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Sept. ì?, i946.
2,407,911 `4
L. TONKS ETAL.
WAVE PROPAGATI ON
Filed April 16, 1942
2 vSheets-Sheet l
Fig. |
MED/UM /
MED/UM 2
/FEFLEG‘TED
WAVE
Fig. 2.
ÍNGIDÁ'NT WAVE
p/mscrLY Eff-L £0750/
/ CUM/’ONENTS
PRoPAßAr/ON caNSTAA/r :be
/MffoA/vcf = za
ng. 3.
lnventors:
Lewi To?ks,
LeRoy Apker,
by .7%
Their` Attorney.
Sept° 17p E946.
2,407,91l
L. TONKS ET AL
WAVE’ PHOPAGATION
lFiled April 16, 1942
2 Sheets-Sheet 2
‘ Fig. 4.
43
60
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Fig. | l .
fa
70
Fig. l0.
F193. l2.
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Inventors :
y
LA /T oA/¿t ¿www
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Patented Sept. 17, 1946
2,407,911
UNITED STATES PATENT.OFFICE
2,407,911
WAVE PROPAGATION
Lewi Tonks and Le Roy Anker, Schenectady,
N. Y., assîgnors to General Electric Company,
a corporation of New York
Application April 16, 1942, Serial No. 439,243
7 Claims. (Cl. 178-44)
1
2
This invention relates to the propagation and
described in the following for each distinctive
control of electromagnetic waves in the range of
wave-lengths below one meter, such waves being
designated for convenience as centimeter waves.
It is well known that the passage of electro
case
By the use of a reflection-controlling system
which embodies several (i. e. two or more) sepa
rate transition elements it is found that many
magnetic waves from a first propagating region
into a second propagating region of different
of the limitations inherent in previously used
impedance transforming methods are avoided.
electrical characteristics is ordinarily attended
That is to say, the relatively greater numberiof
independently variable factors leads to greater
by the reiiection of a portion of the incident en
ergy. Such reiiection occurs, for example, when 10 freedom in the design of the individual compo
nents and to greater flexibility in the matter of
a wave is caused to pass from a section of trans
adjusting them. These considerations will be
mission line having one characteristic imped
come more fully apparent as the details of the in
ance to a section of line having a diiferent ‘char
acteristic impedance, It occurs in another case
when a wave passes from one dielectric medium
into a second medium of diiîerent dielectric
vention
are described;
'
. `
The features of the invention especially de
sired to be protected herein are pointed out in
properties.
the appended claims. The invention itself, to
gether with its further objects and advantages,
It is desirable in many cases to control the
amount of wave reflection occurring at appara
may best be understood by reference to the fol
tus transition points, and certain devices, some 20 lowing description taken in connection with the
drawings, in which Figs. 1 to 3 are schematic il
times referred to as impedance transformers,
lustrations useful in explaining the invention;
have been devised for this purpose. However,
Fig. 4 is a graphical representation of certain
impedance transforming devices heretofore
data of significance in interpreting the inven
available have been usable only in special situa
tions and with somewhat inconvenient limita 25 tion; Fig. 5 illustrates a first exemplary applica
tion of the invention; Fig. 5a is a section on line
tions. It is an object of the present invention to
a-a of Fig. 5; and Figs. 6 to 12 show various
provide reflection controlling agencies which are
alternative applications.
applicable in a very wide variety of cases and
which are highly iiexible in the matters of de
sign and mode of use.
„
30
_ Single surface refiection
In explaining the invention it will be conven
It is a more particular object of the invention
ient first to refer to a relatively simple case and
to provide means usable in connection with the
then to extend the theory to include more gen
propagation of centimeter waves, as above de
eral and complex cases. With this in mind, the
fined, for preventing or eliminating and control
ling reflection of such waves. As will be more 35 line :ru of Fig. 1 may be considered as defining
the boundary between a first dielectric region or
fully explained in the following, special diñ’icul
medium of propagation constant h1 and a second
ties are encountered in this range of wave lengths
dielectric region or medium of propagation con
because of the need for taking into accurate ac
stant h2. It is desired to consider the action of
count certain factors which may be ignored at
an electromagnetic wave which impinges on :ro
longer Wave lengths.
from the left, the direction of propagation of the
In general, the invention involves the use of a
wave being indicated by the arrow A.
plurality of transition elements which by virtue
It is useful to note preliminarily that under
of their dimensions, spacings and other proper
appropriate conditions electromagnetic Waves
ties are able to efîect the reilectionless transmis
may exist in numerous forms. For example, in
sion of electromagnetic waves from one propa
considering free space propagation, plane trans
gating region to another. In one embodiment
verse waves are ordinarily assumed. On the
the transition elements employed take the form
other hand, in a wave guide, such as a rod of di
of two or more dielectric slabs or plates of appro
electric or the space enclosed by a hollow Con
priate configuration and arrangement. In an 50 ductor, confined ultra-high frequency waves may
other they comprise discrete impedance-Varying
sections spatially and dimensionally correlated
be developed and propagated which have ñeld
components not only at right angles to the di
to assure attainment of the desired results, The
rection of propagation but also in the direction
considerations which determine the proper form
of propagation, One such wave, which may be‘
and relationship of the means employed will be 55 produced, for example, in a hollow 'cylindrical
2,407,911
4
0
mensions is more complex, being defined as fol
conductor, is the so-called Ho wave which has
lows in the case of I-I waves traversing a rectan
gular wave guide having a dimension œ which is
magnetic components parallel to and transverse
to the direction of propagation and an azimuth
ally directed electric component in a plane trans
verse to the direction of propagation. Another
type, frequently called the En wave, has lines of
electric force parallel and transverse to the di
perpendicular to the transverse electric field and
a dimension y which is parallel to the transverse
electric ñeld.
(l
rection of propagation and_has lines of magnetic
(25)
force azimuthal with respect to the axis of prop
agation.
In general, however, any electromag
l()
netic wave may be considered as fully specified
for most purposes when its classification is given,
and when the magnitude of one of its field com
where c, fi, and 7c have the meanings assigned
above; a is one-half the operating wave length,
and an is the smallest value which x may assume
and still permit Vpropagation of waves of this wave
length'. (For a circular guide 11:11?, and the ratio
ponents is stated, the remaining components be
ing then readily determinable from relatively
simple relationships.
.1i/:c becomes unity).
' With these considerations in mind, let the Wave
For E waves
indicated by a directed arrow A in Fig. 1 be char
acterized by the transverse component,
__T
20
ZE: C/.L
of the electric field associated with it. Here t
represents time, œ is distance from an arbitrary
origin to the left of ro, and h1 is the propagation
constant of the medium ‘1. If the medium is non
dissipative, h1 is ya pure imaginary; otherwise >it
is complex.
In order to satisfy the boundary conditions at
the surface :L'o in Fig. 1 we must have in addition
to the incident wave a reflected wave
«ke-1
G10
’y
l#
œ
(2C)
a'o
»Where x now represents the wave guide dimen
sion perpendicular to the transverse magnetic
iield, y is the dimension parallel to this ñeld and
the other quantities have the same meanings as
above.>
In general, a definite relationship exists be
tween the impedance, Z, of a propagating system
and the propagation -constant h of the same sys
tem.
For plane waves in free space and H waves
in guides
h2 is the propagation constant of the medium to
the right of :120.
The coeiìîcients r and b` are
determined by matching the electric and mag
netic fields at :1:0 according to a wellunderstood
For E waves in guides Z~h.
procedure. These coeñicients are real ‘in the case
We notice from vcomparison of Equations 1 and
of Fig. 1 if the dielectrics are non-dissipative, but
2 that b=1+r. Although the amplitude of the
in general they are complex. They give both the 40 transmitted wave is greater than that of the
amplitude and the phase of `the reflected and
incident wave if Z2 is greater than Z1, the energy
transmitted waves at :no referred to the incident
transferred by it is necessarily less. The greater
wave at the same boundary.
amplitude is consistent with the consideration
For the case of Fig. 1, r and h are found to be
that in different media the power density is pro
portional not only to the square of electric am
plitude but also the reciprocal of the impedance.
The reñection and transmission coeflicients are
not the same for waves incident from the right as
they .are for those incident from the left. If
50 primed symbols refer to the `former case, we find
The quantity Z in ythe foregoing equations is
>that
defined »as the ratio of the transverse .electric
component of the propagated wave to the trans
(3)
verse magnetic component for the particular
propagating region under consideration and cor
responds to the “characteristic impedance” of
the propagating system as that term is custom
(4)
arily employed.
Reflection and tránsmission at a slab
(See Electromagnetic Theory
We may examine the case of two boundaries
by J. A. Stratton, iirsll ed. pp. 282-284). As thus
by considering the arrangement of Fig. 2, in
defined, Z is dependent both upon the intrinsic 60 which the space to the left of m0 is occupied by
dielectric properties of the propagating medium
and the boundary conditions of the propagating
system. For example, in the case of a Coaxial
conductor transmission line (where the useful
waves are of plane transverse character)
(2a)
where c is the velocity of light, ii is the perme
ability of the medium between the conductors, lc
is the dielectric constant of the medium, and ro
and r1 are, respectively, the radii of the outer and
inner conductors. On the other hand, in a `wave
'guide comprising a single hollow conductor th'e
relationship between impedance and guide di
medium 1, the space between 3:0 and x1 is occu
pied by a refractive dielectric a, and the space
to the right of x1 is occupied by a medium 2
(which may be the same as or different from
medium 1).
Considering the wave situation at the left of
xo, we may attack the problem by summing the
multiple reflections that occur at the various
surfaces as indicated in Fig. 2. In the following,
the characters 1' and T’ represent reñection co
emcients in the forward and reverse directions
respectively, b and b’ represent corresponding
transmission coefficients, and the various sub
scripts identify the surfaces to which these co
e?l'lcients- are referred.
2,407,91 1
5
The complete reñected wave,
hand memfber of Equation 7 is set equal to zero
Arx0eíwt+h1(a:-zg)
as follows:
(10)
If all the dielectrîcs involved are non-dissipative,
so that 0 becomes real, this condition can be satis
is determined by the reflection coeñicient
fro
where A10
= T10
is +the
bzorzlb’zoe
amplitude
_ 2m +ofbzorîlTlxob'roe-uß
the incident wave,
fled if |r¢0!=lre1|.
(lrœol and [fall represent the
respective absolute values of reo and nl.)
When re0=-mp Equation 10 is satisfied pro
Amo is the amplitude of the reflected wave, and 10
vided I0|=-n1r, and when re0=re1, then
The ñrst term of the right hand member of
Equation 5 is the component which is reflected
directly from the surface nto. The second term
is the component which traverses the surface rco,
is reflected at the surface :1:1 and again traverses
:vo out into medium l. Having passed through a
double thickness of the dielectric a assumed to
suffices.
(Here n is an integer or zero.)
1
As we have seen in connection with the deriva
tion of Equation 7a, re0=-1^r1 represents the case
of a plate o-f non-dissipative dielectric separating
identical media. Reference to Equation 7 and
to the considerations stated in the preceding par
be contained between the surfaces xo and cci, it
suffers the phase lag 20. The subsequent terms 20 agraph shows that such a plate gives zero reflec
tion (i. e. R1~(1'e0-l-1'e1e-2f°)=0) when the plate
account for the further multiple reflections. The
is any integral number of half wave lengths thick
resulting infinite series is directly summable to
(i. e. when |6|=n1r) . From a practical standpoint
give
brama-21'“
<6)
R1 - Tzu +__1__
Txlrfzofm
Using Equations 3 and 4 in connection with
Equation 6, we i'lnd that
R
it is important to note further that where non
dissipative media are concerned, the condition of
zero reflection automatically implies a condition
of complete transmission (i. e. in accordance with
energy conservation requirements).
This is a
consideration the value of which will become
30 more apparent in the following.
Consideration of Equation 1 will show that for
(7)
rx0=rz1, v(the second of the two cases proposed
__ T10-traf”
P_Ws
in the next to last paragraph) the media on op
For the transmitted wave
Atzleíwl-hah-:D
a similar calculation gives the transmission coef
ficient
posite sides of the refractive plate must be of
different impedance and the plate must have an
impedance which is the geometrical mean of the
impedances of the media which it separates.
Assuming this condition and assuming the fur
ther condition that the plate is an odd multiple of
Atz
bz bT e-f@
Amo l r :013,16
1 = *l = î¥-îß
(8)
40 a quarter of the operating wavelength (in the re
fractive plate) in thickness (i. e.
and using Equations 3 and 4, we have
T1:
bxubzle-í'7
43 where n is an odd integer, including unity) we
see from (10) that the plate in question may be
An important case is that in which media 1
and 2 are identical. Then
r (Equation 1) =Re0=--nl
and
1.... -21'9
RFHîÃî-za
(7")
Also, bx0=1+r and bzlr-l-r, so that
(1-r2) 6*"1'"
T1=m
,
used to introduce a wave without reflection (i. e.
with complete transmission) from the first of the
separated media into the second. This result
50 holds stricth7 only for non-dissipative dielectrics
but is easily corrected to take into account ap
preciable dissipation in one or more of the media,
and the resulting correction is small. A match
ing plate may thus be used to introduce a wave
without reflection into a dissipative medium
where it may be totally absorbed.
The maximum reflection obtainable from a
non-dissipative plate separating identical media
occurs when
Equations 6 to 9a give the amplitudes and
phases of the waves reilected and transmitted by 60
the plate or slab of dielectric contained between
the surfaces :v1 and :170. These amplitudes and
phases are specified at the surface :12o for the re
flected wave and at the surface :ci for the transmit
ted wave and are referred to the incident wave at
the ñrst surface. The coefficients of Equations
5 to 9a are in general complex for both dissipative
and non-dissipative dielectrics. They completely
describe the effect of the dielectric medium be
tween xo and x1 on the incident wave, and there is
no need for referring to any process inside this
medium once we have them.
#meng
in Equation 7a. Then, by Equation 1
(11)
where 1’ is the reflection coefficient at the incident
surface. From comparison with Equation l it is
seen that such a plate’s reflection is equivalent to
the reflection from a single surface where the im
For a practical application of the results ob
pedance ratio is equal to the square of that for
tained in the foregoing, we may ñrst consider
the plate. Values of reflection between zero and
the situation in which the numerator of the right 75 R1 max may be obtained by using a slab thickness
2,407,911.
7
between the value indicated by 0:1111» and the
value indicated by
8
will be seen that both these quantities are domi
nant factors in determining the total reflection
from a multislab system. In other words, in any
propagating system in which the operating wave
length is not extremely large in comparison with
the dimensions of the structural elements in
volved, reflection cannot be eliminated, as has
‘
Two 0r more4 slabs
For the case to which the present invention
been previously suggested by various writers, sole
especially pertains, namely, in which two or more
ly by a quarter wave spacing of refractive ele
refractive elements are involved, a system such 10
ments.
as that illustrated in Fig. 3 may be considered.
Except for the factor eîi’f, Equation 19 is for
In this figure the refractive regions a and b are
mally the same as that for a single plate (see
understood to -be included between two pairs of
Equation 7a). By setting the numerator of its
separate reference surfaces xo, :1:1 and x2, xs.
right-hand member equal to Zero (i. e., the con
We shall assume that the refractive regions a and
dition for zero reflection) we find that zero re
b are completely specified by known coefñcients
iiection is obtained when
ra, r’a, ba, b’a, applying to a as a -whole and rb,
T'b, etc. applying to b. These coefficients are an
alogous to the reñection and transmission c0
where n is an integer and where, necessarily,
eilîcients for the surfaces of a single slab as pre
l h2 ](x2--œi) is greater than zero.
20
viously derived (e. g. in Equations 7a and 9a).
Fig. 4 is a plot of the phase angle, ip, which
Following an analytical procedure similar to
that used above, we ñnd that the overall reflec
tion and transmission coefficients for the system
which includes the two refractive regions a and b
are formally of the character indicated by VEqua
tions 6 and 9, being specified as follows:
determines the spacing h2(œ2-:1:1) in degrees of
phase, as a function of the phase thickness, 9,
of the plates.
The impedance ratio
25
î=2
is taken as a parameter.
While it is not immediately evident from Equa
tion 19, it can be shown from that equation that
R2 is maximum when e*2m=-1. This is an
equality which is satisfied when
35
These formulas apply to dissipative as well as
to non-dissipative dielectrics and in general are
In the event of the fulfillment of this condition
complex for both cases.
40
Since we have the reñection and transmission
(21)
coefficients for single slabs (Equations ’7 and 9),
we may use them in Equations 12 and 14 to in
vestigate the useful properties of pairs of slabs.
In this connection consider two identical non
dissipative plates immersed in a non-dissipative
medium of different impedance in an arrange
ment generally similar to that of Fig, 3. Under
these circumstances the R1 and T1 of Equations
7a, and 9a are respectively the n, ra', Tb and the
ba. and ba’ of Equations 12 and 14. If they are
expressed in polar form
R1=1R1|ef¢
(15)
T1=lT1[ei(¢+"/2)
(15a)
and
This is equal to the reflection from a single sur
face having an impedance ratio equal to the
fourth power of that for the slabs, as can be
seen by substituting from Equation 11 and corn
paring it with Equation 1. At the same time it
appears that it is equivalent to the reflection from
a single slab having an impedance ratio equal to
the square of that for the two slabs.
Amounts of reflection intermediate between
the minimum value of zero and the maximum
value denoted by Equation 21 can obviously be
obtained by choosing spacings between the points
deñned by Equation 20 and Equation 20a. This
is an important feature of multislab combina
tions when used for neutralizing reflection from
a reflecting boundary outside the combination
__t _1
l-rz
since it means that the reflection obtainable with
IÍ’- an
m2 Cot Ü
60 such combinations is to a large extent independ»
(Equations 15 and 15a are obtainable by expand
ent of the characteristics of the individual slabs.
ing the right-hand members of Equations '7a and
If the two refractive regions are not identical
9a into their real and imaginary components and
slabs, there is, in general, no separation giving
then evaluating the angular arguments of the
zero reflection. However, in the special case inv
where
resulting expressions.) Substitution from
into Equations 12 and 14 yields
15 65 which l Ta [=| rb l, we ñnd that no reflection occurs
when
(19)
where R2 is the over-all reflection of the two-slab
system and
(19a)
Ihzl ($2 _1121) =
(22)
In justifying Equation 22 we may ñrst observe»
that a condition to be fulfilled if there is to beI
cancellation of the portion of the incident wave
which tends to be reñected from the first reflect
ing slab (Fig. 3) is that the various wave com
Since (œ2-x1) represents the slab spacing and
since Blf depends directly upon slab thickness, it 75 ponents which pass through the first slabI and,
2,407,911
.
10
9:
after single or multiple reflection from the sec
ond slab, effect repenetration into medium I
mustbe in opposite phase with respect to the pri
marily reflected wave. To show that Equation
22 represents the condition-for a proper phase
relationship of the internally reflected wave com
ponents, consider an incident wave of phase zero
at :to (Fig. 3) . The phase of the primary reñec
I2 is shown at I3. It is reasonable to assume
that a material of _fairly low impedance may
prove suitable for the slabs II and I2 and since
quartz is such a material, it will be worth while
to investigate the possibility of using this sub
stance. If this is at all possible, it can be done
when [rb] (i. e., the reñection coeflicient of slab
l2) is a minimum. That this Yoccurs when
tion from the ñrst slab referred to the plane 0:0
is tba by Equation 15. The phase of the primary 10
transmitted wave at :L'i is
can be seen from Equation '7, the equation for
reñection from a single slab, in which now both
by Equation 15a. At :v2 the phase has been ad
vanced by | h2 {(:cz-xl) . The portion of the wave
which is reflected from the slab b is retarded by
:pb and this wave is again advanced in phase dur
ing its passage from r2 to x1 by an amount equal
to [hz Mrz-x1). Combining all these phase dif
ferences we get
no and nl are negative because the impedances
of the various successive media are progressively
less in the direction of propagation. The follow
ing data will be used:
A Hm wave having a free space wave length of 10
cm. propagated in a 7.62 cm. (3") rectangular
guide having a limiting wave length of 15.24
cm.
for the relative phase of the internally reñected
wave at mi.
A part of this wave is retransmitted
through the dielectric region a into medium I,
and a still further portion is again reflected at
.r1 and> suffers further internal reflections be
tween the boundaries mi and m2.
Y
'
Dielectric constant of quartz È 3.6
Dielectric constant of water È 70
From these data and by means of known rela
tionships (see definitive Equation 2b) We are able
to compute various impedances that we need:
Considering
only the portion of the wave which is transmit 30
ted through the dielectric a into medium I at
the ñrst opportunity for such transmission, it is
Where subscript 1- refers to the air-ñlled portion
apparent that this portion will suffer a retarda
of the wave guide, subscripts a' and b to the slabs
tion of phase during such transmission of
II and I2 respectively, and subscript 3 to the
water-filled section I3; where »y and a: are re
spectively the minor and major dimensions of the
wave guide, and where the factor Zo is the im
(i. e., according to Equation 15a). The total
pedance encountered by a plane wave in lfree
phase lag of this part of the wave which is avail
space. (_The ratio 'yl/m cancels out in the com
40
able for interference with the primary reflected
putation of reflection and transmission coeiîi
wave is therefore the algebraic sum of the indi
cients ’and therefore does not require to be nu
vidual phase diiîerences:
merically specified.)
'
`
"
The reflection coefficients for the various slab
surfaces are found by using Equation 1:
For this interfering wave to be wholly out of
phase with the directly reflected wave which, as
From (7) ,
we have seen, has the relative phase angle gba, it
is clear that the phase diñ'erence between the in 50
= -l-.321
(23)
terfering wave parts must be some odd number
of 1r radians. Mathematically expressed, this
Now the maximum reflection obtainable from
means that
a quartz plate in airis, from (11)
This reduces directly to Equation 22. This equa
tion shows, among other things, that reflection
cancellation depends upon the maintenance of a
proper spacing between the reñecting agencies by
which the cancellation is to be produced. This
relationship is true moreover, for all points in
medium I since the phase of the two reflected
Since' this is greater in absolute value than rb,
thematching is possible. To make Ira l=| rbl it
is only necessary to use a thinner front plate than
is indicated by (24). From (7a),
wel:
Waves varies equally and in the same sense.
Equation 22 can be applied to the problem of
introducing a wave from air into water (neglect
ing for the moment the slight effect of attenua
tion on the water reflected wave) by using a re
fractive slab for a and a. refractive slab backed
by water for b. This arrangement is illustrated
in Fig. 5 which shows a wave guide in the form
of a hollow conductor ID along which electro
magnetic waves are assumed to be propagated.
The relative position of the refractive slabs is in
where r=rœ0=-.393, the reflection at one sur
face, and where that value of 0 is to be found
for which Ira l=.321. One ñnds that 21.6° is
approximately correct and this is the phase thick
ness 0 >of the ñrst plate.
Its actual thickness
(anexo) is determined from the original defini
tion of@ as being equal tov [ hal (r1-uso).
Having adjusted the amplitudes of the reñec
tion coeñicients properly, we still have to ñx the
phases by choosing the correct separation of the
dicated at II and I2 and water backing the slab 75 plates. This is given by Equation 22.
2,407,9»1 i
i1
In using Equation 22 it should first be recalled
that (x3-m2) was arbitrarily so chosen that
12
location of the plate 32 requires a preliminary
determi-nation by measurement or computation,
of the reflection cceflicient of the surface of di
electric 3 |. With this quantity known, the thick
ness of the plate required to give an equal co
efficient can then be» computed. Finally, the spac
ing of the plate with respect to the dielectric
3| which» is necessary to assure-mutually anni
hilative interference of the »two reflected wave
components may be determined by a procedure
like that used in justifying Equation 22. 'I‘he
spacing chosen should, of course, be such that
at a plane located in advance of both the plate
32 and the dielectric 3| with reference to the
is a matter of convenience only. Some other
direction of wave propagation, a phase displace
value might equally well have been taken in which
ment of mr radians exists between reflections
case the further treatment' of the problem would
attributable to the plate and those attributable
have been complicated to the extent of having
to the dielectric, 71. being an odd integer.
to deal with a finite value of rbb throughout.)
A- singl’e plate such as the plate 32 may alter
Using the impedance ratio Z1/Za=2.'24, Fig.
4 gives yba=-118°. (Fig. 4 shows the variation of 20 natively «be used to annul reflections due to re
flective discontinuities other than a discontinuity
1]/ with 0 for different values of the impedance
attributable toV a change in the propagating di
ratio Zl/Za. For cases where 0 is below. 90° use is
electric. Examples of other discontinuities are
made of the upper abscissa scale and the right
those produced (l) by a change in dimensions of
hand ordinate scale. For cases where 9 is be
a wave guide, or (2) by a change in direction of
tween 90° and 180° the lower left-hand scales are
a waveguide, or (3) fby the junction of a wave
used.)
It follows that [h1 l (m2-:131) =121°, from which
the plate spacing (m2-ain) is, of course, directly
determinable.
If the maximum reflection from the plate ||
had not been greater in absolute value 'than the
minimum reflection from plate I2, it would not
have been possible to eliminate reflections with
two plates of quartz only, although the desired
guideY with a devicehaving an effective charac
teristic impedance different from that of the
wave guide.
Fig. 8’ represents a construction in„which a
wave guide, indicated at 35, is to be employed
to conduct waves from. a high frequency source
within which such waves are generated. The
source, which is indicated in part only, comprises
result could have been obtained by using a ma
terial having an impedance closer to that of
a metallic enclosure 35 within which are con
higher impedance ratio.
wave guide 35, a glass plug 39 is sealed into the
entrance to the wave guide for the purpose of
tained electrode structures 31 such as the elec
trodes of a split anode magnetron. The entrance
water. However, by adding a third plate, identi
of the wave guide 35 is- assumed to be arranged
cal to || and positioned ahead of ||, and by
in such relation to ,the electrodes 31 as to assure
applying the general formulas to the resultant
three-plate system, it is easy to show that the 40 that high frequency wave energy will be propa
gated along the guide.
range of impedance over which zero reilection
In order to preserve the vacuum tightness of
may be obtained is greatly'exten'ded, for, the first
the container 36 in spite of the insertion of the
two plates then behave like a` single plate with a
This arrangement is
illustrated in Fig. 6 which indicates a wave guide
2D (either of cylindrical or rectangular form) con
taining a series of three mutually spaced dielec
forming a vacuum-tight closure.
In accordance
withI the considerations previously given herein,
it willfbe understood that the plug 3€) constitutes
tric slabs 2|, 22, and 23, the plate 23 being backed
at least a partial barrier to the passage of waves
by water, as indicated at 24. A special advan
tage of the three-plate arrangement is that not 50 and may lead to objectionable reflection of such
waves. The geometry of the system in question
only the impedance but also. the thickness of the
makes it inexpedient to eliminate such reflection
individual plates may be chosen within much
by means of slabs located in the guide within
wider limits than is possible where only two plates
the container 36. However, an equivalent effect
are employed.
Y
can «be obtained by means of a pair of dielectric
This three-plate matching `apparatus has an
slabs 4| and 42 arranged Within the guide at
analogue in which single surfaces replace plates.
a point outside the container 35.
A wave may zbe introduced without reflection into
In order to determine the proper arrangement
a body of dielectric if` at the proper distance in
of the slabs.4| and 42, it is necessary first to de
front of the dielectric we place a refractive plate
of the correct thickness. This is indicated in 60 termine the over-all reflection coenicient of the
Fig. 7 in which is shown a hollow wave guide 30
4terminating in a dielectric section 3| and having
within its interior a dielectric plate 32. Since
the condition to be satisfied for zero reflection
plug 39, referred, for example, to the left-hand
surface of the plug. Thereafter Íby use of Equa
tions 19- and 19a a spacing of the slabs 4| and 42
may be determined which will give an equivalent
is merely that they over-all reflection coefficient 65 reñection coefficient referred to the left-hand sur
of the plate shall equal in magnitude that-of the
face of the slab 4|. This spacing will, of course,
single surface of dielectric 3|, the only restric
be a, function of the thickness and dielectric
tion on the impedance ratio of the platev (with
properties of the respective plugs. Once the
respect to the medium in which it is immersed)
is that it be greater than the square- root of that. 70 proper location of the plugs 4| and 42 with respect
to one another is fixed, the distance between the
for the dielectric surface (see Equation 14) .
left-hand surface. of the plug 39 and the cor
Within these limits a plate of any impedancev may
responding surface of the slab 4| required to as
be used provided its thickness and location are
sure destructive interference of the waves respec
properly chosen.
Determination of the proper dimensions and. 75 tivelyreflected from the two reflecting` units may
2,407,911
14v
13?
be computed by an analysis similar to Lthat in
volved in the derivation of vEquation l22.
Fig. 9 represents the application of the inven
similar to those used in connection with the con
structions of Figs. 5 to 10, one may determine
the dimensions and spacing of the sleeves S3 and
tion to the case of a wave guide 43 _which is ter
64 >which are required to cancel the reiiection
minally connected to a smaller wave guide 44. 5 occurring at the extremity of the transmission
line (i. e., at'its junction with the antenna BI’).
Due to the difference-in dimensions of the.Y two
Wave guide sections, they will under ordinary cir
A further .modification of this same principle
cumstances have different characteristic imped
is shown in Fig. 12 in which annular sleeves 13
ances and wave reflection will occur at their junc
and 14, functionally similar tothe sleeves B3 and
tion. `To annul this reflection there are provided
64 of Fig. 11, are secured to the inner surface
two identical dielectric slabs 45 and 45 which are
of a tubular conductor 'lll which forms the outer
respectively spaced from one anotherA and from
member of a coaxial'conductor transmission line.
the entrance extremity of the waveguide 44.>
By appropriate choice of the dimensions and
In designing an arrangement such as that of
spacings of the members 'i3 and 14, terminal re
Fig. 9, the composition of the plates t5 and 46
ilections due to the junction of the transmission
may be chosen rather arbitrarily with a View to
line with an antenna 'H' may be neutralized.
employing materials which are structurally suit
Reflection-preventing sleeves of the character
able. Moreover, the thickness of theplates is
illustrated in Figs. 11 and 12 may also be used in
arbitrary within relatively wide limits. With the
connection with single pipe wave guides. How
impedance and the thickness of the plates given, 20 ever, in the latter application it is considered that
it is possible to vary the spacing of the plates
dielectric slabs have an advantage over transition
With reference to one another in accordance with
Equation 19 to produce a reflection coefficientl for
the combination which equals in absolute magni
tude thecomputed or observed reilection coeffi
cient of the boundary between the wave guide
sections 43 and 4i. Thereafter, the spacing of
the left-hand surface of the plate ¿5 with respect
to the entrance extremity of the guide section de
elements of other forms in that they have no
tendency to introduce new types of waves (i. e.,
waves of a form diiferent from the form of the
incident wave) .
In summary, it may be said that in a large
class of cases unwanted reflection from a reflec~
tion-producing discontinuity may be cancelled or
annulled by providing in connection with the
(i. e., the reflecting boundary) must be adjusted 30 discontinuity a neutralizing system having a re
to assure (2n-1)”- phase displacement between
iîection coefficient equal to that of the disconti
nuity and having a spacing with respect to the
the reflected waves Whose destructive interference
'discontinuity such that at planes in advance of
is desired.
` In the wave guide construction of Fig. 9, the
all the reflecting agencies a phase displacement
reflective slabs or plates may alternatively be
located in the smaller wave guide section d4.'
ñections attributable to the discontinuity and re
A still further application of a multiple plate
of approximately mr radians exists between re
flections attributable to the neutralizing system,
n being an odd integer. It should be noted, how
combination as a reflection reducing agency is
ever, that the question of whether the provision
illustrated in Fig. 10. In this case there is shown
a coaxial conductor transmission line having an 4.0 of equal reflection coeûlcients represents a proper
. condition for complete neutralization depends to
outer conductor 5i! and an inner conductor 5I.
some extent upon the nature of the reflecting
The inner conductor terminates in an unshielded
agencies involved. More specifically, it is a con
portion 5|’ which may be assumed to constitute
dition which is applicable in an arrangement in
a radiating antenna or to connect with an an
which the neutralizing system is ahead of the
tenna or other utilization device. It is obvious
discontinuity desired to be neutralized,.provided
that the effective impedance of the unshielded
a-phase displacement of 90° exists between wave
section 5I’ will be different from theimpedance
components reñected by the system and wave
of the transmission line combination, so that
components transmitted by the system. In other
wave reflection at their junction may be antici
pated. To avoid this, there are provided a pair 50 words, the relationship assumed in Equations l5
and 15a must be valid. Where the discontinuity
of dielectric plates or disks 53, 511 which are fitted
is ahead of the neutralizing means (as in Fig. 8),
into the conductor 59 and which have dimensions
then the discontinuity (and not necessarily the
and spacings calculated in accordance with the
neutralizing means) must comply with the afore
principles previously given herein to neutralize
reflection from the transmission line termination. 55. mentioned relationship.
‘ In connection with a coaxial transmission line
v A phase displacement of 90° between reñected
system, the dielectric plates 53 and 54 of Fig. 10
may be replaced by equivalent transition ele
and transmitted components represents an as
sumption which is justified in the event there
ments of a different structural character.` This
iiection-producing agency in question comprises
possibility is illustrated in one embodiment in Fig. 60 a single, substantially non~dissipative, dielectric
11 which-shows a coaxial transmission line hav
slab or a plurality of identical such slabs.
ing conductors 60 and 6l, the inner conductor
not justified where the reflection-reducing system
It is
is made up of a number of dissimilar slabs or
terminating in an antenna section t l ’. Attached
where it is made up of structural discontinuities
to the conductor 6l within the confines of the
conductor B0 are a, pair of annular conductive 65 such as those illustrated in Figs. 11 and 12. Ac
cordingly, in connection with reflection-reducing
(e. g., metal) sleeves 63, E4 which are of similar
agencies of the latter class, it will be found that
dimensions and which are mutually spaced.
for -complete neutralization rto be obtained the
It is apparent that each of the sleeves 63 and
reflection coefficient of the neutralizing means
64 introduces into the transmission line system
a short section (corresponding to the length of 70 must ordinarily be somewhat different from the
` reflection coeflicient of the discontinuity which
the sleeve in question) having an impedance
give-s rise »to fthe reiiections desired to be an
which is different from that of the transmission
line proper. In this respect then, each of the
sleeves is equivalent to one of the dielectric plates
nulled. This qualification also applies in cases'
where the reflection-reducing means introduces a
53,' 54 .of Fig. 9. _Moreover, by, considerations 7.5.' material .amount of dissipation.V _ ì
2,407,911
While the. inventionhasbeen described by ref
erence to particular applications and specific em
bodiments, it will be understood that numerous
modifications may be made by those .slcilled' inthe
art without departing from the invention. We,
therefore, aim inthe appended claims to` cover
all such equivalent variations of.' structure or use
as, come within the true spirit and scope of the;
foregoing disclosure.
.
What we claim as new and-desire to secure by
Letters Patent of the United States is.: '
164
tinuity with reference to the direction of Wave
propagation and eachhaving a thickness which
is amaterialV fraction ofl the wave length ofV the
waves'to be propagatedY whereby the overall re
ñection from said combination is defined. by a re
flection coefficient in which both the spacing and
thickness of the plates enter as dominant factors,
the spacing of said plates with respect to one
another Abeing adjusted- to produce a reflection
coeihcient for the combination equal to that of
the said discontinuity, and the spacing of said
1. An electromagnetic system. for propagating
plates with respect to the discontinuity being
centimeter waves comprising a wave-propagating
structure having a discontinuity at which reflec
tion tends to occur, and means in proximity to
said discontinuity and in the path of wave propa
such that at any plane in said structure located
in` advance of the said plates a phase displace
ment of approximately mr radians exists between.
reflections attributable to the discontinuity and
reñections attributable to the said plates, n being
gation for annulling the said reflection, said
an odd integer.
4. In combination, a source of centimeter
short section of wave-propagating structure and 20 waves, a wave guide connecting with said source
for propagating waves derived from the source,
having a thickness in the direction of wave prop
and means for annulling the reflection of waves
agation which is a material fraction of the Wave
at the junction between said source and said wave
length of the waves to be> propagated whereby,l
guide, said last-named means comprising a ccm
the overall reflection from said combination is
defined by a reflection coefllcientin which both 25 bination of spaced dielectric plates which are lo
means comprising the combination of a plurality
of spaced elements each constituting in itselfV a
cated within said wave guide in proximity to
the spacing and thickness of the elements enter
the said junction and which are of a thickness
as dominant factors, the spacing of said elements
corresponding to a material fraction of the wave
with respect to one anotherl being so adjusted
length of the waves derived from said source
that at any plane in said structure located in
advance of the said elements and the vsaid dis' 30 whereby the overall reflection from said combina
tion is defined by a reflection coeñlcient in which
continuity with reference to the direction of wave
both the spacing and thickness of the plates
propagation the rellection attributable to the ele
enter as dominant factors, the spacing of said
ments is equal to that attributable .to the said
plates with respect to one another being so ad
discontinuity, and the spacing of said elements
with respect to the discontinuity being such that 35 justed that at a plane between the said source
and the said junction the reflection attributable
at the said plane a phase displacement of ap
to the plates is equal to that attributable to the
proximately mr radians exists between reflections
junction, and the spacing of said plates with re
attributable to :the discontinuity and reflections
spect to the junction being such that at the said
attributable to the elements, n being an odd in
teger.
40 plane a phase displacement of approximately ne
radians exists between reflections attributable to
2. An electromagnetic system for propagating
centimeter waves comprising a wave-propagating
structure having a discontinuity at which reflec
tion tends to occur, and means in proximity to
the said discontinuity and in the path of wave
propagation for annulling the said reflection, said.
the junction and reflections attributable to the
plates, n being an odd integer.
5. In combination, a hollow conductive wave
guide defining a first propagating region, means
adjoining said wave guide and defining a second
propagating region of different characteristic im
pedance than the ñrst, and a plurality of iden
of spaced dielectric plates each having a thick-`
tical dielectric plates successively arranged in ad
ness which is a material fraction of the wave
length of the waves to be propagated whereby 50 vance of the junction of said iirst and second
regions for facilitating the reilectionless transfer
the overall reflection from said combination is
means comprising the combination of a plurality
deñned by a reflection coefficient in which both
of wave energy between the regions, the dimen
said reflection, said means comprising the com
bination of a plurality ofV identical dielectric
and in the path of the propagated waves for as
sisting the non-reflective transfer of wave energy
sions and spacing of said plates with respect to
the spacing and thickness of the plates has domi
one another being such that the overall reflec
nant factors, the spacing of said plates with re
tion coeillcient resulting from their combination
spect to one another ‘being- so adjusted that at
is equal to the reflection coefficient of the said
any plane in said structure located in advance of
junction, and the spacing between the junction
the said plates and the said discontinuity with
and the plates being such that with respect to
reference to the direction of wave propagation
waves which pass through the various plates, are
the reflection attributable to .the plates is equal
reflected at the said junction and retraverse the
to> that attributable to the said discontinuity,
and the spacing of said plates-with respect to the» 60 plates, the phase shift attributable to said spacing
plus the phase shift attributable to the plates
discontinuity .being such that at the said plane a
themselves differs by approximately mr radians
phase displacement of approximately mr radians
from the phase shift of waves reflected directly
exists between reflections attributable to the dis
from the first of said plates, n being an odd
continuity and reflections attributable to» the
integer.
plates, n being: an odd integer.
6. In an electromagnetic system which is
3. An electromagnetic system for propagating
adapted to propagate centimeter waves and which
centimeter `waves comprising a wave-propagat
comprises two adjacent propagating regionsV of
ing structure having a discontinuity at which
reflection tends to occur in an amount deter 70 different characteristic impedance; an arrange
ment which includes at least two spaced elements
mined by a reilection coeñicient assignable to
in proximity to the junction of the said regions
the discontinuity, and means for> annulling the
plates located in advance of the said discon»
75 from one region to the other, each of said ele
2,407,911
ments constituting a short section of Wave-prop
agating structure and being of a thickness which
is a material fraction of the Wave length of the
waves desired to be propagated by the system
whereby the overall rei‘iection from said arrange
ment is defined by a reiiection coefficient in which
both the spacing and thickness of the elements
enter as dominant factors, the spacing of said
elements with respect to one another being so ad
justed that at a plane locate-:l in advance of the
said elements and the said junction with refer
ence to the direction of Wave propagation the re
iîection attributable to the elements is equal to
that attributable to the junction, and the spacing
of said elements with respect to said junction be
ing adjusted to secure phase opposition between
Said reiìections to obtain destructive interference
thereof.
7. In an electromagnetic system, an elongated
hollow Wave conñning structure denning a first
Wave-propagating region, and means for facili
tating the transfer of Wave energy from said
region. to a second region of different eiîective
impedance, said means comprising a plurality of
18
localized constrictions provided within said struc
ture at mutually displaced points near its junc
tion with said second region, the extension of
said constrictions in the direction of wave propa
gation comprising a material fraction of the wave
length of the Waves desired to be propagated
whereby the overall reflection of the 'various con
strictions is donned by a reilecticn coenicient in
which both the spacing and extension of the con
strictions enter as dominant factors, the spacing
of said constrictions with respect to one another
being so adjusted that at a plane located in ad
vance of the said constrictions and the said junc
tion with reference to the direction of propaga,
tion the reflection attributable to the construc
tions is equal to that attributable to the junction,
and the spacing of the constrictions with respect
to the junction being such that at the said plane
a phase displacement of approximately 1in- radi
ans exists between reflections attributable to the
junction and reflections attributable to the con
strictions, n being an odd integer.
LEWI TONKS.
LE ROY APKER.
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