US2258974A

US2258974A - Wave transmission network

Info

Publication number: US2258974A
Application number: US238965A
Authority: US
Inventors: Clarence H Dagnall
Original assignee: Bell Telephone Laboratories Inc
Current assignee: AT&T Corp
Priority date: 1938-11-05
Filing date: 1938-11-05
Publication date: 1941-10-14
Anticipated expiration: 1958-10-14
Also published as: GB532619A

Description

WAVE trnsirslvnssron Nn'rwonn L .iY i

v Clarence E. Dagnali, West Orange, N. J., assigner to Beil eiephone Lahoratcries, incorporated, New York, N. Y., a corporation of New Yer Application November 5, 1938, Serial No. 238,965 f (Cl. ITS-4.4.)

V 17 Claims.

This invention lrelates to Wave transmission and more particularly to frequency-selective transn mission networks.

An object of the invention is to transmit freely -waves falling in one band of frequencies while attenuating waves falling in another band or other bands of frequencies.

Other objects are to increase the discrimination between the transmitted hand and the attenuated band in a frequency-selective transmission network and to reduce the cost and size oi such networks, especially those designed for use at high frequencies.

Another object is to provide for the parallel operation at one end of two or more selective transmission networks each of which will freely l transmit waves falling in a selected band of ire- -quencies While attenuating Waresl of the frequencies transmitted by the other network or networks. l A. further object of the invention is to permi the simultaneous operation on the same antenne.

of two or more translation devices, such as transmitters or receivers.

1f a section of transmission line or other four-v terminal transducer having s. phase ,.hiit equal approximately to an odd multiple of 90 degrees at a certain frequency is shnnted at one end oy an impedance branch which has a low impedance at that frequency, the other end of the line section will present a high impedance at this frequency.

by adding onevor more sections of line similar to the rst, each with a shunt impedance branch of ythe type described connected at its outer end. Each additional line section and associated shunt branch will increase the discrimination by as much as 32 decibels. 1f two or more networks of this type are to be operated in parallel at one end it is desirable to terminate each network at its paralleled end in an additional section of line having a phase shift equal approzdmately to an odd multiple of 9G degrees at the frequency to oe attenuated. v

Waves of this frequency impressed upon the line y section at either end will be greatly attenuated in passing therethrough, since at the one end they encounter the high impedance of the terminated line and at the other end the low impedance of the shunt branch. However, Waves of frequencies at which the impedance of the shunt branch is highv compared to the characteristic impedance of the line section will pass along the line with .small or negligible transmission loss. Greatest The transducer may hea section of uniform transmission line of the coaxial type, of the balanced shielded type or, under some circumstances, an nnshielded pair of Wires. Alternatively, the

transducer may be sieur-terminal network ocmprising lumped reactance elements, the only requirements being that it has a phase shift equal approximately to an odd multiple ci Sli-degrees at.`

the frequency to be excluded and has a low transmission lcss at the frequency to be transmitted.

ATho shunt branch may he made up entirely of minced reactance elements or it may include one or more sections of transmission line used as reactances. The branch may include a reactance element added to provide, in effect, an impedance transformation for the rest of the branch. Also.'

Y an impedance inverting network may be inserted between the shunt branch and its point of connection. l

The networks of the invention are particularly useful in a radio system Where two or more trans- `lation devices, such as transmitters or receivers,r are associated with a common antenna.

- and a receiver operating at a second frequency tainable, if a single shunt gives a discrimination or the network may be further greatly increased may be using the seme antenna at the same time. It is necessary to keep the transmitter frequency, and noise of the receiver frequency generated in the transmitter, out of the receiver. Itis also necessary to provide a transmission path from the transmitter to the antenna for the transmitter frequency, and from the antenna to the receiver for the receiver frequency.

All of these requirements can be satised byinsorting selective networks of the type described in the transmission lines connecting the antenna with the transmitter and the receiver. The net- Work in the line to the transmitter is designed to pass freely the transmitter-frequency while ab tenuating the receiver frequency. rietavorlrv in the line to the receiver passes freely the receiver frequency :but attenuates the transmitter frequency.

For ex-v ampie, a transmitter operating at one frequency f2 t ,i 2,258,974 L The nature of the invention will be more fully understood from the following detailed description and by reference to the accompanying drawing, in which:

Fig. 1 is a schematic circuit showing one embodiment of the frequency-selective wave transmission network of the invention;

Fig. 2 isvthe circuit of a four-terminal transducer comprising lumped reactance .elements which may be used in the network of Fig. 1;

Fig. 3 shows the effect on the transmission loss of the network of Fig. l of deviations from th optimum phase shift in the transducer;

of terminals 23, Zfi-to which a load or utilization circuit may be connected. Por the best results it is desirable that the impedances of the terminal loads match the characteristic impedance of the line section.

The only requirements on the transducer 2li are that it have a phase shift equal approximately to an odd multiple of 90 `degrees at the fre quency f1 to be suppressed and alow attenuation at the frequency ,f2 to be transmitted. These requirements are met ny a section of .uniform transmission line, preferably of the coaxial or Fig. 4 shows the reactancefrequency vchar-n acteristic of the shunt impedance branches of Fig. l when the frequency t'o rbe attenuated is lower than the frequency to be transmitted;

Figs. 5 and 6 are alternative forms of an 'impedance branch having the reactance characteristie of Fig. 4;

Fig. 'I shows' how impedance transformation may be introduced in the'branch of Fig. 6 by the introduction of an added reactance element;

Fig. 8 shows an 'impedance lbranch equivalent I' d to the one of Fig. 6 in which the inductance is furnished by a section of transmission line;

Fig. 9 gives a typical transmission loss characteristic for the network of Fig. 1 when shunt "branches of the type shown in Figs. 5, 6, 7 or 8 ar'eused;

Fig. l0 represents the reactancc-frequency characteristic of the shunt branches `of Fig. 1.

whenthe frequency to be attenuated' is higher than the frequency to `be transmitted;

y Figs. 11 and l2 are alternative circuits of im-' pedance branches having the reactance characteristic of Fig. l0; j

Fig. 13 shows'the introduction of impedance transfurination in the branch o Fig. 12 by the n addition of an inductance;

Fig. 14 shows an equivalent circuit forthe branch of Fig. 12 in which 'the inductances are 'furnished by sections of transmission line;

Fig. 15 gives a typical transmission loss char acteristic obtainable with the network of Fig. 1 when it has shunt impedancehranches of the type'shown in Figs. 1l, l2, 13 or 14;'

Fig. 16 shows'an impedance ranchassociated 'with a section or line used as an impedance in-A -vertem Figs. 1v and is show the effect insider/rations y in the phase shift'of the impedance inverter have upon the transmission 'loss'at the attenuated and at the transmitted frequencies, respectively;

Fig. 19 shows the network of Fig. 1 modified by the addition of a'second section'of line with its associated shunt branch to improve the discrimination, and the addition of a terminal section of line to provide for parallel operation with a second network; and f f Fig-20 shows two networks in accordance with the invention associated with a radio system in which two translation devices use a common antenna. l l

. Fig. 1 is a schematic circuit-of a selective wave transmission network in accordance with the invention adapted to attenuate waves of one fre-- quency while freely transmitting-waves of another frequency. The network comprises a four- 'terminal transducer in `theoriri of a section' of vtranemission line 29 and two shunt impedance branches lZ connected at its ends. At one end he network "has a pair of terminals 2i, 22 to which a'wave source of 'electromotive force may be connected, and at the other end a second'pair balanced shielded type, the length of which is approximately equal to an odd multiple of onequarter of the .length of the waves to be attenuated. Alternatively, the transducer may be made up of lumped reactance elements. When the section of line is found to be unduly long the substitution of lumped elements will generally reduce the cost and size of the network. A suitable transducer using lumped elernents is shown in Fig. 2. The network is ofA the ladder type and comprises a series inductance L with-two shunt capacitances C, C connected at its ends. The

values of the elements may :so proportioned that the network will have a paese shift of apof, at the frequency f1.V ,l

The effect on the transmission 1loss Yof the network'of deviations, either plus or minus, from the optimum phase shift in the transducer 2i! is shown by the curves of Fig. 3. "The ordinates proximat'ely 90 degreesor an odd multiple thererepresent transmission loss in 4decibels and the f' abscissas represent the deviation in degrees from a phase shift equal to an odd multiple of 90 de-v grecs at the frequency of the waves to be attenuated. It is assumed that the attenuation in the falls 'to six decibels for a deviation ofQll degrees.

However, the loss is -greaterthan that introduced by the rst branch Vfor' deviations up -to about 58 degrees. It is seen that if'the second'branchfis connected at the same point-as .the first, or at -a point separated from the rst 'by an interval in which the phase shift is an even multiple of degrees, the second branch will add a lossof -only six' decibels, -but if the phase shiftfhas theoptiznurn value this loss may be increased kt'o`32 decibels. However, as the curve shows, considerles able deviation from the-optimum phase shift l`is lpermissible andthe second branch will still pro f vide a large added loss. vThe effect of deviations ofthe phase shift-upon the lossv 'tothe waves transmitted through the network fis negligible.

Each shunt branch Z'n Figl-'has a lcwimpedance at the frequency f1 which'is'tobelblocked and a high impedance atthe frequency fzwhich is to be transmitted. The branch is preferably vresonant at f1 and vanti-res'criant 'at f2. lhere may, of course-he additional criticar frequencies,

either resonances or arid-resonances. 'In 'soms cases 'extra ycritical frequencies may-be used to advantage to'control'the Values ofthe component reactance elements in the branch, orto-regulate' `fthe sharpness of resonance.` l-

l i. l g. l

,datemi I f f1 is lower than fz the simplest form of the jreactance characteristic for the branch Z will he of the type shown in Fig. 4, with a zero at fi and a pole at f2. Such a reactance may be provided,

Vfor example, by the two-thermal impedance and the capacitance 25 is so chosen that the enf tire branch is anti-resonant at the frequency f2. The capacitances 25 and 2E may be made variable, as indicated by the arrows, to facilitate the adjustrnent of the frequencies of resonance and antiresona-nce. Alternatively, the reactance char` acteristic of Fig. 4 may be provided by an impedance branch of the type shown in Fig. 6 comprising o. variable capacitance 28 in series with au anti-resonant loop consisting of a second variable capacitance 29 in parallel with an inductance i 3E. In converting from the conguration shown in Fig. to the equivalent one of Fig. 6 the capacitance may be divided into two portions, one of which is associated with the capacitance 2E and f the inductance il and converted into a circuit of the type shown in Fig. 6. The resulting structure will be as shown in Fig. 7 comprising a capacitance 3l, shunted by an arm consisting of a second capacitance 32 in series with an. anti resonant loop made up of a third capacitance 33 and an inductance 34 in parallel. By varying the value of the capacitance 3i the values of the rey maining reactance elements may be changed and in this way there is provided a choice of values 'for these elements. The addition of thecapacitance 3l in effect provides an impedance transy formation for the remaining elements in the` branch. The Value of the capacitance 3l may be so chosen that the most desirable values are ob@y tained for the remairing elements.

The inductance in the shunt branch LZ may,

under certain circumstances, be furnished by a y section of transmission line. For example, the

inductance in Fig. 6 may be provided by a v section of line 35 short-circuited at its distant` end, as shown in Fig. 8. Some of the distributed capacitance of the line 35 will be edective across its input terminals and the value of the shunting capacitance 29 is reduced to allow therefor. Of course', an additional capacitance may be con` nested in shunt with the branch shown in Fig. 3 in order to provide impedance transformation, as

explained above in connection with Fig. Y.

If the shunt impedance branches Z in Fig, 1 `taire any one of the forms shown in Figs. 5, 6, 7'

and 8, or an equivalent form, the network will have a transmission loss characteristic of the type shown diagrammatically in Fir. 9 with a maXi- 'mum loss at the frequency fi and a transmission Aregion including the frequency fz and extending to either side thereof. The width of the effective transmission band can be increased by lowering the impedance level of the branch Z, that is, by A making the reactances less stiff. A change in this direction will at the same time raise and broaden the attenuation peak." 0n .the other hand, if the branch Z is raised in impedance level the transmission band is narrowed and the attenuation in the region of the frequency f1 is lowered and made more peaked. In practice the impedance level of the branch is so chosen that the resultant transmission loss characteristic most nearly meets the requirements encountered in. any particular case.

If the frequencyr to be transmitted isv lower than 175 the frequency to be blocked, in its simplest form the reactance characteristic of the shunt iinpedance branches Z of Fig. l will be of the type shown in Fig. l0, with a pole at the frequency f3 to be transmitted and a zero at the frequency f4 to be suppressed. In this case the branch Z may, for exampiex take the form shown in Fig. l1 comprising an inductance 35 shunted by an arm consisting ofv a capacitance 3T in series with a second inductance 38. Alternatively, the branch Z may taire the equivalent form shown in Fig. l2 comprising an inductance 39 in series with an anti-resonant loop consisting of a capacitance 49 in parallel with a second inductance lll. In the same way as already explained in connection with Fig, '7, impedance transformation may be provided by adding the shunt inductance i2 as shown inFig. 13. By properly choosing the value of the inductance i2 the remaining reactance elements 43, 44 and 45 may be given the most desirable values, within certain limits.

In this type of shunt alsothe inductance elec ments may be replaced by sections of transmis# sion line if desired. For example, the two inductances 3S and il of Fig. l2 may be replaced, respectively, by the sections of line i6 and lll as shown in Fig. 14. The line section t1 may be short-circuited at its remote end by a low-impedance strap i8 as shown, and the value of the 3 'inductance 4l may 'be adjusted by changing the location of this strap. Part of the distributed capacitance of the two lines will appear in shunt at their junction, and the value of the capacitance @il is reduced to allow for this. A portion of the distributed capacitance of the line i5 will also appear shunted across` its input terminals, butv the effect of this will only be to introduce another anti-resonance at a frequency above f4. The introduction of this additional pole will ordinarily n .y not be detrimental to the perfomance of the net-y work. In some cases it may be desirable to shunt additionalcapacitance across the input terminals of the line section ,46 in order to bring thisadded anti-resonance nearer to the resonance at f4, q

thereby giving additional control of the trans- Vmission loss characteristic and providing an additional range of selection for the values of the component impedance eiements in the branch.

Fig. l5 mows the type of transmission loss char verter in connection with the shunt impedance.

branches Z. A new impedance Z' having a reactance characteristic which is the inverse of that of the branch Z is connected at one end of the transducer and the other end is connected at the point where the branch Z is ordinarily found.

The only requirements on the tranmucer are that its phase shift is approximately an odd multiple of degrees at all frequencies at which the impedance of Z' is to be inverted and that the transmission loss is low at these frequencies. The

` transducer may, for example, be a section of transmission line having a length which is approximately equal to an odd multiple o a quarter Wave-length at each frequency at which the impenance is to be inverted. Alternatively, the transducer may be made up of lumped reactance Kmme-Primi: slick cc maxaman-rc' of wine-mc elements, as shown in Fig. 2 for cxarnplaproportioned to provide the required phase shift.

Fig. 16 shows an impedance inverter in the form of a section of transmission line 5.9 having input terminals 5B, [il and output terminals 52, 53, with the impedance Z connected across the output terminals. If Z' is resonant at the frequency fr and anti-resonant at the frequency je and at the terminals 5Fl, 5l it is desired to see a high irnpedance at fr and a low impedance at fa, then the length of the line section S9 must be so chosen 'that it is approximately equal to an odd multiple of a quarter wave-length at both of these frequencies. Under these conditions the impedance at each of these frequencies seen at the terminals 50, El is equal to the characteristic im pedance of the line section t9 squared and divided by the impedance Z. If the frequencies fs and ,fr are close enough together the line maybe a quarter Wave-length, or an. cdd multiple thereof, at either of them, or at some intermediate frequency, and the conditions will be satisfied. However, for other spacines of the frequencies it may be necessary to make the line section 4g an odd number of quarter wave-lengths at one of the frequencies and a different odd number of 'quarter wavelengths at the other frequency. For example, the length of the section of line might be nyc-Quarters of a. Wave-length at fa and sevemquarters of a wave-length at fr.

By the addition of an impedance inverter a reactance characteristic oi the type shown in Fig. 10, for example, which ordinarily requires two incluctors and one capacitor may be provided by v an impedance branch Z' consisting of two capacitors and one inductcr. The designer is thus given his choice of two electrically equivalent types f ofbranches and he Will ordinarily select the one which is the less expensive to build. V v v Fig. 17 shows the change in the transmission loss of the network at the frequency to be attenuated caused by deviations in either direction from the optimum phase shift in the impedance inverter 49. The transmission loss in decibels.

introduced by a shuntbranch is plotted against the deviation in degrees from a phase shift equal to an odd multiple of 90 degrees at the frequency of the Waves to be attenuated. It is assumed that the attenuation n1. the impedance inverter 49 is negligible and that the impedance of Z isy equal to one-fortieth of the characteristic impedance ci the inverter at the frequency tol be aitenuated. For comparison, the dotted-line curve represents the transmission loss introduced by a single shunt branch Z. The solid-line curve gives the added transmission loss attributable to asecond shunt branch, consisting of an impedance `inverter @S terminated at its outer end in an impedance Z', connected at the optimum distance from the branch Z. This loss is 32 decibels for zero deviation and falls on' to about l1 decibels for a. deviation of l5 degrees. It is apparent, therefore, that for a high loss the devia tion in phase shift in the impedance inverter from the optimum value should be kept small.

Fig. i8 shows the variation in the transmission loss for the waves to be transmitted due to deviations from the optimum value in the phase shift in the impedance inverter. It is assumed that the impedanceof Z' is equal to forty times 'Y the characteristic impedance of the inverteratv the frequency to be transmitted. For comparison, the dotted-line curve gives the loss introduced by a single shunt branch Z. This loss reline curve gives\.y the added loss due to a second f value as possible fox; the frequency to be attenuated, but a considerable deviation from the optimum value for the frequency to be transmitted is permissible.

The discrimination between the frequency to be passed and the frequency to be blocked can I be increased by the addition of one or more sections of line similar to the first, each with its associated shunt impedance branch. Fig. 19 shows the network of Fig. l modified by the addition of a second section of line 54, similar to the section 23, with a third shunt branch Z connected at its outer end. If the network is to operate in parallel at one end with another similar network it is desirable that each network be terminated at the paralleled end in a section of line which is ay quarter wave-length, or an odd multiple thereof, at the frequency to be excluded. In Fig. 19 such a. line section 55, similar to the line sections 5d and 28, is connected between the terminals. la,

i8 and the remainder ofthe network.

A. useful application of the invention is in a.`

radio system where two or more translation devices operating at dierent frequencies are associated with a common antenna. For example, as shown in Fig. 20, a transmitter operating at the frequency fr and a receiver 5l' operating at some other frequency fn may be simultaneously using the same antenna A Two transmission lines, jointed in parallel at the

terminals

58, 59,

connect the' antenna with the transmitter and the receiver, respectively. It is apparent that the path between the transmitter and the antenna lmust pass freely waves of the transmitter free quency and that the path from the antenna to the receiver must pass freeli,7 Waves of the receiver frequency. In addition, the path between the transmitter and the receiver vmust offer a high loss to the transmitterfrequency to keep these high level waves out of the receiver, and also a high loss to any waves of the receiver frequency which may originate as noise in the transmitter.

The requirements mentioned may be met by using two selective wave transmission networks designed in accordance with the principles of the invention, one included in the transmitter branch and the other in the receiver branch.4

The network 5G in the transmitter branch has a low transmission loss at the frequency fr and a I vhigh loss at fa. and the network 6l in the re y ceiver branch has a lov; loss at fa and a high loss at fr. As shown in Fig. 20 the network El includes a section of transmission line 62 which is approximately an odd multiple of quarter wave-length at the transmitter frequency. The length of this line section is therefore equal to where )fr is the wave-length of the transmitter frequency ,fr and n is any integer. In practice n mains constant at about 0.1 decibel. The solid- "f5 is usually chosen as unity and the line section G2 is a quarter wave-length.

1 2 t E il c At each end of the line section 82 is a shunt impedance branch Zr.v If the transmitter frequency is lower than thc'receiver frequency each branch Z2 may take any one of the forms shown inFigs. 5, 6, 7 and 8, or any equivalent form. The branch connected between terminals 65 and Til is represented as being of the type shown in Fig. 7 except that the inductance 34 and a portion ofthe capacitance 33' are furnished by a section of transmission line 73 short-circuited at its distant end as explained above in connection with Fig. 8. The capacitance 3i is added to provide an impedance transformation for the other reactance elements in the branch and thus permit the use of more easily obtainable values. If, on the other hand, the transmitter frequency is higher than the receiver frequency the shunt should take the form shown in Figs. l1, 12, 13 or 14, or an equivalent form.' in either case the branch Za is resonant at the frequency fr and anti-resonant at je. The network is terminated at its paralleled end in a second section of line 63 of the same length as the section 62. This terminating line section is included so that the network Si will operate satisfactorily Lin parallel with the network B6.

- The network 6B in the transmitter branch ncludes a section of line 6d which is approximately an odd multiple of a quarter wave-length at the receiver frequency. The length of this line section is equal to l v l where la is the wave-length of the receiver fre quency fR and n is any integer. it one end the line section 54 is shunted by an impedance branch Z1 which is resonant at the receiverirequency fR and anti-resonant at the transmitter frequency fr.

' At its other end the line section 64 is shunted by an impedanceinverting line section 65 at the distant end of w ich there is connected an iinpeclance branch Zz. This branch has an impedance characteristic inverse to that` of the branch Z1, that is, Z2 is resonant at the frequency fr and anti-resonant at JR. As explained above in connection with Fig. 16 the length Z of the line section E is so chosen that it is approximately an odd multiple of a quarter wave-length at both of the frequencies fr and fR. Due to the impedance-inverting properties of the line section 65 the impedance seen at its terminals GE, 6l is the same as the impedance of the branch Zr. It is apparent, therefore, that the line section 65 and its terminal. impedance branch Z2 may be veloped. It is clear also that an impedance-inverting line section terminated by an impedance Zi may be substituted for each of the branches Zz in the network Si in the receiver branch. The

network Bil is terminated at its paralleled end in v additional line -sections withl their associated: shuntbranches may be added to the network Gil or the network 6 l, or to both, in order to increase the discrimination between the frequency to be transmitted and the frequency to be attenuated.

The operation of the system shown in Fig. 20.r may be summarized as follows. t the transmitter frequency fr the impedance of each branch Z2 is'nearly zero and-these branches provide, in effect, short circuits across the line at the points of connection.I Because of the impedance-inverting properties of the line section E5 a low irnpedance connected at its outer end will appear' at the terminals 66, G as a high impedance. Waves or' the frequency fr rfrom the transmitter 53 impressed upon the network 6E! at the terminals' 65, will therefore flow along the line 'sectionl 64 and'not into the line section S5. Since the shunt branch Zfhas a'hi'gh impedance at vthe frequency fr the waves will flow past this branchV However, since the antenna A matches the line ,68

in impedance. the transmitter signal will pass freely to the antenna.I A small amount of energy of the frequency fr' will enter the network '6i at the terminals 5B, 59 but at the terminals S9, l5 it encounters the high impedance of the line section `62 which is sliunted at its terminals l, E2 by a shunt ZL?, connected across the terminals 1h72.

Since the impedance Z1 is low at the receiver frexrluency-l'athel impedance looking into the line section '

e8 attire terminals

53, 59 is high at this frequency. Also, at fa the impedance of the branches Z2 ishigh and thebranches may bev Waves of they .Y

considered to be open-circuited. frequency fr. picked up by the antenna and impressed upon the

terminals

58, 59 of the network El will therefore be blocked from entering the network 69 but will pass freely along the line sections 83 and 62 to the receiver 5l, which matches the line in impedance.

Noise energy of the frequency fa generated in the transmitter 5B when it reaches the terminals 6B, 6'! of the network 60 will encounter a high impedance looking into the line section Sil and a low impedance looking into the line section B. Much of this energy will therefore be drained off through the shunt branch at this point. The small amount which passes along the line section 64 will be' largely drained off by the shunt branch Z1 which has a low impedance at this frequency. Thus noise of the frequency fa originating in the transmitter will not enter the network Bi and cannot interfere with the operation of the receiver` In Fig. 2G the two translation devices are shown as a transmitter 56 and a receiver 5T. It is to be` understood. however, that both of these devices may be transmitters or they may both be receivers. Furthermore, the number of translation devices associated with a common antenna is not limited to two, but may be extended to three or more, all operating at different frequencies. In each transmission line connecting thel antenna with a translation device there will be included @t caesars a network, designed in accordance with the gorinciples of the invention, which will the fre-- quency of that device but exclude all of A the other frequencies.- l What is claimed is:

, 1. A frequency-selective wave transmission networkfor attenuating waresjot one frequency fr while transmitting waves of a difierentirequency ,f2l comprising an impedance branch which ncludes two reactors connected series, a third reactor connected in shunt withsaid two reactors, and a fourth reactor connectedl in 'shunt with one of said two reactors, said fourth reactorhaving a reactance at'the. frequencies rf1 and fz which is of opposite sign to the reactance of said other 15- three-reactors at said frequencies and one ci said reactors being-a sectionoT-transmission line.'

2. A'network in `accordance'with claim-1 in which said fourth reactor has a positive reactance at the frequencies f1 and fz.- l

3 .fA network in accordance with-claim 1 in which said fourthvreactor is a section'of trans--l mission linc.-

4. A. network in accordance-with caim- 1 inA whichsaid fourth reactoris a sectionnf trans= 25` missicnline short-circuited at itsdistant end.

5.`A network in accordance with ciaim i in which said rst three reactors .have a .positive react'auce at the frequencies f1 and fz-.-

6J As-network in accordance-with claim 1 in 3u4 which'said rst three -reactorshave a positive reacta-nce at `the Vfrequencies fr and f2 and one of said three reactors is said sectionci transmission line.. 'i

tion of transmission line:

. 8 ."A'network in accordance'with Aciaiin-I in 40! which. said fourthreactor has `a-r1egati\fe ref 9. A network in accordance 'withclcirn lfin which-said -fourth reactor hasa negative -ic= actance at the frequencies f1 and f2 and -the -re actor connected in shunt therewith is a section.' of-transmission line short-circuited at its distant end.

10. A lnetwork in accordance with claim l in' Whichsaid impedance branchis-connectedin.V shunt t 11. A network in accordance with claim 1`nwhich said impedance branch isresonantVv at; the frequencyv f1 and -anti-resonant at the fre-A quency f2;

12. A frequency-selective Wave transmissiony network comprising ari-impedance branch whichl includes two capacitors connected -inseries a third capacitor connected in shunt with said two' capacitors and a section of vtransmission vhneconnected at one end across one ofsaid two. series-connected capacitors, said third capacitor' having a capacitance value so chosen thatsaid section of transmission line may be made of con-f venient physical length.-

7. -Anetworkl in accordance with claim 31 -in- 35= of transmission line.

13. .A network in accordance with ciaim'lZ -inwhich said impedance branch isconnectedin-r shunt. v

14. -A network in accordance `with claim i2 in y which said section of transmissionline isshort` .circuted at its distant end.

15. A. frequency-selective wave--transmissiorr-'r network comprising an impedance branch which inciudes two sections of transmission line connected in tandem, a shunt capacitor connected at the junction of said sections of line and an inductor connected in shunt at' the cuter en'd'cf 'on of said sections-of line.

16. A network in accordance with claim-f15 ini which' the other of 'said sections of line l'is sh'orti-` circuited-at its outer 'end'. I

17. A network in accordance with'cla'im IS-'iz which said capacitor is variable.

A CLARENCE H; DAGNALLE