US3605044A - Filter structures using bimodal, bisymmetric networks - Google Patents

Filter structures using bimodal, bisymmetric networks Download PDF

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Publication number
US3605044A
US3605044A US776398A US3605044DA US3605044A US 3605044 A US3605044 A US 3605044A US 776398 A US776398 A US 776398A US 3605044D A US3605044D A US 3605044DA US 3605044 A US3605044 A US 3605044A
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ports
filter
network
networks
coupler
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US776398A
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Harold Seidel
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AT&T Corp
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Bell Telephone Laboratories Inc
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H7/00—Multiple-port networks comprising only passive electrical elements as network components
    • H03H7/01—Frequency selective two-port networks
    • H03H7/075—Ladder networks, e.g. electric wave filters
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H7/00—Multiple-port networks comprising only passive electrical elements as network components
    • H03H7/01—Frequency selective two-port networks
    • H03H7/0115—Frequency selective two-port networks comprising only inductors and capacitors

Definitions

  • quadrature hybrid coupler One of the better known of the four-ports is the quadrature hybrid coupler.
  • a quadrature hybrid coupler maintains an impedance match over a relatively broad frequency range.
  • impedance match over a relatively broad frequency range.
  • it is particularly useful in systems requiring low loss, impedance-matched conditions over a wide frequency range. This, typically, is the case, for example, in systems using tunnel diodes, since they are known to exhibit a negative resistance over a range of frequencies which extend down to direct current.
  • This potential for instability accordingly, requires that circuits used with such active elements, such as filters, for example, be impedance-matched both outside, as well as within the frequency band of interest.
  • a filter in accordance with the present invention comprises a plurality of cascaded four-ports, all of which are characterized by the same pair of normal propagating modes. Adjacent pairs of four-ports are coupled together by means of a mode converter which converts all the energy from one to the other of said modes.
  • a transmission line filter is synthesized using sections of twin-conductor coaxial cable coupled together by a phase shifter which introduces a 180 relative phase shift between signal components propagating along the two inner conductors.
  • a coupler filter is synthesized by cascading quadrature hybrid couplers.
  • FIG. 1 shows, in block diagram, a filter in accordance with the present invention
  • FIG. 2 shows a first specific embodiment of the invention employing twin-conductor coaxial cable as'a bimodal network
  • FIG. 9 shows the symmetric mode equivalent circuit of each network section of FIG. 4.
  • FIGS. 10A, 1013, 11A and 11B show a quadrature coupler excited in the antisymmetric mode with respect to selected pairs of ports, and theantisymmetric mode equivalent circuits of the coupler with respectto the selected ports;
  • FIG. 12 shows the antisymmetric mode equivalentcircuit of each network section of FIG. 4;
  • FIG. 13 shows the equivalent circuit of the filter of FIG. 4 excited in a symmetric mode
  • FIG. 14 shows the equivalent circuit of the filter of FIG. 4 excited in the antisymmetric mode
  • FIG. 15 shows a signal source coupled to one port of the filter of FIG. 4; a nd 7 FIGS. 16 and 17 show the symmetric mode and the antisymmetric mode equivalents of the manner of excitation shown in FIG. 15.
  • FIG. 1 shows a filter 10, in accordance with the present invention, comprising a plurality of cascaded bimodal network sections 11, 12, 13 and 14 coupled together by means of mode converters 1,5, 16 and 17.
  • a signal source 18 is coupled to ports I and 2 of filter 10 through port 1 of a four-port input coupling network 19. Port 2 of input network 19 is resistively terminated.
  • ports 3 and 4 of filter 10 are coupled through a four-port output coupling network 20 to a load 21 connected to port 1 of coupling network 20.
  • Terminal 2 of network 20 is resistively terminated.
  • network sections While four networks and three mode converters are shown in FIG. 1, it is understood that, in general, the number of network sections used in any specific instance will depend upon the particular application at hand and, as such, can vary from a minimum of two sections, coupled together by means of a single mode converter, to an unspecified maximum number of sections.
  • All of the bimodal networks 11 through 14 are characterized by the same pair of normal propagating modes, where the term normal mode refers to a specified configuration of excitation that remains uniform throughout the network. As such, they can either be similar networks in which the network configurations are the same but in which thenetwork parameters are different, or they can be identical networks. In either instance, each network sectionresponds differently to the two different modes of excitation.
  • a signal derived from signal source 18, and coupled to, the input end of filter l0 propagates through networkll in one modal con-' figuration and elicits a corresponding responsefrom the network.
  • the signal then traversesmode converter 15 wherein the modal configuration is changedtoa-second mode of excitation. The effect is to elicit a correspondingly different,
  • the net output signal derived from this filter, and coupled to output circuit 20, is a function of the cascade of the responses elicited from each of the network sections, and as such can be shaped by the proper selection of circuit parameters and modes.
  • each network 11, 12, 13 and 14 is a section of twinconductor coaxial transmission line comprising a pair of inner conductors 30 and 31, symmetrically located with respect to the transmission line axis zz, surrounded by an outer conductor 32.
  • Mode converters 15, 16 and 17 comprise phase-inverting transformers 24, 25 and 26, respectively, connected between one of the inner conductors 30 and outer conductor 32 in a manner to couple adjacent segments of conductor 30.
  • the filter is energized by means of signal source 18 connected to port 1 of input coupling network 19.
  • Port 2 of network 19 is resistively terminated, and ports 3 and 4 are connected to conductors 31 and 30, respectively.
  • Input coupling network 19 comprises a hybrid transformer such that when signal source 18 is connected to port 1, as in FIG. 2, conductors 30 and 31 are energized in phase, or in the symmetric mode. If, on the other hand, signal source 18 were connected to port 2, conductors 30 and 31 would be energized 180 out of phase, or in the antisymmetric mode.
  • output coupling network 20 comprises a second hybrid transformerwhose output ports 1 and 2 are connected to loads 21 and 22. When ports 3 and 4 are energized in phase, all the signal is coupled to load 21. When ports 3 and 4 are energized out of phase, all the signal energy is coupled to port 2 and load 22.
  • FIG. 3 is a symbolic representation of the filter of FIG. 2 showing alternate sections of transmission line of impedance 2,, followed by a section of lower impedance 2,. It will be noted that by exploiting the different modal responses of a twin-conductor coaxial transmission line, distinctly different electrical characteristics are realized without changing the physical structure of the line. More generally, the introduction of periodic modal transitions along a bimodal structure has the effect of cascading the network characteristics of the two modes.
  • FIG. 4 shows an embodiment of a coupler filter 40, in accordance with the present invention, comprising a cascade of quadrature hybrid couplers 41 through 46 where the term quadrature hybrid coupler" is used in its accepted sense to describe a power-dividing network having four ports in which the ports are arranged in pairs with the ports comprising each pair being conjugate to each other and in coupling relationship with the ports of the other of said pairs.
  • the divided signal components are 90 out of time phase, hence the designation quadrature? coupler.
  • Examples of such hybrids are the Riblet coupler (H. J. Riblet "The Short-Slot Hybrid Junction," Proceedings of the Institute of Radio Engineers, Feb. 1952, pages 180-484), the multiple directional coupler (S. E.
  • a lumped-element coupler comprises a pair of conductively insulated conductors whose electrical length is a small fraction of a wavelength at the operating frequencies. Lengths of the order of one-eight of a wavelength and less are typical.
  • the conductors can either be twisted about each other as a means of maintaining a constant orientation with respect to each other, or they can be mounted on opposite sides of a dielectric material.
  • the equivalent circuit of such a coupler can be represented by lumped-impedance elements as shown in FIG. 5 wherein the two conductors as represented by two, tightly coupled inductors 50 and 51.
  • the conductor-to-corrductor capacitance is represented by the two capacitors 52 and 53.
  • the four coupler ports are identified by the numerals l, 2, 3 and 4 of which ports 1 and 4 comprise one pair of conjugate ports and ports 2 and 3 are the other pair.
  • the characteristic impedance Z, of the coupler is given by
  • the signal distribution, as a function of frequency, is given by curves 60 and 61 in FIG. 6, which show the amplitudes of the transmitted signal component t and of the quadrature reflected signal component k, where Basically, the transmitted component is a maximum at zero frequency and decreases as the frequency increases.
  • the reflected component on the other hand, is a minimum at zero frequency, and increases as the frequency increases. The two components are equal at the crossover frequency to As can be seen from the equivalent circuit of FIG.
  • a quadrature hybrid coupler is bisymmetrical with respect to two, mutually perpendicular axes z-z and y-y, each of which bisects the coupler into two, identical two ports.
  • the latter are referred to as bisected prototypes" and can be conveniently used to study the coupler since each has within it all the properties of the original four-port.
  • the coupler is also bidual, as will be shown hereinbelow by separately exciting the coupler in the symmetric and antisymmetric modes.
  • the couplers comprising filter 40 are arranged in pairs 41-42, 43-44 and 45-46, where each pair corresponds, respectively, to one of the bimodal network sections 11, 12 and 13 of FIG. I.
  • the second coupler is rotated with respect to the first coupler such that a pair of ports 3 and 4, symmetrically situated with respect to one of the axes of symmetry, is coupled to a pair of ports 1 and 3 that are symmetrically located with respect to the other axis of symmetry.
  • Adjacent network sections are coupled together by means of relative phase shifters 47 and 48 located in one of the interconnecting wavepaths. These phase shifters correspond to mode converters and 16 ofFIG. 1.
  • Port 1 of hybrid 41 is the filter input port to which a signal source 49 is connected. Output signals are taken from port 2 of the first hybrid 41 and from port 2 of the last hybrid 46. Port 4 of hybrid 46 is resistively terminated.
  • filter 40 The operation and characteristics of filter 40 will now be examined by first examining the modal characteristics of a quadrature hybrid coupler with respect to its two symmetry axes.
  • the modal characteristics of the coupler are determined by exciting the coupler in its normal modes and observing the responses thereto produced by the coupler. These responses, while they take into account all internal interactions, are represented only with respect to their externally observable manifestations. Thus, for example, the modal response representations do not concern themselves with mutual inductive effects since, for any specific mode, this internal interaction is uniquely defined and is included in the externally observed response.
  • the first modal response to be examined is the symmetric mode with respect to ports 1 and 2 (and, because of the symmetry of the coupler, with respect to ports-3 and 4). This is determined by energizing ports 1 and 2 by means of two, equal amplitude, in phase signal sources 70 and 71, as illustrated in FIG. 7A. Ports 3 and 4 are match-terminated. Since inductors 50 and 51 are always at the same potential when ports 1 and 2 are energized in the symmetric mode, there is no capacitive current flow and each of the signals sees a symmetric mode impedance L, which is inductive, and which, because the mutual inductance between the two conductors is close to unity, is approximately equal to 21...
  • the symmetric mode equivalent circuit with respect to ports 1 and 3 and, because of the symmetry of the coupler, between ports 2 and 4, is determined by energizing ports 1 and 3 by means of two, equal amplitude, in phase signal sources 72 and 73, as illustrated in FIG. 8A, Since opposite ends of inductors 50 and 51 are always at the same potential when ports 1 and 3 are energized in the symmetric mode, there is no inductive current flow. The only current flow is through capacitors 52 and 53.
  • the symmetric mode equivalent circuit for each of the bimodal network sections 11, 12 and 13 of filter 40 is obtained by cascading the equivalent circuits of FIGS. 7B and 88 as in FIG. 9.
  • the result is a simple series L-C circuit whose resonant frequency w, is given by 41.,0' (4)
  • Substituting 2L for L, and C/2 2 for C, gives frequencies and the resonant frequency of the equivalent circuit can all be different.
  • the antisymmetric mode equivalent circuit is derived by connecting ports 1 and 2 to opposite terminals of a common signal source 80, as shown in FIG. 10A. Ports 3 and 4 are resistively terminated. Excited in this manner, conductors 50 and 51 are energized l out of phase. As a consequence, the currents in the two conductors flow in opposite directions, producing no net component of inductive current. The only net current flow is capacitive, due to the interconductor capacitance represented by capacitors 52 and 53. Accordingly, with respect to ports 1 and 2 (and 3 and 4), the antisymmetric equivalent circuit, shown in FIG. 108, comprises a shunt capacitance C equal to the couplers conductor-to-conductor capacitance C, connected between terminals 1 and 2 (and 3 and 4).
  • the equivalent circuit of the coupler in the antisymmetric mode with respect to ports 1 and 3 (and 2 and 4) is, therefore, as shown in FIG. 11B, a shunt inductance L equal to the self-inductance L of a single inductor.
  • phase shifter 47 serves to convert symmetric mode excitation applied to the input ports 1-2 of hybrid 41 to the antisymmetric mode of excitation at terminals 1-2 of hybrid 43.
  • the first bimodal network 11 appears as a series L-C circuit in response to the symmetric mode of excitation applied to it
  • the second bimodal network 12 appears as a shunt L-C circuit in response to the antisymmetric mode of excitation applied to it.
  • the third network is excited in the symmetric mode and appears as a series L-C network.
  • the equivalent circuit of filter 40, excited in the symmetric mode, is shown in FIG. 13. It comprises the series circuit of network 11, the parallel circuit of network 12 and the series circuit of network 13.
  • FIG. 14 The equivalent filter circuit for the antisymmetric mode of excitation is illustrated in FIG. 14. The latter, it will be noted, is the network dual of the circuit shown in FIG. 13.
  • filter 40 is typically not excited exclusively in either the symmetric or the antisymmetric mode, but rather in both modes simultaneously. That this is so can be seen by referring to FIG. 15 which shows a signal source 49 connected to port 1 of the first hybrid 41. With respect to ground, therefore, the signal applied to port 1 is +E whereas the signal applied to port 2 is zero.
  • This manner of excitation can be considered, however, to comprise two components. The first is a symmetric mode of +E/2 applied to both ports, and the second, an antisymmetric mode of +E/2 applied to port 1 and E/2 applied to port 2. The sum of these two at port 1 is +E, while the sum at port 2 is zero.
  • FIGS. 16 and 17 show the overall signal distribution at the four ports of the filter in response to the symmetric and antisymmetric modes of excitation.
  • a symmetric mode signal of amplitude E/2, applied to ports 1 and 2 of the first hybrid coupler 41 produces a transmitted signal component 13/21, at each of ports 2 and 4 of coupler 46, and produces a reflected signal component (E/2)k, at each of ports 1 and 2 of hybrid 41, where t, is the symmetric mode coefficient of transmission for the filter, and k, is the symmetric mode coefficient of reflection for the filter.
  • FIG. 16 shows the response to the antisymmetric mode signal of +E/2 applied to port 1 of coupler 41 and E/2 applied to port 2 of coupler 41.
  • Signal E/2 produces a transmitted signal in port 2 of coupler 46 of (E/2)r,, and a reflected signal component E/2)k,,, in port 1 of coupler 41.
  • signal E/2 produces a transmitted signal component E/2)! in port 4 of coupler 46 and a reflected signal component -(E/2 )as in port 2 of coupler 41, where t is the antisymmetric mode coefficient of transmission for the filter, and k,, is the antisymmetric mode (E/2 of reflection for the filter.
  • the net signal at each of the ports can be obtained by summing the normal mode responses at each of the ports when the filter is energized at port 1 of coupler 41 in the manner indicated in FIG. 15.
  • the reflected signal E is
  • the filter is reflectionless.
  • a filter comprising:
  • each network comprises a section of cable having two inner conductors surrounded by an outer conductor
  • said mode converter comprises means for introducing relative phase shift between signal components propagating along said two inner conductors.
  • the filter according to claim 1 including means for externally energizing said filter in at least one of said modes.
  • the filter according to claim 1 including a signal source for simultaneously energizing an external port of said filter in both of said modes.
  • each of said networks is a four-port.
  • each of said networks comprises a pair of coupled four-ports, each of which has two axes of symmetry;
  • each of said fourports is a quadrature hybrid coupler.
  • each of said bimodal networks is bidual.

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Cable Transmission Systems, Equalization Of Radio And Reduction Of Echo (AREA)
  • Control Of Motors That Do Not Use Commutators (AREA)
  • Waveguide Switches, Polarizers, And Phase Shifters (AREA)
US776398A 1968-11-18 1968-11-18 Filter structures using bimodal, bisymmetric networks Expired - Lifetime US3605044A (en)

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BE (1) BE741726A (de)
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SE (1) SE362323B (de)

Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3723913A (en) * 1972-05-30 1973-03-27 Bell Telephone Labor Inc Quadrature hybrid coupler using one-port, linear circuit elements
US4390236A (en) * 1981-03-19 1983-06-28 Bell Telephone Laboratories, Incorporated Tunable polarization independent wavelength filter
US20100205233A1 (en) * 2009-02-09 2010-08-12 Matthew Alexander Morgan Reflectionless filters
US9130653B2 (en) * 2011-11-08 2015-09-08 Filtronic Wireless Limited Filter block and a signal transceiver comprising such a filter block
WO2015199895A1 (en) * 2014-06-25 2015-12-30 Associated Universities, Inc. Sub-network enhanced reflectionless filter topology
US9923540B2 (en) 2014-11-05 2018-03-20 Associated Universities, Inc. Transmission line reflectionless filters
US10263592B2 (en) 2015-10-30 2019-04-16 Associated Universities, Inc. Optimal response reflectionless filters
US10374577B2 (en) 2015-10-30 2019-08-06 Associated Universities, Inc. Optimal response reflectionless filters
US10530321B2 (en) 2015-10-30 2020-01-07 Associated Universities, Inc. Deep rejection reflectionless filters

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3184691A (en) * 1961-11-29 1965-05-18 Bell Telephone Labor Inc Branching hybrid coupler network useful for broadband power-dividing, duplexing and frequency separation
US3192490A (en) * 1962-08-23 1965-06-29 Westinghouse Electric Corp Hybrid network having interconnected center tapped autotransformer windings
US3252113A (en) * 1962-08-20 1966-05-17 Sylvania Electric Prod Broadband hybrid diplexer
US3329884A (en) * 1964-06-08 1967-07-04 Bell Telephone Labor Inc Frequency multiplier utilizing a hybrid junction to provide isolation between the input and output terminals
US3423688A (en) * 1965-11-09 1969-01-21 Bell Telephone Labor Inc Hybrid-coupled amplifier
US3444475A (en) * 1967-04-19 1969-05-13 Bell Telephone Labor Inc Broadband hybrid-coupled circuit
US3452300A (en) * 1965-08-11 1969-06-24 Merrimac Research & Dev Inc Four port directive coupler having electrical symmetry with respect to both axes

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3184691A (en) * 1961-11-29 1965-05-18 Bell Telephone Labor Inc Branching hybrid coupler network useful for broadband power-dividing, duplexing and frequency separation
US3252113A (en) * 1962-08-20 1966-05-17 Sylvania Electric Prod Broadband hybrid diplexer
US3192490A (en) * 1962-08-23 1965-06-29 Westinghouse Electric Corp Hybrid network having interconnected center tapped autotransformer windings
US3329884A (en) * 1964-06-08 1967-07-04 Bell Telephone Labor Inc Frequency multiplier utilizing a hybrid junction to provide isolation between the input and output terminals
US3452300A (en) * 1965-08-11 1969-06-24 Merrimac Research & Dev Inc Four port directive coupler having electrical symmetry with respect to both axes
US3423688A (en) * 1965-11-09 1969-01-21 Bell Telephone Labor Inc Hybrid-coupled amplifier
US3444475A (en) * 1967-04-19 1969-05-13 Bell Telephone Labor Inc Broadband hybrid-coupled circuit

Cited By (17)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3723913A (en) * 1972-05-30 1973-03-27 Bell Telephone Labor Inc Quadrature hybrid coupler using one-port, linear circuit elements
US4390236A (en) * 1981-03-19 1983-06-28 Bell Telephone Laboratories, Incorporated Tunable polarization independent wavelength filter
US20100205233A1 (en) * 2009-02-09 2010-08-12 Matthew Alexander Morgan Reflectionless filters
CN102365784A (zh) * 2009-02-09 2012-02-29 联合大学公司 无反射滤波器
US8392495B2 (en) 2009-02-09 2013-03-05 Associated Universities, Inc. Reflectionless filters
CN102365784B (zh) * 2009-02-09 2014-07-30 联合大学公司 无反射滤波器
US9130653B2 (en) * 2011-11-08 2015-09-08 Filtronic Wireless Limited Filter block and a signal transceiver comprising such a filter block
TWI581494B (zh) * 2014-06-25 2017-05-01 聯合大學公司 子網路增強之無反射濾波器拓樸
WO2015199895A1 (en) * 2014-06-25 2015-12-30 Associated Universities, Inc. Sub-network enhanced reflectionless filter topology
US9705467B2 (en) 2014-06-25 2017-07-11 Assoicated Universties, Inc. Sub-network enhanced reflectionless filter topology
US10230348B2 (en) 2014-06-25 2019-03-12 Associated Universities, Inc. Sub-network enhanced reflectionless filter topology
US9923540B2 (en) 2014-11-05 2018-03-20 Associated Universities, Inc. Transmission line reflectionless filters
US10277189B2 (en) 2014-11-05 2019-04-30 Associated Universities, Inc. Transmission line reflectionless filters
US10263592B2 (en) 2015-10-30 2019-04-16 Associated Universities, Inc. Optimal response reflectionless filters
US10374577B2 (en) 2015-10-30 2019-08-06 Associated Universities, Inc. Optimal response reflectionless filters
US10516378B2 (en) 2015-10-30 2019-12-24 Associated Universities, Inc. Optimal response reflectionless filter topologies
US10530321B2 (en) 2015-10-30 2020-01-07 Associated Universities, Inc. Deep rejection reflectionless filters

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GB1277250A (en) 1972-06-07
FR2023512A1 (de) 1970-08-21
DE1957760B2 (de) 1973-02-01
SE362323B (de) 1973-12-03
BE741726A (fr) 1970-04-16
DE1957760A1 (de) 1970-05-27

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