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Patented Feb. 13, 1940 2,190,131
UNITED STATES | PATENT OFFICE.
2,190,181
REENTRANT NETWORK
Andrew Alford, New York, N. Y., assignor to
‘Mackay Radio and Telegraph Company, New
York, N. ¥., a corporation of Delaware.
Application January 2, 1937, Serial No. 118,886
. 17 Claims. (CL 178—44)
. his invention relates to transmission modify- special circumstances the dissipation is compara-
ing networks connected between a high fre- tively high.
quency source and a load, or a passive circuit, for It is another object of the present invention to
altering the magnitude and/or phase of the provide a transmission modifying network which
g§ transmissions and/or reflections of the high fre- shall be conveniently adjustable and which shall 5
quency waves traveling between the source and have sufficient degrees of freedom so that it may
the load. In its simplest embodiment. this in- be flexibly adaptedto widely different conditions.
vention comprises a reentrant network inserted Although in the simplest applications of my in-
in a single conductor or two conductor transmis- vention the network is connectedin a transmis-
10 sion line which is connected to transmit energy Sion line between a source of alternating current 10 _
. from a source of high frequency alternating cur- - and a useful load to which the alternating cur-
rent to a load. The reentrant network may be a rent energy is to be delivered, it is also contem-
simple section of single conductor or two con- Plated that the network may be connected between
ductor line similar to the main single conductor any live circuit such as @ circuit containing both
13 or two conductor line in which it is inserted, the the source' of alternating current energy and 15
ends of this section being connected together to the useful load to which said energy is to be de-
' form a, closed loop. The energised part of the livered and any passive circuit, which need not
. Main transmission line joins into this loop at some - bé truly a load in the ordinary sense. This passive
point of its circumference. The passive part of circuit may for example, be a non-dissipative im-
20 the main: transmission line branches from this pedance whose function is to modify the distri- 99
loop at some other point of its circumference. _bution of energy in.the live circuit. In such a
The loop introduces reflections in any waves case my network serves the purpose of modifying
transmitted over the transmission line in which the influence which the non-dissipative passive
it is inserted and modifies fhe transmission of circuit exerts upon the live circuit.
25 waves along that line. The magnitude and/or The invention may be more clearly understood 25
‘ phase of the reflections and the modifications in by referenceto the accompanying drawings. Fig.
transmission depend on the circumference ofthe 1 represents a simple embodiment of my inven-
-loop in terms of wavelengths and on the relative tion in which the transmission modifying reen-
positions around the loop of the two points of trant network is connected between a source of
30 junction with the main line. In certain special alternating current and a load. Fig. 1A repre- 30
cases the circumference alone or the relative sents one particular detailed structural form of
position of the junction points alone is control~ Fig. 1
ling. Figs. 2, 3 and 4 represent alternative embodi-
A principal object of the present invention is to ments of my invention in which the network is*
35 provide a structure which may be used variously connected similarly to Fig. 1 but-in which differ- 35°
as a highly efficient transformer, filter or phase ent types of transmission liné are employed.
shifting device. Another object is to provide such. Fig. 5 represents an alternative form of Fig. 1
a structure which shall be simple, economical, and in which a transposition is used to replace a 180°
‘well adapted for application to existing construc- length of line.
40 tion. A further object is to provide such a struc- Pig. 6 schematically represents an arrangement 40
- ture which may be applied to an. existing line -whose structural form may be like any one of Figs.
without cutting the line. 1, 2,3 or 4 but whose load is assumed to be matched
One distinctive feature of. the present inven- to the surge impedance of the line. . .
tion resides in the fact that the reentrant network ’ Fig. 7 schematically represents an arrange-
45 is made up of sections of transmission line hav- ment whose structural form may be like any one 45
ing distributed constants as. distinguished from . of Figs. 1,.2, 3 oF 4.
lumped impedances. Another feature of the pres- Figs. 8 and 9 are sets of curves which repre-
ent invention is that it provides a transmission sent the intensity and position of the standing
_ “influencing network whose dissipation is ordinari- waves in such a special circuit as Fig. 6 and
50 ly exceedingly low, thus giving low losses when which may be used for determining the influences 50
the network is employed as a transformer and exerted on the transmission and/or reflection of
giving low losses and sharp cut-off characteristics waves by any of the networks in accordance with
. when the device is employed as a filter, Further- my invention. |
more, my invention provides a filter whose char- Fig. 10 is a tamily of curves which may be used
55 ‘acteristics result ina sharp cut-off even if in in determining
the influence of a network in 86
2 2,100,181
accordance with my invention, particularly when wire under the rubber insulation or. by employing
such a network is employed as a rejection filter. @ very non-hygroscopic textile or paper for this
. Fig, 11 represents a further set of curves which layer. Also the rubber should be free from hy-
may be useful in the preliminary design of a net- groscopic fillers or other materials which in-
work in accordance with my invention espécially crease the high frequency losses. If an outer
when the network is intended to reject a certain textile braid is provided over the rubber it is ad-
predetermined frequency and pass or reject cer- vantageous to varnish this braid or impregnate
tain other predetermined frequencies. it with a water resisting compound.
Figs. 12, 13 and 14 represent schematically The network of Fig. 4 is built of single-con-
10 certain embodiments of my invention in which ductor line and is connected in a single-conduc- 10
. the reentrant networks serve as filters connected tor line which might be employed for example, in
between sources of alternating current. energy feeding an antenna. —
and loads. Although these various constructions differ in
Fig. 15 represents schematically an embodi- structure and in their practical applications, they
16 mentof my invention in which a network is - may be treated together as regards the electrical
employed as a filter between an active circuit theory of their reentrant networks, Thus, unless
containing both a source of alternating current certain forms are specifically excluded, the anal-
and a useful load and a passive circuit, which ysis given hereafter may be considered as apply-
comprises an essentially non-dissipating imped- ing to any of the structures of Figs. 1, 2, 3 and 4
20 ance. as well as to polyphase or single-phase multiple- 20 -
Figs. 8A and 9A are enlarged reproductions of conductor lines and to structures comprising dif-
certain sportions of the curves shown in Figs. 8 ferent types of lines in the different branches..
and 9, The schematic representations of Figs. 6, 7, 12,
* Referring more particularly to Fig. 1, 104 is a 13 and 14 also are to be understood as represent-
25 source of alternating current, 102 isa load. This ing structures built of any type or types of single-
source and load are connected together by a sim- conductor or multiple-conductor transmission
‘ple, parallel two-wire transmission line 103, 104. line, although for simplicity the line is represent-
‘At an intermediate point in this transmission line ed by a single line in these figures. To avoid un- .
a reentrant network is inserted which comprises necessarily complicating the formulae and rules
30 the two limbs 105 and 106. These two limbs are of dimensioning, these formulae and rules have 30
composed of sections of transmission line having ben derived on the assumption that all sections
the same characteristics as the transmission line _of line in one system have the same impedance
103.and are generally of different lengths A and and, where the attenuation is significant, the
B respectively. For convenience in notation the same attenuation, but although this form is pre-
36 total perimetral length around the reentrant net- ferred structures built up of sections of line of 35
work, that is, A+B, will be represented by u different charactéristics are within my invention
while the difference in the lengths of. the limbs and may, in special cases, be advantageous. ;
of the reentrant network, which for-definiteness For. simplifying the preliminary explanations
is considered to be. A—B even if B is larger than reference will first be made to Fig. 6 which sche-
40 A, will be represented by v. ‘matically represents an arrangement similar to 40.
“The lengths A‘and B of the limbs of the net- any one of Figs, 1, 2, 3 or 4, excepting that the
work, as. well as the derived lengths wu and v, are load 602 is an impedanée whose value is the same
measured in. degrees with respect to the fre- as the surge impedance of the transmission line § ~
quency under consideration, the wavelength of 603—604. The influence exerted by network
45 traveling waves of this frequency along the trans- 605—606 upon the transmission between this
mission line being taken as 360°. It willbe noted . transmitter and load can be described in terms of
that this wavelength is twice the distance be- the vector reflection coefficient Ret of the net-'
. tween successive peaks of standing waves, and is work and its vector transmission coefficient Ge's,
equal to These vector coefficients have the ordinary ac-
50. c
cepted significance and refer to the voltage wave, ;
F so that @ zero value of 7 represents reflection
without phase change of voltage, such.as for in-
- where c’ is the velocity of propagation of the stance reflection from: the end of an open line.
traveling’ waves .along the transmission line. All phases are referred to the phase of the in-
“55 The above interpretation of the lengths A, B, u, coming wave at the point where it arrives at the
and.v is used throughout the specification. _ - network. These coefficients are given by the fol-
The structure shown in Fig. 1 is illustrated in . lowing equations in which it is assumed that k
"greater detail in Fig, 1A which shows one Par- represents the number of decibels of attenuation
ticularly. advantageous. type of construction. in 0.115 degree of line length, i. e., in 0.000320
60 This construction enables the reentrant network wavelength of line ca
to be effectively associated with an existing trans-
mission line without cutting the line. Also this Bem2G+) — 34 g-oli+) 4 Beuli+h) 4 gost)
construction permits the difference v in the Reir=s eG —3—e sD oeuH—em (1)
lengths of the limbs A, B of the reentrant net-.
Geie=
65 work to be readily adjusted without altering the es)
position of junction points 120A and without al- Achat) G+) 1 Ag Mu- od) G+) — de Mluto) 4%) — Apu 9) G48)
tering the total circumference u of the network. WG — 8 — gH FH) | Gen Fe) — guurte)
The network of Fig. 2 is constructed of two-
wire transmission line of the concentric type. — @)
70 This type of line is well known. -The network - ‘Tf, however, the attenuation coefficient is .suffi-
of Fig. 3 is made up of rubber insulated two-wire . ciently small so that it may be neglected for the —
twisted pair. This twisted pair may be ordinary frequencies of waves and lengths of wires under
lamp cord but for high frequency transmission * Gonsideration, the above formulae may be con-
it should preferably be slightly modified either siderably simplified. Setting k equal to zero and
{3 by omitting the textile layer usually served on the separately expressing the absolute magnitudes R 76
2,190,181 3
and G and their vector angles rand g respective waves, as represented by curve 628, in line 603.
yy we obtain an The ratio of the maximum r. m. 8. voltage to the
minimum r. m, s. voltage of standing waves 628,-
R= a4 cos u-+ cos v (3).
which is the Q ratio of waves 623, will hereinafter -
a cos o+-5 cos u)*+-(4 sin u)3] - -be known as the “natural standing ‘wave ratio” of
tan : 4sinu - (4) the network and will be designated by the letter
4-+ cos v-—5 cos & P. Also the distazice from a voltage maximum
of these’ standing waves 623 to the terminals 610
‘The quadrant of r may be readily determined, will hereinafter be known as the “natural posi-
0 remembering that Ris always positive as indi- tion parameter” of the network and will be desig- 10
_ cated by the absolute symbols in Equation 3, from nated by the letter p. These natural coefficients
“the following auxiliary equation — P and p are characteristicsof the network itself,
cos r_t-tcos o— 5. cos u and may be referred to even when the network is .
B 4—3 COs U—-COB Y e) connected in some more general arrangement
6. than that shown in Fig. 6. In such a case, how- 15
G=+ 1-8 (6) ever, P or p will still represent the standing wave
ratio Q or position length ¢ of the waves which
= Wr On would be produced in such an ideal arrangement
“These ‘coefficients R, 7,,G and g define the elec- as Fig, 5 and should not be taken to represent
20 trical effects of a loop network according to my the Q ratio or position coefficient of the waves 20°
invention'in terms of reflection and transmission which are actually produced in the more complex .
regardless of whether the ne in which the loop arrangement wherein the network happens actu-
sis connected contains other points of reflection ally to be connected.
or not.. If however the system which contains Since the value of Q of the waves 623 in the
25 the network is a simplified arrangement such as special arrangement of Fig. 6 is equal to 25
shown in Fig. 5, then these coefficients may be
very simply interpreted to directly represent the
A+R
1-8
waves traveling in lines 603 and 604. Assume for the natural standing wave ratio for any network
example that the total forward wave entering the is
30 network 605—606 has a unit amplitude and a 30
zero phase at the terminals 610, then the total
backward wave along line 603 is Re", Also the
Pai“4 tsR )
total forward wave along line 604 is Ges, These Similarly ‘since the postion coefiiclent qa of the
phases refer respectively to the phase of the wave - standing waves 623 in Fig.6
as it leaves terminals 610 and 620 and are meas-
ured with respect to the phase of the forward 2
wave incoming: to the network at terminals 610. the natural position coefficient of the network is
. Even when the network is connected in some
more general arrangement than that of Fig.’ 6
Geile and Re" represent the transmission and re-
p=y 8)
flection coefficients in the usual manner, though. - The ‘curvessof Fig. 8:and Fig. 8A show how the
the above described simple relationship between value of P varies with the perimeter u of the net-
these coefficients and the total forward and back- _ work, the difference. in length-» between the
ward waves no longer holds. : limbs of the network being kept constant for any
If we consider as standing waves not only those one curve.. From these curves it is possible to
“pure” standing waves whose minima are zero find the value of P for any given values of the:
‘put also those. whose minima have definite values, dimensions u and v. Similarly the curves of Fig.
we may find it convenient to define the ratio of § and Fig. 9A show the variations of p with the
the maxima and minima. ‘For
any. standing variations of the perimeter uw, v again being kept
50 ‘wave the ratio of the maximum r, m, 8. voltage, constant for any one curve. From this family. 50
‘measured at the voltage antenodes, to the mini- ‘of curves it is, therefore, possible to find the
‘mum r. mM. s. voltage, measured at. the. voltagevalue of » for any given. values of network dimen-
"nodes, is hereinafter called the “standing wave sions wand 2.
ratio” or “2. ratio” of the ‘wave and is Aesignated Conversely any desired value ‘of P may be
55 by Q. . obtained by properly adjusting the dimensions u 55
Because of the greater facility with which and v. . For example, to obtain a value of 7.0 for
standing waves can be measured it is for many P in any network we may dimension the network
purposes more convenient to define the properties so that u=121° and v=-90°; or so that u==88° and
‘of a reentrant network in terms of standing v==100°; or so that u==33° and v=100°, etc. -
60 waves rather-than by its reflection and transmis- These primary sets of values are obtained with-
sion coefficients—which refer to traveling waves. out interpolation from the successive curves of
or traveling wave components. Use is therefore Fig. 8A which correspond to the left lower portion
made: of. two ‘auxiliary’ coefficients called the of Fig. 8 but are drawnto a larger scale. By .
“natural standing-wave ratio” of the network and . interpolation an infinite number of such primary -
2
sets of dimensions can be obtained. Further- |
the “natural-position parameter” of the network.
These characteristics of any network may most more, each of the sets of primary values ob-
conveniently be defined by supposing that the tained from these curves or from interpolation
‘network is connected in an arrangement such as has associated. with it an infinite number. of
shown in Fig. 6 in which the load is matched to.. “equivalent” values. For example, in the first
70 the surge impedance of the transmission line. set of primary values given above u=121°, 70
In this arrangement, which is assumed for analy- v=90°, there. may be used for u any one of the
. gis, there will be no reflections from the load 682 values 121°, 239°, 481°, 689°, 841°, etc., obtained
and hence no standing waves in the line 664.. In. ‘ from. Nx 360°121° and. similarly there may be
general, however, there will be standing waves in used for » any one of the values 90°, 270°, 450°,
75 each of the limbs 605 and $06 and also standing | etc., obtained from x30" OO". 15
4 2,190,181
Examining all the above sets of values for u is equal to p; then the standing wave ratio Q
and v, it will be noted that some of these sets of of waves 7168 will be equal to
values are not physically realizable with real
PL
or
positive lengths Aand B. Referring to the third
primary set of values (w=33°, v=100°), for ex- L™P
ample, it is impossible to construct a network whichever is larger. Alternatively the network
whose perimeter has a length of 33° and whose may be positioned so that the distance between
two limbs differ in length by 100°. In such a case its terminals 120 and a voltage peak of wave
use is made of one or more of the “equivalent” 124 is equal to P+90° in which case the Q ratio
10 values above mentioned. For example, by se- of waves 123 will be equalto PL. 10
lecting a u of 327°, which is equivalent to a w of If it is desired to give waves 123 a2 smaller
33° as above noted, and by retaining the value of standing wave ratio than waves 124, the first
100° for va physically realizable set. of dimen- mentioned location of the network must be used.
sions is obtained. Such a network would, for ex- On the other hand, if it is desired to give waves
ample, have a length, A, of 213.5° and a length, 123 a very high standing wave ratio, the second
B, of 113.5°.- However, a great number of the mentioned position may sometimes be more con-
structures which may be read off directly from venient.
the curves, including many of the best ones from | In the most usual application of this embodi-
a practical standpoint, are physically realizable ment of my invention the network 705—106 is
~ 20 without any replacement of wu or v by equivalent adjusted so that waves 123 will be completely ~
values. For example, the first set of primary eliminated, i. e., will have a Q ratio equal to
values previously mentioned (u=121°, v—90°) is unity. To-obtain this result the network should
physically realizable. Generally the region to be so adjusted that its natural standing wave
the right of the small circles in Fig. 8A repre- ratio P is the same as L, the standing wave ratio:
28 sents sets of values which are physically realiz- Q of waves 724, and should be located in the
able without resorting to equivalents. first mentioned position so that its terminals 720
There is another set of equivalent structures are at a distance p from a peak wave 724.
which may be obtained by the. use of a trans- By this adjustment of the network,.waves 123
position in one of the limbs of the reentrant net- will be eliminated. Thus, the impedance of that
30 work. Since a transposition in any limb is portion of the circuit beyond terminals 710 will
equivalent to.a delay of 180° it is possible to short- be the same as the surge impedance of the trans-
en the length of some of the structures by re- mission lines, or in other words, the total im-
_placing 180° of physical length by a transposition. pedance. of. the network together. with line 104
For example, the structure referred to above in and the load 702 will be equal to the surge im-
which A=213.5° and B=113.5° may be replaced pedance of line 703..
by a structure in which A=33.5° with a trans- In certain casés it may be desired’ to adjust
’ position and B=113.5°. A structure which in- the network so as to act as a transformer hay-
cludes such a transposition but which is other- ing a ratio different from that required to match
wise similar to Fig. 1 is illustrated in Fig. 5. ‘the load to the line. In other words, it may be
The use of a transposition
plicable to networks built of two-wire line such
is particularly ap- desired, insteadof matching the load to the trans-
mission. line, to introduce a deliberate amount
40
_ a8 shown.in Fig, 1 and to twisted wire lines such Of mismatch for some purpose. In this case it
as shown in Fig, 3: Other phase changing © is merely necessary to express the desired mis-
means may also be employed to replace part of match in terms of the standing wave ratio de-
45 the physical length of the network, but the trans- sired in waves 123. Then by the use of the —
a position is particularly desirable becauseof its above rules for proportioning and positioning the
simplicity and its freedom-from reflections at network the waves 123 may be caused to have
all frequencies. the desired Q ratio.
In one very useful embodiment of my invention “In addition to its use as a transformer the re-
‘50 a reentrant network as illustrated in Fig. 7 entrant network structure of my invention may !
serves, in conjunction with certain portions of also be adjusted to act as a cut-off filter. In
the transmission line 103—-104, as a transformer. other words, the network may. be adjusted so
In this figure, 101 represents a transmitting that for one particular frequency ~its natural
equipment; 103—104 a transmission line connect- standing wave ratio P is substantially. infinite.
BB ing that transmitter with a load 702 and 105-—-106 In terms of the reflection and transmission co- °:
oO
=
a network inserted in this transmission line. Tf efficients this means that R==1 and G=0. The
.the load 192 is not exactly matched to the surge frequency at which the cut-off takes place will
impedance of the transmission line there will be - be referred to as the cut-off frequency and
standing waves 724 dependent on the mismatch will be designated by F. At certain special other
60 of the load in the portion 104 of the transmission ’ frequencies the network will again cut off as will co
line. Also, in general, there will be standing be more fully described in connection with Fig. 12.
waves. 123 in the portion 103 of the transmission “In general, however, at a frequency f, which is
line, ‘ not the cut-off frequency F, the filter will trans-
In accordance with the present invention the mit more or less satisfactorily. -
dimensions of the reentrant network 105—106 The conditions: for cut-off are substantially
may be so adjusted that standing waves 123 will . satisfied either when u=360°, or 720°, 1080° etc.,
or when 0== 180°, or- 540°, 900° etc., and especially
have any desired Q ratio. Let the Q ratio of
complete cut-off occurs when both. these condi-
the given standing waves 124 which are produced
ticns are‘simultaneously satisfied.
' 70| “py the load be represented ‘by, L. ‘The natural The cut-off networks. having v=180° will be 70
standing. wave ratid and the natural position pa- referred to as “difference”. filters and the net-
rameter of the network ‘are P:and p. Now the works having —360° will be referred to as “sum”
network may.be positioned along the transmission filters. The special network which has. u==360°
'‘ line so that the distance between its terminals ‘and v=180° and which is thus.a stim filter as
15 120 and a. voltage peak of standing waves 124 well as a difference filter will be referred toasa 75
2,190, 181
“hybrid” filter. Although this hybrid filter is sent sum filters which have a u of 360° at ‘the
theoretically a sum filter as well as a difference cut-off frequency F. The first four curves, re-
filter it is, in the following discussion, considered spectively, represent filters whose v at the cut-
to be excluded from each of these classes; thus off frequency is 60°, 120°, 180°, 240°. ‘The addi-
general statements as to the properties of sum tional curve, designated as 60--#, represents a
and/or difference filters are not ‘considered as sum filter whose perimeter has a physical length
applying to the hybrid filter unless it is specifi- of 180° and whose limbs differ in physical length
cally included. _by 66°, the longer or the shorter limb of the
The transmission and refiection coefficients of filter being equipped with a transposition so that
10 all these three classes of filters are given by Equa- the effective. value of u at frequency F is 360° 10
tions 1 and 2 as set forth above. while the effective value of v at the cut-off fre-
Fig. 10 shows a set of curves which directly quency F is 240° or 120°. .It will be noted that
represent the coefficient G in terms of frequency the curve of the filter 60-+-# is very different from
for filters of the sum and hybrid types. In these the curve marked 240° although at the cut-off
15 curves the attenuation is assumed to be .043 deci- frequency itself, both curves represent filters hav- 15
bel per wave length of line (i. e., 0.0000137 deci- ing a. u of 360° and 2, » of 240°. The reason for
bel per 0.115 degree length of line which corre- the divergence between the two curves is, that as
spond to k=0.0000137). This attenuation is of the frequency is varied from F the transposition
the order actually found in ordinary open-wire which is designated by # continues to represent
20 transmission lines. A simple, parallel, two-wire @ fixed electrical length, namely 180°, whereas a 20
line structure of number 6 A. W. G. copper clad length of wire which at frequency F represents
‘steel wire with a 12 inch spacing, for example, 180° will vary in electrical length as the fre-
has an attenuation of approximately 1 decibel quency is changed.
in 2000 feet at a. freqiency of 10 megacycles. It will be noted in general that a simple sum
25 Since the wavelength at 10 megacycles is approx- filter will cut off not only at the nominal cut-off 25.
imately 95 feet, this attenuation amounts to very frequency F but also at 2F, 3F, 4F, etc. Similarly
nearly 043 decibel per wavelength. This value a difference filter generally cuts off at 3F, TF, etc.
for attenuation, moreover, will not vary. rapidly -In order to cut off at F.and yet pass 2F a sum
with frequency because as the frequency is in- filter. may be used having a transposition. such
30 creased the attenuation per foot,of wire also in- that w= 180°+# and v= 60+4-#, or u=180°-+# 30
creases; at the same time the number of feet per and »=90°+-#. Or a difference filter such that
wavelength of line becomes smaller so thatto a ‘t= 230° and v=180°, or a hybrid, may be used. |
certain.extent these two changes counteract each If it is desired to cut off F and pass 3F a sum
other. Thus, the curves of Fig. 10 fairly accu- filter with a transposition or a sum filter whose
35 rately represent the transmissions through a sum . value of v is such that 3v—N360 where N is any
or: hybrid filter in the nefghborhool of the cut-off integer, may be used.
frequency for all frequencies between 6 and 16 In some cases the above described multiple cut
megacycles. From Equations 1 und 2 it is possi-
ble to plot a corresponding set of curves for the
off properly may be used to great advantage.
network which is particularly useful for passing
A
difference and hybrid types of filters. Also simi- frequency f while suppressing the principal har-
lar sets of curves for sum, difference and hybrid ‘monics of /, for example, can be constructed by
filters may. be plotted using other values of k . making u=180° and v=60° at frequency f.
than that assumed for Fig. 10. For coaxial lines Then at 2f w=360°, at 3f v-=180°, at 4f u='720°.
the attenuation is ordinarily higher and, there- ‘Thus the second, third and fourth harmonics are
fore, typical curves for this type of line would eliminated.
show a somewhat broader cut-off. For the From this Figure 8 it is apparent that when-
twisted pair lines also attenuation would ordi- ever u==360° then p=0°; which means that the
narily be. higher. cut-off frequency voltage maximum always occurs
In the regions more remote from the cut-off at the terminals of sum or hybrid networks.
50 point the transmission and reflection coefficients. Since the reflection of waves at the cut-off fre-
may be reasonably accurately calculated from quency is very nearly complete it follows that the
the approximate Equations 3, 4a, 5 and 6 instead ‘impedance looking into such networks at the cut-
of from the more complex Equations 1 and 2.- off frequency is extremely large in comparison
Generally, moreover, in the regions remote from. with the surge impedance of the line. This prop-
55 the cut-off the primary interest is in the natural . erty is independent of the value of v of the par-
standing wave ratio P since in this region the ticular network and is a characteristic of hybrid
problem is one of passing another frequency / networks and of all sum networks with one excep-
without developing standing waves of high Q tion, namely, those which have v—0°, 360°, ete.
ratio, which would result in comparatively great Such networks are not cut-off networks at all.
losses. In’ this region remote from the cut-off The filter networks of my invention may be
point, therefore, Figs. 8 and 8A serve to indicate used for a variety of purposes. For example, Fig.
the behavior of the network at frequencies which 12 shows a system in which two high frequency
-it is desired to. pass. If, however, it is desired transmitters 1201 and 120!’, working on two dif-
to visualize clearly the pass characteristics of a ferent frequencies f and f’, are connected to the.
given filter or if the problem of designing filters same antenna 1202. In this figure reentrant net-
is to be facilitated it may be convenient to plot works 1205—i206 and 1205’ and 1206’ are utilized -
a-set of curves such as shown in Fig. 11.. The for the purpose of minimizing the interference
curves of Fig. 11, like the curves of Figs. 8 and between the two transmitters. Network {205—
8A, represent the value of the natural standing 1206 is designed so that its perimeter wu
wave factor P. But instead of being plotted equals 360° at frequency /’ delivered by trans- 70.
against uw these curves are plotted against ‘the mitter 1201’, while network 1205’—1206’-is de-
value of frequency F (expressed in terms of the signed .so that its perimeter is equal to 360° at fre-
cut-off frequency. F taken as unit frequency). quency f delivered by transmitter 1201. 'Thus
Also, the curves ef Fig..11. are drawn to loga- reentrant network 1205—1206 does not allow fre-
rithmic scale. ’ All the curves of Fig.:.11 repre-. quency f’ delivered by transmitter 1201’ to enter 75.
S 2,180,132 ; -
transmitter (201. At the same time, however, depends on the value of v and in difference filters
this network passes frequency f coming from on the value of uw. Thus under some circum-
transmitter {20{ wtihout unduly serious refiec- stances it may be unwise to select a set of values
tions. A matching network schematically repre- which gives a very low standing wave ratio on line
sented by 1215 is placed between the transmitter 109, if at the same time these values result in an 5
-and the network (205—{206. This matching net- insufficiently complete cut-off. A :compromise
work is designed and positioned according to the _ must be effected..
principles previously explained so as to match the For example, in network {365—1{366 the amount
surge impedance of transmission line 1214 to the of filtering which is required is usually not nearly
10 impedance resulting at terminals {216 of network as high as would be required in network 10
1205—(206 at the frequency / of transmitter 1204. 1305’—-4306’. On the other hand, in line sec-
Similarly reentrant network {215’ matches the tion 1303 the standing wave losses would be of
impedance resulting at terminals (2108’ of net- more moment than the losses in the section of .
work 1205’—1206’ to the surge impedance of the Tine 1303’, Thus in actual practice the network
16 transmission line 1214’, {305’—-1386’ would usually be designed so as to
The distance between network {215 and net-. have maximum or nearly maximum cut-off and
work (205—{206 will, in accordance with the rule with only minor regard to the standing waves and
previously given for positioning matching net-. the losses which result therefrom on line §3023’,
works, be simply the natural position parameter while network 13905—13@6 in the same arrange-
20 p of network 12/5 plus the natural position pa-~ _ ment would be designed to provide a less complete 20
rameter p of network {205—(206 both computed cut-off but with greater consideration to the losses
with respect to frequency f. . Preferably network in line 1303.
{215 is designed so as to also to act as a cut-off Fig. 14 represents a system in which a reen-
filter for frequency f’ thus providing double filter- trant filter network is utilized for stabilizing the
25 ing. Usually this is most conveniently accom- frequency of an oscillator. In this figure {430
plished by making networks 1215 and 1205—(206 is an oscillator adapted to generate a high fre-
identical to each other. In this case the distance quency, for example-100 megacycles, and con-
between these networks will be twice the natural nected by means of coaxial line {431 to an ampli-
position parameter p of either network at fre- fier 1432. The output of this amplifier is con-
30 quency f. Similar considerations hold with re- nected over line {433 to a radiating antenna 30
spect to networks 1215’ and {205’—1206’. {434.. A smali portion of the energy delivered to
The distancez should be such that at frequency line (433 by amplifier 1432 is diverted into the
f’ the impedance of line {204, with all the struc- branch line #403—{404 in which the network
ture connected to it, will be substantially infinite {405—i406 is connected. The current delivered -
35 as seen from. junction point 1250. If network by line 1404 after detection in diode 1435 is passed
1205-1206 is a sum or hybrid filter x should be through resistor 1436. The voltage thus devel-
0°, 180°, 360°, etc. If; however, this network is oped across this resistor, after smoothing in fil-
a difference filter the natural position parameter ter ‘{437, is applied across a portion of the oscil-
p of the network at frequency f’ must be com- lator circuit suitable for controlling the oscillator
puted. Then x should equal this p, or should ex- . frequency. .Heater 1407 is connected through 40-.
40
ceed it by an integral number of half wavelengths. thermostatic control 1408 to a source of power
Fig. 13 shows an arrangement similar to that of 1409.
Fig. 12 except that one of the transmitters has The operation of the device of Fig. 14 is as fol-
been replaced by a receiver. The networks lows: The reentrant network is adjusted so that
1305—i1306 and 1305’—1306’ enable simultaneous the perimeter u is nearly equalto 360° at the 45
operation of the transmitter and receive without assigned frequency of the oscillator, preferably
‘ interference with one another. Or either may be so that the frequency which is cut off by the
" used individually. network is slightiy different from the assigned
The networks utilizedin such arrangements as frequency of the oscillator, for example, just be-
shown in Figs. 12 and 13 should be designed in low this assigned frequency. The heating. wires 50
such a way that the standing waves which they {407 in conjunction with thermostat 1408 main-
cause at the transmitted frequencies are not so tain the temperature of the limbs of the reen-
‘intense as to cause either great losses due to cir- trant network nearly constant so that the cut-
‘culated currents or undue voltages on the various off frequency will remain substantially the same.
limbs of the networks or in lines {203 and 1203’ The v of this network is made small, for example,
or {303 and 1303’. That is, the designof net- 30°, so. that the network would be relatively com-
_ work 1205—!206 should be such that the standing pact. In accordance with Fig. 10 it may be seen
waves in line section 1203 have a sufficiently low that the amount which a sum filter transmits
Q ratio. varies very rapidly with the frequency in the
60. andIn current
order to avoid the danger of rise in voltage neighborhood of the cut-off frequency. For this 60.
along the section of transmission line reason in the arrangement of Fig. 14 the total
{210 it is desirable to select the constants of. net- amount of current which is transmitted to de-
‘ work !205—i206 in such a manner that the tector 1435 will depend in a critical manner on
amount of reflection at its terminals at the pass- the frequency of oscillator 1430. If the cut-off
65: ing frequency .is relatively small. In practice, ‘frequency of the reentrant: network 1405-1406 65
however, I have found that standing wave ratios lies below the normal oscillator frequency, then
_ of the order of 7 or lower are entirely practical. as the latter increases the amount of current
By means of curves like those of Figs. 10 and 11 it transmitted to detector. 1435 increases and vice
is possible to choose for any given frequency ratio -versa. Accordingly, the direct current output of
70. a set of values of zu and v which results in a stand- the detector which is carried by wires 1438 to the
ing wave ratio Q of 7 or less. oscillator also decreases and increases in accord-
. When choosing the value of u and’v under ance with the fluctuations of the frequency de-
these circumstances it is well to keep in mind that livéred by the oscillator. This direct. current
the completeness of cut-off which may be ob- which is carried by wires 1438 may be applied to
% tained at the cut-off frequency, in sum filters, vary, for example, the grid voltage of the oscil-- 15
2,190,181 T
lator in a well known manner in order to affect ‘from the voltage maxima position noted in ‘step
the frequency delivered by it. In this manner the one is M as measured in step three.
frequency of the oscillator may be decreased when Now it will be found that there are substan-
the oscillator is drifting upwerd in frequency tially no standing waves between junction 1545
and vice versa, whereby the frequency of the and source {501 either at frequency F or fre-
oscillator may be kept: substantially constant. It - quency f. If it is desired to still further reduce
will be clear from the above discussion that it is . any slight standing waves.that may be present
not necessary in order to carry out the above the perimeter u of loop 1505—1506 may be slight-
control of frequency by means of a reentrant net- ly changed to eliminate the standing waves of |
10 work such as 1405-1406 to have all of the ele- frequency F, and then the length of line 1504 10.
ments shown in Fig. 14. In fact, for example, it and/or the position of junction {545 may: be -
is not at all necessary to have an amplifier. ’ slightly adjusted to eliminate waves of frequency
In each of the above described embodiments }. The impedance 1602 is preferably a short cir- -
of my invention the reentrant network has been ‘cuit. The length of line 1803 is preferably zero.
15 connected between a source and a load. This is One reentrant. network may be used to neu- 15
not essential to all applications of my invention. tralize standing waves caused by another reen-
Fig. 15 shows a network 1505—-1506 connected. trant networkin the same. way in which a reen-
between a live circuit and a passive circuit. The .trant network may be used'as a matching trans- . -
live circuit comprises source 150! connected over former to match the impedance of.a load to the -
20 ‘line {540 to load (541. The passive circuit com- surge impedance of a line, i. e., to eliminate the 20
prises reactive impedance 1502 which dissipates. standing waves caused by a mismatched load.
no power and is therefore not truly a load. This Such arrangements have alre&dy been described
impedance is connected to some point of line - in connection with Figs. 12. and 13 in which at
1540 by line 1§03—-f504. The network [508-—I506 least one of the two mutually neutralizing net-
25 modifies the influence exerted by 1502 on the works served as a filter for cutting off an unwant-
waves transmitted from source 150! to load 1540. ed frequency. Such a pair of networks which
This structure is used as follows: source 1601 ‘mutually neutralize each other’srefiectorsatsome »
delivers two different frequencies F, f simulta- given frequency is hereinafte: x referred to as a.
. neously or successively. Matching device 1542 is conjugate pair with respect to that frequency.:
36 adapted to match load (54f to line (840 at fre- _ Expressed in other words a conjugate pair of net-.
quency F.. This device may for example be a re- works is a pair which {s connected in a reftection-
entrant network dimensioned and positioned for less line like that of Fig. 6 would cause no. re-
simple matching at one frequency as previously flections except inside the networks themselves
explained... Network 1505 is adjusted as a sum and in the section of line between them.
35. filter to-cut off frequency F so that the waves of ‘Two networks are conjugate if the P of one
that frequency are unaffected by adjustments of equals the-P of the other and if the distance along
the position or length of line 1504 nor by adjust- the line between the closest: terminal of the net-
ments in the impedance of {602.: Line [503 Is ‘ ‘work is equal to the p of one network plus the
made 0°, 180°, 360° etc. in length at frequency F p of the other. Since the conjugacy of two net-
40: so that at that frequency line (503 will have an ‘works depends not only on the dimensions of the
infinite impedance as measured at junction (846. networks but. also on. their. relative position’ it
Now the length of line (604 is adjusted, thus will be useful to consider the two networks of a
varying the impedance at frequency. / of branch conjugate pair together with the section of line -
1503—(504 as seen from junction (646. Also the between: them as a unit having for two conductor
position of junction 1848- along line ¢540 is ad- lines two input terminals and two output termi-
justed. By-these two adjustments the impedance nals, or in the case of single conductor line, one
of all the structure beyond junction 1846 may be input and one ‘output terminal. Such a com-
matched at frequency f to the surge impedance plete unit will be called a “complete conjugate
of line 1440. In other words the standing waves ne Lid
50 of frequency f in that portion of Iine (540 be- -A complete conjugate net may be used to
tween source. 150! and junction 1846 may be change phase of forward or backward traveling - .
eliminated. This may conveniently be performed waves without changing the magnitude of these.
by the following steps. First the Q ratio of stand- waves. The total phase delay due to insertion of.
ing waves of frequency f in line f 840 between a complete conjugate net ig 180° minus the length: .
55 matching device 1542 and junction {548 are of the section of line which: joins the two. reeti-: os
measured or computed. This is the Q ratio of trant networks and together with them’ con- ~
those standing waves which are caused by the stitute the complete conjugate net. -In other.
device {542 and the load (843. The position of words if we call the insertion delay D and repre- .
voltage maxima of these waves are also noted.
sent the natural position parameters. p of the
60 _ Second, line 1840 is cut-open between junction component reentrant networks by 7: and pz, then 60.)
D=180°—pi—m._ Ordinarily of course the reen- -
1545 and matching device 1542, and the cut end
trant networks are applied to a line without
of this line is connected to a load equal to the
“eutting the line as shown in Fig. 1A. In such a
* surge impedance, of, the line so to terminate the case the phase delay introduéed by adding the two
line ina reflectionless manner. Third, the effec- can be computed by {mag- 65 -
65 ‘tive impedance of line 1808--1504 is adjusted by conjugate networks
ining that a piece of line as long-as the over-all
varying the length of line 1504 until the.standing Jength of the complete conjugate net is cut out
- waves. between junction (545 and source (80! and then the complete conjugate net is inserted.
‘have a Q ratio equal to thé Q ratio which was Usually the over-all length of the complete con-
70 measured or computed in the first step. The dis- _ jugate net will be 2:-++-2-+-8:-+28; where B: and 70.
tance M of a voltage maximum of these standing’ Bz: are the lengths of the shorter sides of the two:
waves from junction (545 is also noted.. Fourth, reentrant networks which are comprised in the:
the reflectionless termination used in step two is complete conjugate net. ‘In such a case the phase
removed; the cut line is reconnected; the junc- delay introduced by. applying the networks is
re) tion point 1645is adjusted so that its distance 180°—2p1—2p2—Bi—Ba. 6.
8 2,190,181.
A complete conjugate net may y also be used to account of attenuation by replacing 7 by j-+-k
introduce a desired amount of reflection at one in the equationsas above written. It should be
frequency without introducing any reflection at noted that the actual maximum voltages in the
the frequency for which it is conjugate. The limbs may be far lower than the limits a and b
complete net taken as a whole may be consid- if it happens that a voltage peak does not fall
ar
ered as a unit which has a natural standing wave within each limb. Also if the atenuation is ap-
ratio P and a natural position parameter p of its preciable the actual maximum voltages will usu-
own. The P and p of the complete network will ‘ally be slightly lower than-these limits even if
be designated by Pz and g3 respectively; the P Equations 10 and 11 are corrected for attenua-
~ 10 and p of the component network which is nearest tion. By use of Equations 9, 10 and 11 it is 10
to the source will be designated by Pz and 73; © possible to avoid so dimensioning the reentrant
which the P and p of the other component net- networks of my invention, that intolerable poten-
work which is nearest: the load or passive im- tials or power losses occur in the networks.
pedance may be designated by Pi and p91. The In connection with the preceding description
distance between the nearest terminals of the it should be understood that the sources and loads
component networks is designated by S.. All dis- may be interchanged in accordance with the well
tances are in degrees at the frequency under con- known reciprocity rule. For example, in Fig. 12
sideration which is usually not the conjugate the radiating antenna may be employed as a
frequency. coliecting antenna and the two transmitter equip-
20 ments may be replaced by receiver equipments 20
Pyswtyw—-1
having the same terminal impedance.
where w is given by While I have described. particular embodiments
of my invention for purposes of illustration, vari-
wea Pte )(Ptp)- a(R BMP 4) ous modifications and adaptations thereof, occur-
25 cos (2S —2pe— 2p) ps=R(re+ m) - ring to one skilled in the art may be made within
the spirit of the invention as set forth in the
where m is given by appended claims.
2Pon sin (28—2p.—2p1) I claim:
30
tan m= (pa— 1) —n eos BS—2m—Bpid) 1. A filter network for use at a given high fre-
quency in cooperation with a frequency line com- 30
the quadrant of m being such that sin m has
- prising a closed loop conductor having two termi-
the same sign ¢ as sin (2S—2p2—2p1)
nals connected to said line at spaced points there-
__(P2+)) (P?—1) by forming two parallel paths through said loop
~(Pi—-1) (PP+D the sum of said paths in electrical degrees at
A complete conjugate net which is conjugate at said given frequency being 360 and the difference
cs
oT
- frequency F and which has a desired Ps at fre- between said paths being other than zero elec-
-quency f may be substituted in Fig. 15 for the trical degrees.
branch line. {503—1504 containing network 2. A filter network for use at a given high fre-
1505—1506. The complete net is inserted in quency in cooperation with a high frequency line.
- series In line 1540, which can actually be accom- comprising*a closed loop conductor having two 40
plished without cutting line 1540; Becauseof the - terminals connected to said line at spaced points
conjugacy at frequency F the matching which thereby forming two parallel paths through said
has been effected at that frequency by device 1542 loop, the difference of said paths being 180 elec-
is not disturbed. Yet by adjusting the Ps of the trical degrees at said given frequency.
complete net at frequency f matching may be 3. A high freqency transmission circuit com- 45
effected at this frequency in accordance with the prising a two-wire transmission line, each wire of
rules previously explained for matching by means which has at corresponding points serially con-
of a single reentrant network. nected therein a closed loop conductor in such
For the various applications of reentrant net- manner that two parallel paths of unequal
-works according to my invention the waves circu- lengths through said loop are presented. 50
lating around the reentrant loops themselves may, 4. A high frequency transmission circuit in ac-
in exceptional cases, considerably exceed the ‘cordance with claim 3 wherein the total length of -
waves in the main transmission line, thus mak- said loop is 340 electrical degrees at a frequency
ing it desirable in some cases to consider these _ which it is desired to cut off.
waves. The fraction H of the total transmitted . 5. A high frequency transmission circuit in 55
power which is dissipated within the loop is given accordance with claim 3 wherein the difference
by between the two parallel paths of each loop is
H=1—R?—G?, (9) 180 electrical degrees at a frequency which it is
desired to cut off.
This fraction H may be evaluated in any given 6. A high frequency transmission circuit in- 60
‘case by computing the values of G and R from cluding a two-wire transmission line having.a
Equations 1 and 2. The upper limits of the matching device connected thereto for matching —
voltages which may be built up at voltage maxima the impedance of the line to that of a translating
within the loop are given very nearly by the fol- . device said matching device comprising a closed
lowing equations in which a is the uper limit of loop conductor connected serially between each of 65
65
voltage within the limb whose length is A, b is the said wires and said translating device, thereby
uper limit of voltage within the limb whose length forming two parallel paths through said loop,
is B. the sum of said parallel paths being other than
_ [4 2e-s— Dei] + 14 — Ge. ei] 360 electrical degrees at the frequency for which
70 or Ble + 9e-#—72—
Derr —De-F] £10) a@ match of impedances is desired and the differ-
ence between said paths being other than 180
|4-- 2e~iu— Qe? 4 |4— Get Qe-ir] electrical degrees at said frequency.
b |Sle™+ Dei — 72— Dei? — De-F*| (12)
7. A high frequency transmission system com-
In Equations 10 and 11 the attenuation is neg- prising a first transmission line, a second trans-
rf) lected but the equations may be corrected to take ‘mission, line connected thereto, and a reentrant 75
2,190,181 9
transmission modifying network forming two first point to a second point and a transmission
paths. of unequal length operatively associated ‘modifying means associated therewith compris-
* with each of said transmission lines. . ing a second coaxial cable having a different elec-
- 8. A high frequency transmission system com- trical length. than said first coaxial cable: and
prising two separate sources adapted to supply a connected in parallel therewith. 5
' first frequency and a second frequency, respec- 13. A high frequency circuit comprising a
tively, a common load for said two sources, a source, a load, a transmission line connecting
separate transmission line for conducting energy said source and said load, an impedance and .
from each of said sources to said load, and a: means including a reentrant network having two
10 transmission modifying reentrant network oper- arms of different length for interconnecting said 10
atively forming two paths of unequal length impedance and said line.
operatively associated with each of said trans- 14. A transmission line adapted to carry waves
mission lines. of two different frequencies, two closed loops
9. A high frequency transmission system in ac- | serially connected in said line, the dimensions
1 cordance with claim 8, wherein said reentrant and spacing of said loops being so interrelated. 16
networks each comprise a closed loop conductor that no reflections are caused at one of said
serially connected in said associated transmission given frequencies in those portions of the trans-
line, thereby forming two parallel paths through mission line outside said two loops, while at the
said loop, the sum of said paths of the loop asso-. same time a desired reflection is produced at the .
ciated with the transmission line carrying said other of said given frequencies in one of said 20
first frequency being 360 electrical degrees at outside. portions of said line.
said second frequency and the sum of said two 15. A high frequency circuit comprising an os-
parallel paths.of said loop conductor associated cillator, an output circuit therefor, two parallel
with. the transmission line carrying said second paths of different lengths adapted to conduct
energy from said output circuit to a common
frequency being 360 electrical degrees at said first.
frequency, the difference between the paths of junction point and means for controlling the fre-
each of said loop conductors being other than quency of said oscillator in accordance with the
180 electrical degrees at the frequency carried . energy received at said common junction point.
by. the transmission line in which it is connected. 16. A high frequency cireuit comprising a two-
10. A high frequency circuit comprising a con- wire transmission line for transmitting energy. 30
ductor adapted to carry a high frequency cur- from a first pointto a second point and trans-
rent and a transmission modifying network mission modifying means associated therewith
therefor comprising a single conductor connected comprising a second transmission line of differ-
to said conductor at two spaced points said single ent length than said first line connected in par-
conductor being longer than the part of said first allel therewith, said second transmission line 35
named conductor between said space points. -having phase'shifting means therein.
11. A high frequency circuit comprising a ‘17. A high frequency circuit. comprising a two-
transmission line for transmitting energy from wire transmission line for transmitting energy
a first point to a second point and transmission from a first point to a second point and trans-
modifying means associated therewith compris- mission modifying means associated therewith
ing a second transmission Hne of a different comprising a second transmission line of different
length from said first line connected in parallel length than said first line connected in parallel
therewith.. therewith, said second transmission line having
12..A high frequency cireuit comprising a co- a transposition therein.
& axial cable adapted to transmit energy from a ANDREW ALFORD.