close

Вход

Забыли?

вход по аккаунту

?

код для вставки
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
Документ
Категория
Без категории
Просмотров
0
Размер файла
2 086 Кб
Теги
1/--страниц
Пожаловаться на содержимое документа