U.S. patent number 3,605,044 [Application Number 04/776,398] was granted by the patent office on 1971-09-14 for filter structures using bimodal, bisymmetric networks.
This patent grant is currently assigned to Bell Telephone Laboratories, Inc.. Invention is credited to Harold Seidel.
United States Patent |
3,605,044 |
Seidel |
September 14, 1971 |
FILTER STRUCTURES USING BIMODAL, BISYMMETRIC NETWORKS
Abstract
A variety of filter structures are synthesized by means of a
cascade of bimodal networks. By including mode converters between
adjacent pairs of networks, successive networks can be made to
respond to one or the other of said modes. A transmission line
filter and a coupler (channel dropping) filter are described.
Inventors: |
Seidel; Harold (Warren
Township, Somerset County, NJ) |
Assignee: |
Bell Telephone Laboratories,
Inc. (Murray Hill, NJ)
|
Family
ID: |
25107270 |
Appl.
No.: |
04/776,398 |
Filed: |
November 18, 1968 |
Current U.S.
Class: |
333/202; 333/110;
333/168; 333/21R; 333/112 |
Current CPC
Class: |
H03H
7/075 (20130101); H03H 7/0115 (20130101) |
Current International
Class: |
H03H
7/075 (20060101); H03H 7/01 (20060101); H03h
007/10 () |
Field of
Search: |
;333/73,73C,11,31,21,10 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Saalbach; Herman Karl
Assistant Examiner: Chatmon, Jr.; Saxfield
Claims
I claim:
1. A filter comprising:
a cascade of bisymmetrical, bimodal networks all of which are
characterized by the same two normal modes;
and means, connecting adjacent pairs of said networks, for
converting all of the wave energy from one of said normal modes in
one network to the other of said normal modes in the next adjacent
network.
2. The filter according to claim 1 wherein each network comprises a
section of cable having two inner conductors surrounded by an outer
conductor;
and wherein said mode converter comprises means for introducing
180.degree. relative phase shift between signal components
propagating along said two inner conductors.
3. The filter according to claim 1 including means for externally
energizing said filter in at least one of said modes.
4. The filter according to claim 1 including a signal source for
simultaneously energizing an external port of said filter in both
of said modes.
5. The filter according to claim 1 wherein each of said networks is
a four-port.
6. The filter according to claim 1 where each of said networks
comprises a pair of coupled four-ports, each of which has two axes
of symmetry;
and wherein two of the ports, symmetrically disposed with respect
to one of the axis of one of said four-ports, are connected
respectively to two of the ports, symmetrically disposed with
respect to the other of said axes, of the other of said
four-ports.
7. The filter according to claim 6 wherein each of said four-ports
is a quadrature hybrid coupler.
8. The filter according to claim 1 wherein each of said bimodal
networks is bidual.
Description
This invention relates to filter circuits employing multimode
network sections.
BACKGROUND OF THE INVENTION
It is customary to think of circuits in terms of two-ports, such as
inductors, capacitors and resistors. These basic components, in
addition to being the traditional circuit components, can be made
very inexpensively and are sufficiently small to permit their use
in very large numbers. Recently, however, the quadrature hybrid
coupler has been developed to such a state where it too can be made
to be very inexpensive and very small, thus providing the circuit
designer with an additional basic circuit component having a
variety of interesting and useful properties.
To construct a filter using two-ports, however, requires that the
two-port components be arranged in distinctly different ways in
order to form the necessary combinations of series and shunt
circuits needed to synthesize characteristic. desired filter
characteristic.
Four-ports, on the other hand, are bimodal and, as such, are
characterized by two different normal modes and two different modal
responses. As a consequence, the same circuit component can be used
to produce distinctly different network effects within a filter
circuit.
One of the better known of the four-ports is the quadrature hybrid
coupler. As is known, a quadrature hybrid coupler maintains an
impedance match over a relatively broad frequency range. As such,
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.
It is, accordingly, the broad object of the present invention to
synthesize filters using bimodal network sections such as
quadrature hybrid couplers.
SUMMARY OF THE INVENTION
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.
In one of the embodiments to be described in greater detail
hereinbelow, a transmission line filter is synthesized using
sections of twin-conductor coaxial cable coupled together by a
phase shifter which introduces a 180.degree. relative phase shift
between signal components propagating along the two inner
conductors.
In a second embodiment of the invention, a coupler filter is
synthesized by cascading quadrature hybrid couplers.
It is a feature of the present invention that, though distinctly
independent of each other, the different modal responses of a
four-port are made simultaneously available. Thus, the same
four-port can be used throughout the filter to simulate either a
series or a shunt network component.
These and other objects and advantages, the nature of the present
invention, and its various features, will appear more fully upon
consideration of the various illustrative embodiments now to be
described in detail in connection with the accompanying
drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
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. 3 shows the impedance of each of the network sections
comprising the filter shown in FIG. 2;
FIG. 4 shows a second specific embodiment of a filter, in
accordance with the present invention, comprising a cascade of
quadrature hybrid couplers;
FIG. 5 shows the equivalent circuit of a lumped-element quadrature
hybrid coupler;
FIG. 6 shows the frequency response of the lumped-element coupler
shown in FIG. 5;
FIGS. 7A, 7B, 8A and 8B show a quadrature coupler excited in the
symmetric mode with respect to selected pairs of ports, and the
symmetric mode equivalent circuits of the coupler with respect to
the selected ports;
FIG. 9 shows the symmetric mode equivalent circuit of each network
section of FIG. 4;
FIGS. 10A, 10B, 11A and 11B show a quadrature coupler excited in
the antisymmetric mode with respect to selected pairs of ports, and
the antisymmetric mode equivalent circuits of the coupler with
respect to the selected ports;
FIG. 12 shows the antisymmetric mode equivalent circuit 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; and
FIGS. 16 and 17 show the symmetric mode and the antisymmetric mode
equivalents of the manner of excitation shown in FIG. 15.
DETAILED DESCRIPTION
Referring to the drawings, 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 15, 16 and 17. A signal source 18 is
coupled to ports 1 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.
At its output end, 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.
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 the network parameters are different, or they can be
identical networks. In either instance, each network section
responds differently to the two different modes of excitation.
Thus, in operation, a signal derived from signal source 18, and
coupled to the input end of filter 10, propagates through network
11 in one modal configuration and elicits a corresponding response
from the network. The signal then traverses mode converter 15
wherein the modal configuration is changed to a second mode of
excitation. The effect is to elicit a correspondingly different
response from network 12. The process of converting back and forth
between modes, as a means of producing a different response from
adjacent network sections, continues until the last network section
14 is reached. 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.
A simple embodiment of such a filter is illustrated in FIG. 2. As
shown, each network 11, 12, 13 and 14 is a section of
twin-conductor coaxial transmission line comprising a pair of inner
conductors 30 and 31, symmetrically located with respect to the
transmission line axis z--z, 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.degree. out of phase, or in the
antisymmetric mode. At the output end of the filter, output
coupling network 20 comprises a second hybrid transformer whose
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.
With signal source 18 connected to port 1 of network 19, as shown
in FIG. 2, conductors 30 and 31 are energized in phase. As a
result, both inner conductors are at the same potential and the
section of transmission line comprising bimodal network 11 appears,
insofar as the signal is concerned, as a length of coaxial
transmission line of characteristic impedance Z.sub.1. Upon
reaching the end of section 11, however, the signal in conductor 30
undergoes a 180.degree. relative phase shift in transformer 15 with
respect to the signal in conductor 31. As a consequence, the
signals in the two inner conductors are now equal in amplitude but
180.degree. out of phase, or in the antisymmetric mode. Section 12,
as a result, appears to the signals as a two-wire section of
transmission line of characteristic impedance Z.sub.2, where
Z.sub.2 is less than Z.sub.1.
At the next mode converter 16, the signals experience a second
180.degree. relative phase shift, restoring the symmetric mode of
excitation to conductors 30 and 31. Accordingly, section 13 appears
as a section of coaxial transmission line of characteristic
impedance Z.sub.1. Similarly, section 14, energized in the
antisymmetric mode, appears as a section of line of lower impedance
Z.sub.2.
FIG. 3 is a symbolic representation of the filter of FIG. 2 showing
alternate sections of transmission line of impedance Z.sub.1,
followed by a section of lower impedance Z.sub.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. In addition, the divided signal components are 90.degree.
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 180-184), the multiple directional
coupler (S. E. Miller, "Coupled Wave Theory and Waveguide
Applications," Bell System Technical Journal, May 1954 pages
661-719), the semioptical directional coupler (E. A. J. Marcatili,
"A Circular Electric Hybrid Junction and Some Channel-Dropping
Filters," Bell System Technical Journal, Jan. 1961, pages 185-196),
the strip transmission line directional coupler (T. K. Shimizu
"Strip-line 3 db. Directional Coupler," 1957 Institute of Radio
Engineers, Wescon Convention Record, Vol. 1, Part 1, pages 4-15),
and the lumped-element quadrature hybrid couplers disclosed in the
copending application Ser. No. 709,091, filed Feb. 28, 1968 by H.
R. Beurrier and assigned to applicant's assignee.
As will now be shown, the principles of the present invention can
be applied to quadrature hybrid couplers to synthesize a variety of
coupler filter structures. For purposes of explanation, particular
attention will be directed to the lumped-element type of coupler
since it is the simplest to describe. However, it is to be
understood that the results and conclusions to be drawn are equally
applicable to all of the various types of quadrature couplers.
As described in the above-identified application by H. R. Beurrier,
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.
Because of its short electrical length, 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-conductor
capacitance is represented by the two capacitors 52 and 53. The
four coupler ports are identified by the numerals 1, 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.
As explained by Beurrier, if the self-inductance of each conductor
is L, and the total conductor-to-conductor capacitance is C, the
characteristic impedance Z.sub.o of the coupler is given by
Z.sub.o = L/C (1)
and the power division ratio is equal to unity at
.omega..sub.o= 1/LC (2)
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
t .sup.2 + k .sup.2 =1 (3)
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 .omega..sub.o.
As can be seen from the equivalent circuit of FIG. 5, 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.
Referring again to FIG. 4, 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. 1. With respect to each pair, the second
coupler is rotated 90.degree. 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
180.degree. relative phase shifters 47 and 48 located in one of the
interconnecting wavepaths. These phase shifters correspond to mode
converters 15 and 16 of FIG. 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.
While only three bimodal network sections are shown, it is
understood that, as indicated hereinabove, additional sections can
be added as required.
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.
SYMMETRIC MODE REPRESENTATION
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.sub.s which is inductive, and
which, because the mutual inductance between the two conductors is
close to unity, is approximately equal to 2L. Thus, the equivalent
circuit of the coupler in the symmetric mode domain, with respect
to ports 1 and 2 (and ports 3 and 4) comprises a pair of series
inductors of magnitude L.sub.s =2L, as illustrated in FIG. 7B. It
should again be noted that in this modal representation, there is
no mutual coupling between inductors L.sub.s.
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. Thus, the equivalent
circuit of the coupler in the symmetric mode domain with respect to
ports 1 and 3 (and ports 2 and 4) comprises a pair of series
capacitors of magnitude C.sub.s =C.sub. 2, as illustrated in FIG.
8B.
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 8B as in FIG. 9.
As can be seen, the result is a simple series L-C circuit whose
resonant frequency .omega..sub.o is given by
.omega..sub.o =1/ L.sub.s C.sub.s (4)
Substituting 2L for L.sub.s and C/2 2 for C.sub.s, gives
.omega..sub.o =1/ LC (5)
which is the crossover frequency for each of the couplers.
Accordingly, in the symmetric mode domain, two identical couplers,
connected in the manner shown, are equivalent to a series L-C
circuit whose resonant frequency is equal to the couplers'
crossover frequency. Typically, the two couplers will not be
identical. In this more general case, the inductive component will
come from one coupler while the capacitive component will come from
the other coupler. Thus, the crossover frequencies and the resonant
frequency of the equivalent circuit can all be different.
ANTISYMMETRIC MODE REPRESENTATION
The antisymmetric mode equivalent circuit, with respect to ports 1
and 2, 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 180.degree. 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. 10B, comprises a shunt capacitance C.sub.as equal to
the coupler's conductor-to-conductor capacitance C, connected
between terminals 1 and 2 (and 3 and 4).
The antisymmetric mode equivalent circuit with respect to ports 1
and 3 (and 2 and 4) is derived by connecting a signal source 81
between ports 1 and 3, as illustrated in FIG. 11A. Because of the
tight coupling between inductors 50 and 51 (M.apprxeq.1), the two
inductors are essentially at the same potential and there is no net
capacitive current flow. 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.sub.as
equal to the self-inductance L of a single inductor.
FIG. 12, comprising a cascade of the equivalent circuits of FIGS.
10B and 11B, gives the antisymmetric mode equivalent circuit of
each of the bimodal network sections 11, 12 and 13 of filter 40.
Since C.sub.as =C and L.sub.as =L, the circuit is a simple shunt
L-C circuit whose resonant frequency .omega..sub.o is equal to the
crossover frequency of the two couplers comprising each
section.
It will be further noted that since the symmetric mode equivalent
circuits (FIGS. 7B and 8B) are the network duals of the
antisymmetric mode equivalent circuits (FIGS. 10B and 11B) the
lumped element quadrature coupler is seen to be bidual. This, in
general is the characteristic of all quadrature hybrid couplers.
The actual circuits, however, tend to be more complex for the
distributed, or transmission line type couplers.
It is evident that merely to cascade network sections would not
produce the desired filter configuration since such a cascade would
comprise a cascade of series L-C circuit when energized in the
symmetric mode, and a cascade of parallel L-C circuits when
energized in the antisymmetric mode. What is required, therefore,
is a means for converting between modes such that whatever mode of
excitation is applied to the first section is converted to the
other mode at the second and subsequent even-numbered network
sections in the cascade, and is converted back to the incident mode
of excitation at all subsequent odd-numbered network sections. This
mode conversion function is provided by the 180.degree. relative
phase shifters 47 and 48 located between adjacent network sections
11-12 and 12-13, respectively. Thus, for example, 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. Thus, the first bimodal network 11
appears as a series L-C circuit in response to the symmetric mode
of excitation applied to it, whereas the second bimodal network 12
appears as a shunt L-C circuit in response to the antisymmetric
mode of excitation applied to it. Similarly, 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.
If, on the other hand, ports 1 and 2 of hybrid 41 are excited in
the antisymmetric mode, the first and third networks 11 and 13
respond in the antisymmetric mode, shunt L-C equivalent, whereas
network 12 responds in the symmetric mode, series L-C equivalent.
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.
In practice, however, 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. We
can, therefore, analyze the response of the filter to each of the
two modes separately, and then sum these responses to obtain the
total response.
This is now done with reference to FIGS. 16 and 17 which show the
overall signal distribution at the four ports of the filter in
response to the symmetric and antisymmetric modes of
excitation.
Referring to FIG. 16, 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 E/2t.sub.s at each of ports 2 and 4 of
coupler 46, and produces a reflected signal component (E/2)k.sub.s
at each of ports 1 and 2 of hybrid 41, where t.sub.s is the
symmetric mode coefficient of transmission for the filter, and
k.sub.s 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)t.sub.as and a reflected signal component
E/2)k.sub.as in port 1 of coupler 41. Similarly, signal -E/2
produces a transmitted signal component -(E/2)t.sub.as in port 4 of
coupler 46 and a reflected signal component -(E/2)k.sub.as in port
2 of coupler 41, where t.sub.as is the antisymmetric mode
coefficient of transmission for the filter, and k.sub.as is the
antisymmetric mode (E/2 of reflection for the filter.
Since the symmetric and antisymmetric mode equivalent circuits are
network duals of each other, they have the same coefficients of
transmission whereas their coefficients of reflection are the
negatives of each other. That is
t.sub.s =t.sub.as (6)
-k.sub.s =k.sub.as (7)
By superposition, 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.
At port 1 of coupler 41, the reflected signal E.sub.rl is
E.sub.rl =(E/2)k.sub.s +(E/2)k.sub.as =0 (8)
Thus, the filter is reflectionless.
The reflected signal E.sub.r2 at port 2 of coupler 41 is
E.sub.r2 =(E/2)k.sub.s -(E/2)k.sub.as =Ek.sub.s (9)
The transmitted signal E.sub.t2 at port 2 of coupler 46
E.sub.t2 =(E/2)t.sub.s +(E/2)t.sub.as =Et.sub.s (10)
The transmitted signal E.sub.t4 at port 4 of coupler 46
E.sub.t4 =(E/2)t.sub.s -(E/2)t.sub.as =0 (11)
Thus, the signal applied to port 1 of coupler 41 divides between
port 2 of coupler 41 and port 2 of coupler 46 in proportion to
k.sub.s and t.sub.s. Since both t.sub.s and k.sub.s vary with
frequency, a broadband signal applied to the filter is divided such
that one output signal is band-limited by the frequency
characteristic of t.sub.s, and the other output signal is
band-limited by the frequency characteristic of k.sub.s, where
k.sub.s .sup.2 + t.sub. s/ .sup.2 =1 (12)
SUMMARY OF THE INVENTION
It has been shown that while a bimodal network can be characterized
by two manually independent modal responses, both can,
nevertheless, be made simultaneously available notwithstanding
their independence. It has also been shown that the modal responses
can be used to synthesize a variety of filter structures. While
only two specific filter circuits have been described in detail, it
is understood that the above-described arrangements are merely
illustrative of but a small number of the many possible specific
embodiments which can represent applications of the principles of
the invention. For example, at the higher frequencies a filter
similar to that shown in FIG. 2 can be synthesized using a
conductively bounded transmission line instead of a twin-conductor
coaxial cable since it is known that the various transmission modes
have different field distributions and, hence, a distinctly
different modal response is produced by discontinuities at a
particular location within the waveguide. Similarly, the different
response of gyromagnetic materials to oppositely rotating
circularly polarized waves can be exploited in a manner consistent
with the principles disclosed hereinabove by a judicious array of
longitudinally spaced half waveplates. Thus numerous and varied
other arrangements can readily be devised in accordance with these
principles by those skilled in the art without departing from the
spirit and scope of the invention.
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