle 0 from the longitudinal axis The e?ect of this on the transmission of a single section of pipe antenna can be obtained by solving the network shown in Fig. 3 which con sists of a transmission line 50 or 56 of length U2 and characteristic impedance Zn on either side of the shunt capacitance 54 and resistance 52, where Z is the distance between the centers of two ad J'acent holes. By lumping the shunting imped ances 52 and 54 together as the impedance Zs, ' and writing out the transmission line equations, 2,408,435 5 axis of the pipe, the phase shift inside the pipe in the form shown by Equation 8 of a paper en has to equal that outside the pipe or - titled “Filters and Transformers Using Coaxial and Balanced Transmission Lines,” by applicant wl and R. A. Sykes, Bell System Technical Journal, July 1937, page 2'78, it is readily shown that the relations between the output voltage and cur rent, and input voltage and current, take the cos ?=cos B Solving Equations 5 for this case we ?nd form 00 where A is the attenuation per section in napiers which will be a small quantity. It is readily shown from Equation 1 that if we,’ Wish to radiate in only one direction, the holes‘ ml cos? Z; (3) should be placed closer than half a wave-length of the frequency to be radiated. On the other hand, the nearer to half a wave-length the holes locity of propagation in the tube which is equal are placed the greater will be the directivity. A to that of radio waves in space provided no in termediate dielectric beads supports for the cen 20 useful compromise is to let ter conductor are used within the radiating sec tion. B=£l= 81r C If intermediate supports for the inside con ductor are needed to provide sufficient mechani for which case tan cal rigidity, they are preferably obtained for sin gle frequency or narrow frequency range opera i1 = — .7265 tion, by using short sections of conductor of an where w is 21r times the frequency and c is the ve odd number of quarter wave-lengths in length shunted across the radiating conductor at radi We see then from Equation 6 that the shunt re ating points therealong, the resulting structure actance for equal phase shift outside and inside being similar to those shown in Figs. 43 and 5 30 should be a very high negative or capacitative re actance. This shunting capacity will be the except that where the short sections are em ployed merely for mechanical rigidity one is not usually needed at each radiating point. These short sections are closed and short~circuited at their free ends and since they will introduce only 35 a very high shunting impedance, their effect can be in many instances entirely neglected. From Equations 3 and from conventional elec trical network theory, we may write the image transfer constant and impedance as fringing capacity between the radiating inside electrode and the outsideshield or pipe minus the loss of capacity for the inside conductor caused by cutting the hole. While this can not readily be calculated exactly, the two will usually nearly o?set each other so that Equa tion 6 will be satisfied. If this were not so we wovdd have the anomolous condition of a wave propagation medium with an air dielectric and no attenuation which depends on frequency cosh 0: cosh(A—}-2'B) = which had from waves to be true, by a shunt ‘ cosh A cos B+i sinh A sin B: a different velocity of propagation in free space. When this is not found the excess capacity can be annulled indictance at each section as will be discussed hereinunder. The resistance required by Equation 6 can be obtained at high and ultra— zl= a - Z0 1 Z wl Z0 1 2‘ col high frequencies by adjusting the hole size. An illustrative example of this adjustment is con (4) 1+5 X-l-R>tan Z: 1~§('X+R>CO’G% sidered hereinafter. The directivity formula (1) was obtained by calculating the pressures resulting in the termi I nation ‘when a plane wave at an angle with the axis of the tube‘impinges on the holes. The di rectivity as a radiator can be calculated by as suming that each hole a point source of given Now if a constant size hole is employed through out the length of the radiator the characteristic impedance 2.1 will be constant and no re?ections Will take place in the structure. To produce the strength and phase and calculating the resultant correct radiation it is only necessary to have a given phase and amplitude for plied across the radiating hole. tion of (ii) permits solution for and R required to give a stated phase shift in the tube. ?eld at a distant point at an angle 0 from the axis of the tube. If the point is so distant that all of the lines from the hole to it can be consid ered as subtsantially parallel, the directivity can the voltage ap The ?rst equa the values of X attenuation and be calculated, for example, from the structure of Fig. 4A which represents a pipe antenna of the Solving, we ?nd variety indicated in Fig, 2, parallel rays 60, 62 . ml and 611 being emitted at an angle 0 with respect to the longitudinal axis of the pipe from the ?rst S111 —— three holes at the left end. The ?rst source or hole will put out a wave Aiei‘di which after trav 2 cosh A cos B-cos 3;! eling‘ a distance D will have the relative value and 10 sin w——l _£@ ___c__ R_ 2 sinh A sin B Aleiw t6 (5) Now if we wish to radiate directly along the 75 in’ 0 ~ , <7) The second-hole will have a strength and phase with respect to the ?rst ‘one equal to Azew‘i'B), 2,408,455 and will arrive at the distant point with a rela about 14 decibels down from the fundamental. For some purposes this may be undesirable. It tive strength and phase —l‘3(D—Z cos 0) A2ei(wt—B)e c has been shown in Patent 2,225,312, issued to ap plicant on December 17, 1940, that, for a plural (3) ity of radiators, if we vary the amount of radia Similar expressions may obviously be derived for tion from radiator to radiator, the secondary the other holes. The sum total of the ?eld at the distant point will then be lobes can be reduced at the expense of a slight amount of sharpness for the fundamental lobe. If, for example, we have n radiators all different 10 in phase by equal steps, and arrange the amount of radiation from them according to the series —i—w(D—nl cos 9) c If the energy radiation from each of the holes is +Anei(wt—nB)e -. substantially the same, this series is a geometri cal progression whose sum is 15 [1_6—m(B-—3cZ 0050)] [Meagan] (10> this will be recognized as the square of a series The absolute value of the ratio of this ?eld to the ?eld along the axis (when 0:0) will then be with equal radiation from half the number of holes. The absolute value of the summation will be _E_g=l sin n4: E; . n sin¢ where 95: T n 2 (11) B74765) sin ¢ If the phase shift inside the pipe or tube 44 is equal to that outside, i. e. 11 0 this relation reduces to Equation 1. A plot of Equation 1 when 30 (14) The result would be to make the ?rst secondary lobe down about 27 decibels with respect to the primary lobe. If we carried the process farther and made the successive strength of the radiation from the holes vary according to the fourth power equation and n is 50 is shown in Fig. 6, curve 66. Prac tically all of the energy is con?ned in a cone 10 degrees from the longitudinal axis. For a wave length of 10 centimeters this would require a 40 the effect would be to reduce the secondary lobes pipe 2 meters or 6 feet long. If we make the with respect to the primary one by four times the number n=200 and use a tube 8 meters (or 24 number of decibels. Fig. 6, curve 10, shows the feet) long, practically all the energy will be con e?ect of a ZOO-hole radiator on this basis as com ?ned in a cone of angle 5 degrees. The angle of pared to a 200-hole radiator 0n the equal power the cone, for small angles, becomes inversely as basis, Fig. 6, curve 68. The primary lobe is not the square of the length. To con?ne the radiation quite as sharp but the secondary lobes are great within a 2.5 degree angle would require a 100 ly reduced. ' foot pipe antenna. This process could be applied exactly to the We have calculated the radiation on the as type of radiator discussed here by varying the sumption that all holes radiate equally. Actu sizes of the radiating h'oles provided we placed ally, if we keep the hole size constant down the resistances in parallel to make each total resist length of the tube, the radiation from each hole ance the same. Then the characteristic imped~ will decrease in strength by a factor e—A, where A ance would be the same for all sections of the is the attenuation in napiers between each hole. The effect of this modi?cation is readily taken 55 equivalent network of the antenna, no re?ections would occur, and the successive radiation account of in Equation 9 and the result is strengths would be in the required ratio. This process is objectionable, however, on the grounds Eg_\/ cosh A-—l )(cosh nA—-cos 2n¢ (12) of complexity and loss of radiated power. It can F0_ (cosh nA-l cosh A-cos 2¢> be applied, however, with substantial exactitude A plot of this equation is shown in Fig. 7 assum 60 and without objectionable complexity for it can ing a ?fty-hole tube for the conditions 50 per be sh'own that the effect of the reflections is to cent, 75 per cent and 90 per cent of the input change the phases of the voltages applied to the energy radiated by the pipe, curves 82, 89 and ‘I8, radiating resistances by small and progressive amounts so that the directivity is not substan the characteristic is to decrease the separation 65 tially impaired. From Equation 4 since X is very between the low points and thehigh points. A large and the ratio Zo/2R is very small, the char slight loss of discrimination against the second acteristic impedance of a section becomes ary peaks is also experienced, amounting to .1 decibel for 50 per cent power radiation, .5 decibel for 75 per cent and 1.4 decibels for 90 per cent 70 respectively. As can be seen, the main effect on power radiation. It appears desirable, therefore, to keep the radiation at substantially 75 per cent of the input power. All of the directional characteristics shown ‘have secondary lobes the nearest of which is 75 2,408,435 9 where Am is the attenuation caused by the mth hole, since _. S11] 10 diameter to wave-length of the correct value, the phase shift inside can be made any desired ratio to that outside. Other effects obtainable with radiators having wave-?lter structure incorpo rated therein will be described hereinafter. An airplane landing beacon using ultra-short 60 0 will be nearly unity. waves and electromagnetic horns was described in a paper by W. L. Barrow in the Journal of Suppose that we arrange the resistance values the Institute of Radio Engineers, January 1939, This landing system consisted of two electromagnetic horn radiators to produce two in such a way th'at 10 page 41. beams ‘making an angle 61 and 02 from the ground. The two beams have the same carrier frequency but slightly different signal frequen cies. An airplane coming down at an angle where n is the total number of radiating holes. The total attenuation down the tube, will be the sum of the individual attenuations or (18) 20 hears equal strength from both beams and hence If we radiate three-fourths of the power A=.691 napier. For a 50-hole radiator, A1 will be .00106. Since there is a change in the characteristic im pedance in going from one section to the next, there will be a ?rst order current re?ection equal for the mth hole (m<n/2) to (19) When m>n/2 the sign of the re?ected current will be reversed. The phases of the re?ected currents will be disturbed randomly with respect to each other, so that the sum total of all the currents will not add up to more than several times that of any single re?ection. Hence the re?ected current will be only in the order of 1/1000 of the transmitted current and hence will not a?ect the strength or phase of the original radiation suniciently to produce any measurable change. Another radiation characteristic of some in terest is one in which the maximum radiation ccurs at an angle 9 from the axis of the tube. This can easily be obtained with the device by making the phase shift inside the tube somewhat smaller for the same frequency than it is outside the tube. From Equation 10 or 11 We readily see that if B=9cl cos 60 ‘(20) the maximum reception will occur at the angle 0. The directivity pattern will be the same as shown in Fig. 6 with 00 taken as the zero angle. In order to get the phase shift B smaller than col 6 it is necessary to shunt the section with positive reaction as shown by Equation 5 which gives the value necessary for a given value of B, As shown by Fig. 5, this can be done by putting on shunt ing short-circuited sections of line 45 of the proper length and impedance to give the react ance X desired, This, in effect, makes a high pass filter out of the transmission line. is able to control its landing angle, The diffi culty with the system is that in order to obtain a narrow enough beam, even for a 10-centimeter wave, the length of the two horns becomes exces sive, and since they are above ground they are likely to cause damage or to be damaged when the airplane lands. The pipe type radiators of this invention can be arranged in such a landing system so as to eliminate these dif?culties. For example, in Fig. 8 are shown schematically two long pipe radia tors S8 and 92, similar to that shown in Fig. 5, placed flat on the ground (they may be set in concrete for protection), one of which is pro portioned to radiate at an angle 01, and the other at an angle 02. This can, of course, be accomplished as explained above. Since the best airplane landing angle is about 2.5 degrees, it appears that one radiator should radiate at an angle of 01:0 or directly along the ground, while the other one should radiate at about 62:55 degrees. In order to concentrate most of the beam in a 2.5 degree angle it requires, as above explained, a pipe radiator with 800 holes, 100 feet long, assuming a lil-centimeter wave is used. For any other wave-length, the size would be in proportion to the wave-length. The 5 degree angle beam can be obtained either by using shunt short-circuited sections of line as in the struc ture of Fig. 5, or alternatively, a wave-guide of the correct ratio of outside diameter to wave length as in the structure of Fig. 1 may be used. If it is desired to send these beams out in a large number of directions, so that an airplane can land from substantially any direction, a cir cular arrangement of a number of these paired pipes, in parallel, can be used as, for example, is indicated in Fig. 9. On the other hand, if two-plane beams are desired, it is necessary to electrically connect a number of these radiators, placed in parallel positions-together, arranged so that they are an integral number oi‘ electrical wave-lengths apart. Since in all such arrangements all the radiators can be placed parallel to the earth, they can be imbedded in concrete and the aircraft can land on them without injury to the radiating system or to the aircraft. The same eiiect can be obtained more easily By way of example, an approximate calcula 70 and effectively, particularly at high and ultra tion of the constants of one of these radiators is high frequencies, by using a wave-guide of the given below for a ill-centimeter wave-length. proper ratio of diameter-to wave-length to pro Assuming that all of the holes are to be equal duce the desired phase shift. This follows from radiators, and that the radiator radiates three— the fact that the wave-guide is inherently a high fourths of the power, the ratio of the radia pass wave ?lter and by choosing the ratio of 2,4=0.8, 43 5 . 11]. tion resistance to the characteristic impedance holesfor radiating surfaces will not be satisfac- ' ' of the pipe antenna must be R=578Z0 (21) If Z0 is taken as 80 ohms, in’order to obtain an optimum line, we ?nd b; < 9) log tory for use with wave-lengths substantially longer than 10 centimeters, because the radia tion resistance of the holes will be found to be Cl objectionably high. For longer wave-lengths, however, it is easily possible to employ analogous radiating structures which inherently provide more radiation and hence have lower radiation resistance. Fig. 10 (22) 10 shows one such arrangement which consists of where b is the radius of the hole and a is the radius of the stub conductor centered in the hole. This is satis?ed by quite a range of ratios conductors S4 and 95 and shield 98 with half wave or shorter pairs of radiating conductors a =1.59 balanced and shielded transmission lines having I00 connected at regular intervals along the two conductors 94 and 96, respectively, and extending through shield 98. The conductors $4 and 98 are insulated from each other and from the shield 98 and the radiating conductors I [it] each connect b a for example by b=1 centimeter; a=.22 centi to one of the conductors st or 96 only and extend through holes in shield 93 without making con tact therewith. Since the radiating pairs or On the other hand, if it is desired to eliminate doublets can be made half-wave radiators they some of the secondary lobes, by having the suc— can be proportioned to introduce low resistances cessive radiation resistances vary according to and substantially no reactance in shunt with the Equation 17 the lowest resistance which corre sponds to ROI/2), will be half the value shown by 25 line. By making the angle between the two members Equation 21. This is satis?ed by making b=1 of such a doublet small, the radiation resistance centimeter; a=.3845 centimeter. The highest re can be made large, while if the angle between the sistance will be 400 times this value. This can be met by letting b=.25 centimeter; a=.059 centi- 9 members of the doublet is made 130 degrees, the meter. , meter so thatthe entire range can be met with practicable values. A smaller range of hole sizes would result if resistance will be'minimum. . Thus by gradually changing the angle between would be much higher. If this method were em the members of successive pairs of radiating members, as indicated in Fig. 10, where the ra diating members of the several pairs are sub stantially parallel at the ends of the structure and substantially 180 degrees from each other at the center thereof, secondary lobes may be ployed it would be possible in many instances to substantially reduced in magnitude relative to the the inside stub conductors were not brought out to the outside shield but only extended part way to it. In this case the ?eld outside would be con siderably less and hence the radiation resistance let the hole size remain constant for the whole length of the antenna. In order to get the second radiator to radiate at an angle of 5 degrees it is necessary to shunt a positive reactance +:i57.5Z0 across each radiat ing hole. If the shunt line has the same charac teristic impedance as the main conducting tube, this, requires a short~circuited line whose phase angle is 89 degrees at the radiating frequency, since the impedance of a short-circuited line is . + 1Z0 tan Z and the value of the tangent will be 57.5 when main lobe. The effect, is of course, analogous to that de scribed above for the case of‘ simple perforated pipe-type radiators where it was demonstrated that minor lobes can be suppressed by tapering the size, and consequently the radiation resist ' ance, of the successive radiating holes along the pipe in accordance with relations such as are set forth in Equations 13 and 15 above. As for the simple pipe radiators, the far end of the trans mission line should be terminated inva resistance 93 which substantially matches its impedance. By using combinations of this type the princi ples described above for pipe antennas can be applied for use with systems operating at much longer wave-lengths. 21 (V corresponds to a phase shift of 89 degrees. The only quantity not determined is the di ameter of the transmission tube. In order to make the power radiated large compared to that lost in transmission we should make the tube diameter large. On the other hand, if itis made too large some of the more complicated wave A similar arrangement is shown in Fig. 11 and comprises two concentric lines having outer con ductors I 02, inner conductors Hi4 and resistive terminations 506, the radiating elements I00 be ing connected at regular intervals along each of the two inner conductors 1M and extending through holes. in the outer conductors 562 as shown. .The radiating elements can be paired and proportioned as half-wave doublet radiators. Obviously the angles between successive pairs of radiators may be varied as illustrated for the structure of Fig. 10, if desired. The particular advantages of these arrangements will be de shapes of the wave-guide will be transmitted which may, in some instances, be objectionable. If the inside diameter of the outer tube is taken as 5 centimeters, or nearly 2 inches, nothing but scribed in detail hereinunder. plane waves will be transmitted and the attenu Such arrangements radiate in only one direc ation down the 100-foot pipe at 10 centimeters 70 tion and can be combined as units in more com will be .7 decibel and for the case considered here plicated antenna arrays, such as the well-known 70 per cent of the power input will still be radi MUSA systems. ated. Viewed more broadly, the wave-?lter pipe an In many instances it will be found that a simple pipe-type electromagnetic radiator with 75 tennas of this invention may be considered to be a new form of prism. They are, of “course, appli a: k 2,408,435 13 14 the surrounding space, which occurs when the frequency is the anti-resonant frequency, or cable to electromagnetic waves, to sound and su peraudible acoustic waves and even to heat or any other type of radiant energy. Calculations are given below to illustrate this broader view and to demonstrate the angle sensitivity and an gle change as a function of the dimensions of the radiating structure and the frequency of the radiant energy. For wave-lengths in the neighborhood of 10 mid-band frequency in, the radiation occursdi rectly along the axis of the tube. It the phase shift between holes at this fre quency is 180 degrees, which is the most» advan tageous condition, the radiation will also occur directly along the tube in the reverse direction at this frequency, as shown by Equation 31. As the frequency is further increased, all or 10 centimeters, and for shorter-wave-lengths, the the radiation will be directed toward the genera electromagnetic prism consists, in one form (the essential mechanical features of which when ap tor at an angle 0 from the axis which increases with increasing frequency, till at the upper cut off the radiation is again perpendicular to the propriately proportioned are similarto-those for the radiator illustrated by Fig.’ 5) of a concentric line with short-circuited sections of a similar line spaced at less than half a wave-length of the anti-resonant frequency of‘the latter sections and axis of the tube. , The frequency band over which these changes occur can be regulated by regulating the width of the transmission band of the wave-?lter pipe connected as shunt'circuits across the ?rst-men system. tioned concentric line. In “parallel with” the shunt sections are small holes for radiating from each hole a portion of the energy of the electro magnetic waves, being transmitted along the ?rst-mentioned line, into the surrounding re gion. The construction and calculations are very similar to those given above where we were con sidering the structure simply as a single—fre If it is desired to keep this range small, the shunting elements should have a low impedance for then the band widths are small. These rela tions are discussed hereinafter. Such a device constitutes a good marker beacon for use in aircraft navigation since a‘plane at some distance from the beacon will receive a quency pipe-type directional electromagnetic ra diator. The shunting, short-circuited sections connected across the main conducting line are in this instance, however, proportioned in accord ance with principles well known in the art, for examplev see the above-mentioned paper .by ap certain frequency the value of which is indicative of its angular direction from the beacon. By ?ying a course which causes the received fre quency to increase most rapidly, the planev will pass over the beacon. A still better beacon from which more information can be obtained is the combination of two such devices at right angles plicant and R. A. Sykes, to constitute an electro to each other in a horizontal plane, as indicated magnetic wave ?lter. in Fig. 12. The devices can be two identical As will appear presently, in the majority of 35 radiators H0 and ill with the applied fre filter is preferably of the ? applications this wave quencies generated in the wide band frequency band-pass (rather than the high-pass) type and oscillator H6 modulated at different rates by "' 'the filter so constituted should have as many sections as there are shunting elements. modulators H2 and H4 so that the signals from the two beacons can be readily distinguished, or, v In aband-pass wave ?lter, including those of the above indicated type, the lower cut-off fre quency is somewhat below the anti-resonant fre quency of the shunting sections of line as is at alternatively, they can be proportioned to oper ate in different frequency ranges, the single os cillator sweeping the combined ranges of the two radiators. Numerous other similar arrange ments of this character will readily occur to those skilled in the art. In the system of Fig. 12, since the aircraft pilot can tell the angle of the craft from the positive direction of both radiators, he can locate its ab solute angle and approximate position with re spect to the beacon. If, in addition, the altitude once apparent from elementary wave ?lter the ory, since the shunt arms of a band-pass wave ?lter are anti-resonant at the mid-frequency of the band. Similarly, the upper cut-off frequency is somewhat above the above-mentioned anti-res onant frequency; At the lower cut-off frequency the phase shift between adjacent sections is zero so that the en ergy radiated from all of the holes will be in phase. Consequently, a narrow radiated beam will be sent out in a plane which is perpendicular to the axis of the antenna. As the frequency is raised, there will be a phase diiference o between is known from barometric pressure or an alti respect to’ meter, the distance and position with the earth and the beacon can be completely de termined. Such a system of cross radiators can also be used to produce a glide path landing beam. When the plane receives equal frequencies from the two radiators, assuming identical radiators energy emanating from successive radiating holes. If 31 V is the phase shift in the surrounding air between succeeding holes, the angle of radiation from the axis of the pipe along the direction of 60 propagation, is given by cos 6-1552 if e< 180 (31) V are being used, it is on a path running through the center of the beacon at an angle of 45 degrees with respect to each of the radiators. If the fre quencies are below the mid-band frequency of radiation, it will be approaching in the positive direction, whereas if the frequencies are above the mid-band it will be approaching in the nega tive direction. If the frequencies correspond to the 45-degree radiation, the glide path Will be directly along the ground, while if the. frequencies correspond to a radiation angle of a given by and cos 0=(£—;3—l@i)< if ¢>180 (32) V When the'phase shift in the ?lter is the same 75 as the phase shift between the radiating holes in Equation 33, below, the glide path willbe at an angle of on with respect to the ground, cos 45° cos. a =————— q/l-l-SiIFQ . (33') 2,408,435 15 " In order to make the system moresensitive to‘ the landing angle 0, the landing radiators can be tipped with respect to the horizontal. This can be done by mounting the radiators on ya tilt ing platform of light weight Which will prefer ably swing down to a level position in .the event that the airplane lands on it. ‘ In instances where wave-lengths considerably longer than 10 centimeters are to be used, the 16 ' the cup I24 vibrates in the manner of a circular plate, or diaphragm, in flexure clamped around its periphery, when a di?erence of pressure oc ours on the two sides. The equivalent circuit of the structure is as shown on Fig. 17. The series resonant circuit M2, lM‘represents the reaction of the clamped diaphragm, while the transmission lines I40, I 46 represent the propagation of the acoustic wave in the cup cavities. The combination can, obvi ously, readily be proportioned to be a band-pass ?lter, the dimensions and width of the pass-band of which can be adjusted and controlled by mak ing the diaphragm thicker or thinner, as discussed above, can conveniently be used. . For the glide path beacons discussed above the 15 hereinafter. By providing small holes or ori?ces I28, Figs. 15 and 16, in each section of the ?lter so balanced construction of Fig. 11 is preferably used formed, a speci?ed amount of energy can be radi so that horizontal or vertical doublets can be used ated from each of the sections, and the opera to radiate the energy. By reducing the over-all dimensions of the doublet pairs, the resistance of 20 tion will, obviously, be similar to the electromag netic prisms described above. The energy which each pair can be reduced until the desired resist gets through the last ?lter section is absorbed ance is obtained. The reactances introduced, by a terminating resistance or energy absorbing which will be capacitative if the doublets are less member I26, as is also recommended for the elec than half a wave-length, can be incorporated with tromagnetic prisms, in order that substantially short-circuited line sections, added in shunt in radiation resistance of the holes per se is, as stated above, too large to permit the radiations of the required amount of energy from each; In such instances the constructions of the general type illustrated by Figs. 10 and 11 and described the same manner as for the structure of Fig. 5, to produce an anti-resonance at the correct fre quency. The same fundamental principles can be read ily applied in the construction of acoustic prisms , for use in ?lters, in frequency division systems, and such systems as those employed for the acoustic viewing of obstacles, etc., through sea water. Prisms constructed in accordance with the principles of this invention will in general have advantages over the prisms of the prior art in that the frequency ranges of radiation can be adjusted by adjusting the dimensions, the losses in the transmission ranges are considerably smaller, and a greater angle of sweep can be no reflections from the far end will occur. In the acoustic case, it is frequently desirable to employ the device for submarine detection, the location of submerged objects and for similar pur poses. For such purposes the prism may be im mersed in the water and the cups are then per mitted to ?ll with water. By way of example, for a prism to be employed submerged in sea water and to operate over a band of frequencies centered about the frequency of 55 kilocycles each cup should have an internal radius of .54 centi meter, an over-all length of 1.204 centimeters and a diaphragm .109 centimeter thick. The side walls of the cup should be at least .25 centimeter thick. These dimensions assume that the ma terial of which the cup is made is brass. The obtained when desired, with a given frequency change. ori?ce should be centrally located with respect to A simple structure for one form of acoustic or the cavity and should be about .25 centimeter in diameter. Such a structure will have a band width of 22,000 cycles. compressional wave-energy prism of the inven tion is indicated in Figs. 15 and 16. The speci?c form of prism illustrated by Figs. 15 and 16 con sists of a pipe with transverse diaphragms and intermediate ori?ces regularly spaced therealong. As a matter of convenience in manufacture the pipe may be an assembly of a series of cup-shaped 0 members I24, a single cup being shown in detail ' in Fig. 15 with a portion broken away to expose the interior. A number of the cups (at least twenty-?ve should be used for the majority of The equivalent circuit of the pipe-type electro magnetic prism illustrated by Fig. 5 when propor tioned to have band-pass ?lter properties is that shown in Fig. 13. Inductance I52, resistance I53 and capacity I54 represent the shunting im pedance including the stub lines 49 of Fig. 5 and I50 and I56 represent lengths of the concentric line between shunting points. The equations for this circuit are applications) are arranged coaxially in arow as shown in Fig. 16 with the bottom of one cup firmly pressed against the top or rim of the ad iacent cup. Any convenient external clamping means vhich does not interfere with the driving mech tnism or with radiation from the ori?ces may 1e employed to clamp the cups in a row as indi Iated. Since any mechanic can, obviously, read ly devise a suitable clamping means none has ieen shown in Fig. 16 as it would unnecessarily omplicate the drawings. Each cup is provided with an orifice I28 to perlit the radiation of an appropriate amount of nergy and a piezo-electric crystal or similar type f driving element I32 is pressed against the in ut end of the acoustic transmission line so )rmed. At the far end a member I26, designed L accordance with principles well known in the ft to absorb any residual sound energy reaching , is provided. The thin part or bottom I30 of where Z5 is the total shunting impedance be tween lines, i. e. the combined impedance of ele ments I52, I53 and I54, Fig. 13, Zn and V are the characteristic impedance and velocity of propa gation of the coaxial conductor, respectively, and I l is the distance between shunting points. From these equations, the propagation constant and the characteristic impedance can be written as 70 cosh P=cosh( A+jB) = cosh A cos B+j sinh A sin B=cos l-é-I 75 LZO Fin %’ e <36) 2,408,435 17 18 where we is the‘ resonance frequency of the series resonant circuit. Neglecting the radiation re em £é+ Z0 $122211? Z1=Z0 sistance, the cut-0T1c frequencies and characteris ’ (37) 1 tic impedances are given by 2V The shunting impedance in this case will consist of the short-circuited line shunted by the high radiation resistance R (I53 of Fig. 13) , so that . coll JZMR tan '7' 10 . m2 Sill . w S1112 5- v i where Z01 and Z1 are the characteristic impedance and effective length of the short-circuited line. 15 For the case .of greatest interest which occurs when the resonant frequency w“ occurs at the 180 Inserting these values we have A sin '7' = cosh A cos B: cos 5%;4- 2Z01 OJ tan T,- degree phase shift point, the cut-oii frequencies and characteristic impedance at the mid-band C (39) frequency are given by 20 K (52) If we neglect the radiation resistance R, the lower and upper cut-off frequencies are given by solv 25 ing the equation _ (OZ col1___Z_0_ tan W tan T,- -— Z01 I cot .‘ii 2V tan aV —— _a Z01 If we let (41) col 2wC0Z0 Sm if 30 (53) (42) 1 e12 If ,I for example, we let =5?’ sin ‘27L wCJ’Z: case-29%. 9l___.2.<°7'i V V (54) 35 the phase and attenuation characteristics are given by Equations 45 and 46. The directivity of the electromagnetic radiat ing prism can be calculated by employing Fig. 4B. ‘To calculate the ?eld strength at a point which represents a most useful case because it gives a symmetrical frequency angle curve, the lower and upper cut-offs are, respectively, (43) 4:0 P situated a distance ‘L measured along the axis from the center of the tube and, a distance a: perpendicular to it, the ?eld strength at the point P due to the energy radiated from the mid die hole is Taking account of the radiation resistance, the 45 phase shift and attenuation per section are given by the equations E: Eoe'iivl") 10 "_ i (55) where E0 is the ?eld strength near the radiating 50 ho1e, lo the distance from the hole to the point P and V the velocity of propagation. The next hole will have a ?eld strength 55 where the negative sign is used outside the pass band and the positive sign inside the pass band - with respect to the ?rst where A is the atten uation of one section, and B the phase shift. Similarly for the other holes. The sum total of all of the radiations from all the holes will he for sin B and vice versa for sinh A. As an exam ple, we take the case where 1 V V (57) or there is 180 degrees phase shift between radia tion points at the anti-resonant frequency of the side branch. The value of Zia/Z01 is taken as 20, 65 and the radiation resistance R is taken as 50 Zn. Then the phase shift and attenuation per section are as shown in Fig. 19, curves I60 and “52, Zo=R=\/L2+$2,l1=\/(L-Z)2+$2yL1=\/(L+Z)2+x2, etc. respectively. Solving the acoustic case represented by Figs. 70 where Z is the distance between radiation holes. 15 to 17, inclusive, in a similar manner we ?nd "13.? (1@002“ “2) cos2 ml (47) 2,408,435 19 29 upper cut-0T1“, the beam will go from 9:180 de Now if R is large vcompared to half the length of grees to 0:90 degrees. If we select certain an gles, say 0:45 degrees and 5 degrees, it is a mat the radiating prism, we can write ter of interest to ?nd out the frequency spectrum received at that angle. By inserting the value of 13 versus frequency given by curve l?ll of Fig. where 0 is the angle between the axis of the ra diation and a line from the center of the radiator to the point P. Similarly, 19;_ and assuming-that half the power input is radiated, the frequency spectrum received is shown rby curve use of Fig. 20 for a radiator 25 10 wave-lengths long. The solid curve its shows the decibels down from the maximum received \ signal, as a function of frequency. The solid curve is for 6:45 degrees. As can be seen, the maximum is rather broad. but the ?rst minimums 15 are very narrow and‘ can be accurately placed. If, for example, the spectrum received is exam ined by using a frequency modulated oscillator and a narrow band ?lter, the two minima on either side of the principal maximum can be ac 20 curately located and the angle from the radiator determined within a small fraction of a degree. Such a receiving ‘system is shown in Fig. 14. It consists of a ‘equency modulated oscillator Hill whose frequency range is suf?cient to cover the 25 maximum and at least the two minima on either side. The control of this oscillator is geared to one pair of de?ecting plates of a cathode ray tube I88 through a, slope circuit i92'and recti?er we, so- that the spot sweeps across the tube in 30 accordance with the frequency of the oscillator. Oscillator I96 also modulates the output of the antenna H32 in modulator I80 and the resulting The terms of Equation 5'? then take the form modulation is sent through a low-pass ?lter I84 whose frequency range is smaller than the fre quency breadth of the minima of the curve. The output is recti?ed in recti?er H86 and put on the other pair of de?ecting plates of the cathode (63) ray tube. The ray of the tube then will trace a pattern of the frequency versus amplitude curve which is a geometrical progression having the sum 40 . of the spectrum received. By varying the range of the frequency modulated oscillator let, the ac curacy of the frequency determination can be varied. A wide range is usually used in locating the maximum and then the range is narrowed to more accurately locate the two minima. Increasing the number of wave-lengths in the over-all length of the radiator will cut down the frequency separation {between the two minima in. proportion to the number of wave-lengths. How 50 ever, it appears unnecessary to go to a radiator We desire to know the absolute value‘ of this equation since the relative phases are not of im portance for this application. Taking the abso lute value of Equation 54.- we ?nd larger than 25 wave-lengths for this purpose since by using the minima the angle can be located with great accuracy. In fact, a radiator shorter than 25 wave-lengths can be used and hence it appears entirely feasible to use such a system with wave-lengths as long as 50 centimeters. The dash curve £56 of Fig. 20 shows that when the angle between the :axis of the radiator and" the line of‘ direction of the signal becomes small the ac sin2 g-l- sinh2 22 curacy of location also becomes smaller. In order to determine the dimensions of the From an inspection of the equation we see that acoustic prism of Fig. 16, it is necessary to calcu the maximum radiation will occur when B=0 or late the value of the series mechanical impedance 211'. For these values of the clamped diaphragm which is acted upon on both sides by a plane wave. The following meth~ cos 0= where m=0 or 1 (67) 65 od may be followed to determine this impedance. The equations of motion of a diaphragm in V simple harmonic motion are given by Rayleigh’s Hence, at the lower frequency cut-off the beam Theory of Sound, vol. I, chapter Equation 8, will be radiated perpendicularly to the axis. As the frequency increases, the angle 0 decreases un 70 in the form til at mid-band with 13:11", the radiation will oc 2ph (68) lETl—' IE1 R 1 (so) cur along the axis of the tube in the direction of propagation. Simultaneously, it will also occur in the opposite direction since 1r=21r/1r=—1. As the frequency increases from mid-band to the where 2,408,435 E=Young’s 21 modulus - -f the material, 2-72. is the for most practical cases. Introducing these con thickness of the plate, a’ is Poisson’s ratio, .p is ditions we have ' the density, or is 21r times the frequency f, and (pi-p2) is the resultant of the pressures applied A=._B_2 5 to the two sides of the diaphragm. In this case _... _. 2PM’ we assume plane Waves on the two sides so that (1+coshvrél)(l__cos\/_‘iz)_sin\/%lSinh J}? ' p=p1-pz will not vary across the diaphragm. For this case, motion can only occur in one direction, 2(1__ 008 v 31 cosh 331) the 1:, so that » vhjé a. . a 74 1o ( ) fbraé Hence the equation to solve becomes 64W B=§7J%;2 ‘ . 554T — w2W- -§%%=0 " _ (69) 15 sin %l<cosh‘/%l— 1) + sinh\/%l(cos\/%l— 1) W ‘in this equation "is the displacement perpen- 2<1_ dicular to the plane of the diaphragm. _ 21 00s h 11 cos a This equation is solved by letting ‘(75) W=A cosh azv+B sinh wail-C cos Bsc-‘i-D sin 20 C=mzl52 Upon differentiating this equation and substituting in Equation 69 we ?nd that Equation '70 is a solution provided 5 E . S . 5 (1 + C05 110(1 '- °°Bh'\/‘,;l) “F BMW/'51 SmhJ'51 Mfr/f; I; ' 5 2 - 2<1——-cus El ‘coshJ-j) This gives W A cosh f2 . w c ‘w Y ax+Bs1nh 7150+ 00S x/Ew-l- (77) D sin J31? 2-213 v(72) 35 Introducing these values into the expression for a’ P ‘*’ W we obtain 2‘: Costa/é —% sinx/Zi Q2- sinhJg T; cow/3i p WC'QTe) [sin 2 l coshr\/—ztc+sinh'\/j-, l cos 1/2 in] 7 a 2 a a 2 1——cos x/j-lw cosh'\/:la, a ‘ (78) a '1 a We are interested in the average displacement over the surface which can be obtained by in tegrating W with respect to X and dividing by the interval 1. This gives To evaluate the constants A, B, C and D we let so Now the series impedance introduced by the clamped diaphragm is given by W==0 at X=O and X=l xW 65 where W is the velocity, which for simple har monic motion is given by W=§iwW. We have which, though they are the conditions for ‘a bar then that the series impedance introduced by the clamped at both ends, are valid for a diaphragm diaphragm is 2,408,485 23 24 We note that at the resonant frequency of the . _ and that the prism ‘is immersed in Water having diaphragm, the impedance Z becomes zero as it a Zn of 1.5><105 ohms per square centimeter. should. The ?rst resonant frequency is obmined when Then introducing these values and noting that fR=\/.f1f2=866 kilocycles, we ?nd that wt _ _(4-73004)2a -- VFLLLROM °r ‘m’ Zt==.03645 centimeter=143 mils; 5 Ii (82) z=_.2v2 centimeter-:10’? mils (93) To obtain the impedance of the clamped dia- At the resonance in the water should be a half frequency wave-length so that thecolumn depth 1°- of the cavity in each cup should be phragm near the resonant frequency we let A 21 Jwe(1+;-R) w=(wR+A)’ then “J; = --T a 15:.0865 centimetei~=3i mils l: A A J “( 2“ 15 given by Equation 52 2% we <94) The characteristic impedance of this prism is K:-1-'1%>—<—1-9i-=1.01><105 Introducing this value in Equation 81 and ex- (95) 1+? 5:353 panding means of the of multiple angle formulae We ?nd tobythe ?rst power A _ This is nearly the same as water and can easily mFA ' ——_7'25hwR(c0sh in sin m-cos m sinh 110-27,; ' 2(cosh 1%” sin g—sinh g!’ cos ;L')(sin g2’ sinh m+sinh 32-1 sin m) where m==4.'73004. Introducing the numerical values we ?nd. " be matched by the driving or driven crystal. Should air or some other ?uid medium fill and 30 surround the radiator a di?erent characteristic 1 076 Z=j(2phom)( ' “R A>=j(1_076)(2ph)A (g5) impedance (Z0) corresponding the particular medium, would of course be to employed in the This impedance corresponds to the impedance above calculatlons' of a series resonant circuit in the neighborhood of the resonant frequency ’ which is _ 50 or more wave-lengths long depending upon the degree of directivity desired as explained _ 40 above for similar structures. or small frequency dl?el‘ences from “R, thls becomes 2D ‘ __~ __ _ is employed as a wave-guide in the order of 10 to m2 (86) . _ 35 tion of 18 thewhere principles of conducting the invention is shown in Fig. pipe of material 200 [1__w____1:2] F _ , A further styuqiure exempllfymg ‘the _apphca" =- ultra-high Z?JwRL0<¢°R> JZAL“ This wave-guide has been converted, in accordance with principles known in the art, into a band-pass ?lter a1 (87) frequencies by placing crosswise therein discs 202, in which are small central ori comparmg this with Equation 85 we?nd a value ?ces 206, at intervals of slightly less than one for the equivalent inductance equal to 45 half of the shortest to 204 be radii ated.wave-length Energy is radiated from anwave ori?ce cen L°=-533 (2Ph)=-538Rh (88) trally located in each section of the ?lter thu where It is in the thickness of the piece. The formed and the arrangement is obviously a fur equivalent motional mass then is slightly over the!‘ speci?c embodiment of a prlSm employin half the static mass. The compliance can be cal- 50 the general 1311110113168 0f the invention Tb culated from the formula, end section 208, as for the other prisms aboi 1 1 Z4(1__dz) described, contains an energy absorbing men C0=_._- =_-_______-—-—= (89) her 1210 to prevent re?ection of energy from tl “R213 i?ghix .538 P; L (4'73)2_VZ*SE end of the structure. structures are illustr: 65 farThe above-discussed It now we introduce the ?lter equations given tive 1of the principles of the invention. It is 0' above, we ?nd from Equation 51 that vious that a large number of other arrangemer - (jz?eoz within the spirit and scope of the invention w OO=W ‘ (90) ° readily occur to those skilled in the art and th 60 no attempt has here been made to exhaust su / Introducing this into Equation 89 and determining the frequency by Equation 82 the expressions for the length I i and the thickness lt become possibilities. The scope of the invention is C ?ned in the following claims. What claimed is: 1. In aisradio directional system a radiator co Z-=_____'// (84) l: .881 V g,\/ (fr-f1) p E _ l =.755Z0fR (91) e5 prising a coaxial line, the length oi the line 1 p(]_-——0'2), ‘ Mfg-fly _ ceeding ten times the wave-length of the long , wave to be radiated, the outer conductor of s As a further example, consider a prism of the ie?fml tyg’e iglusgrateglm 151g‘ 16 fir grass-in? "8 -. egacyc e an - wi a ower cu -o a . 0 line having a row of small apertures along ' side thereof the diameter of said apertures -n m -’ 1 ' - ' ilocycleihaildtgn paper one at 1500 k?ocycles' 7o 1axgiaisl li’lllewtig 1:525:51‘: jtgii?arrgg?argé tgfa ssume 2‘ e c amped dlaphmgms (1' 9" with respect to each other, the distance betw ‘ ‘ which the constants the cugasbottoms) are m ade ’, ‘1" m m l ’ alumnum ' p=2.68; EV='l.01><1011; o'=.3'1 - b adJacent being less than the w: . length ofapertures the shortest wave to behalf radiated, (92) 75 number of apertures exceeding twenty, an 2,408,435 25 26 outer conductor, the holes being regularly spaced plurality of auxiliary sections of coaxial line, one of said auxiliary sections being shunted across the line opposite each aperture, the said plurality of auxiliary sections of coaxial line, each being in length one-quarter wave-length of the median wave to be radiated and being short-circuited at in alignment along a side of said outer conductor, the interval between holes being less than one half wave-length of the energy to be employed, a stub conductor concentrically positioned with respect to each hole, said stub conductors being connected to and'supported by the inner con its free end. ductor of said coaxial line, the length of said stub 2. In a system for directively emitting or re conductors being not greater than the distance ceiving wave energy of a plurality of frequencies, between the respective outer surfaces of the 10 energy of each of said frequencies to be radiated inner and outer conductors of said coaxial line. or received at a particular di?erent angle, a wave 8. The antenna of claim '7, one end of said co ?lter having at least twenty sections, the trans— mitting region of said ?lter including the fre quencies to be emitted by said system, a terminal axial line being terminated in a resistance sub stantially equal to the characteristic impedance the line. for introducing or abstracting the energy to be 15 of . 9. In a radio system for directively radiating radiated or received at one end of said ?lter, and receiving a band or spectrum of frequencies, means for radiating or receiving a portion of said each frequency of said spectrum being radiated energy from corresponding points in each sec or received with greatest amplitude with respect tion of said ?lter and means for absorbing sub stantially all energy reaching the other end of 20 to a particular direction, the direction of maxi mum amplitude being diiferent for each fre said ?lter. quency of said spectrum, a radiating and receiv 3. The arrangement of claim 2 the plurality ing device comprising a substantially uniform of radiating means being proportional to emit equal portions of energy from the several sections of said wave ?lter. 4. In a radio directional system, a multisection wave ?lter comprising a long coaxial line shunted 25 radio transmission line, the length of said line being great with respect to the longest wave length of said system, said transmission line being enclosed within an outermost member of conductive material, said outermost member at regular intervals by short auxiliary sections of comprising solely a tubular member of uniform coaxial line the ?rst~stated line having a small ori?ce at each of said regular intervals for radi_ 30 ating and absorbing a small amount of radio energy. cross-sectional area throughout its length, said member having therein a plurality of holes regu larly spaced in a straight line extending substan tially the entire length of said member, all di— mensions of said holes being small With respect to one-quarter of the shortest wave-length of 5. An electromagnetic radiator comprising a tubular member of conducting material its length exceeding ten times its internal diameter, a plu said system, the intervals between holes being rality of diaphragms having small ori?ces there between one-quarter and one-half of said short in, said diaphragms being spaced at regular in est wave-length whereby each frequency of said tervals within said tubular member, said tubular spectrum will be radiated or received by said de member having a plurality of ori?ces spaced mid way between successive diaphragms, the tubular 40 vice with greatest amplitude with respect to a particular direction, the direction being different member and diaphragms being proportioned and for each frequency within said spectrum. arranged to constitute a band-pass wave-guide 10. The device of claim 9 the transmission line ?lter and said ori?ces in said tubular member being proportioned to radiate substantially equal quantities of energy. ‘ 6. The radiator of claim 5 and means at the thereof being a wave-guide. 45 _ 11. The device of claim 9 the transmission line thereof being a coaxial line. 12. The device of claim 9 and a terminating impedance connected to one end of said device, the said terminating impedance being substan far end thereof for absorbing ,energy which reaches that end. '7. A perforated pipe antenna for electromag 50 tially equal to the characteristic impedance of netic wave energy comprising a coaxial line, its said device whereby re?ection from the termi length being in excess of twenty times the in nated end of said device is substantially elimi ternal diameter of its outer conductor, said outer conductor being free from external obstructions nated. WARREN P. MASON. and having therein a row of holes exceeding twenty in number, the diameter of the holes 55 being small in proportion to the diameter of the

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