Branch line directional coupler having an impedance matching network connected to a port

The invention is an improvement over the conventional branch guide directional coupler and gives better performance by providing flatter coupling over a broader band. A branch guide (line) directional coupler fundamentally is a four port electrical network. The invention improves the performance of the conventional branch guide coupler by employing matching devices at the ports of the fundamental network. In most embodiments of the invention, it is contemplated that matching devices will be used at each of the ports and that all those matching devices will be of like construction. However, it is not essential that a matching device be employed at every port nor is it essential that all the matching devices be of like construction. For example, in some embodiments of the invention, matching structures need be employed only at the output ports. In the stripline and microstrip embodiments of the invention the matching device can be formed by a half wavelength open-circuited stub in combination with a quarter wavelength transformer or by a short-circuited quarter wavelength stub in combination with a quarter wavelength transformer. Although the invention is described principally in strip line or microstrip form, the invention can also be embodied in waveguide or coaxial form.

BACKGROUND OF THE INVENTION 
The present invention relates generally to branch line directional couplers 
which may be of the strip line, microstrip, coaxial, or waveguide type. 
More particularly, the invention relates to a four port power-coupling 
network provided with like matching networks at each port to provide 
matching at more than one frequency and characterized by a very flat VSWR 
curve. 
PRIOR ART 
FIGS. 1A and 1B show two structures of a prior art coupler network in strip 
line construction. FIG. 1A depicts the fundamental structure which is a 
four port device comprising four networks each of preferably quarter 
wavelength. This coupler inherently is matched at only a single frequency 
which is usually selected at the center frequency of the desired operating 
band. For example, if the operating band is the 3.7-4.2 GHZ band then the 
device is perfectly matched at only the center frequency of 3.95 GHZ. 
Proper balance is obtained only at that frequency and the VSWR is at 1.0 
only at the center operating frequency. If the coupler is constructed as a 
quadrature hybrid equal power coupling from the input port to the output 
ports occurs at the center frequency. To improve the VSWR bandwidth it is 
known to add further branch networks, or in the case of strip line devices 
to add further network strips essentially in parallel as depicted in FIG. 
1B. For examples and discussions of prior art branch line couplers refer 
to C. G. Montgomery, R. H. Dicke, and E. M. Purcell, Principles of 
Microwave Circuits, McGraw-Hill, New York, 1948; J. Ried and G. J. 
Wheeler, "A Method of Analysis of Symmetrical Four-Port Networks", IRE 
Trans. Microwave Theory and Technology, Vol. MTT-4, P. 246-252, Oct. 1956; 
and R. Levy and L. F. Lind, "Synthesis of Symmetrical Branch-Guide 
Directional Couplers", IEEE Trans. Microwave Theory and Tech., Vol. 
MTT-16, P. 80-89, Feb. 1968. These added networks tend to flatten the VSWR 
curve for the device and do somewhat broaden the band over which proper 
coupling is obtained. However, even though the device is matched at more 
than one frequency, the power division has not substantially changed as is 
apparent from the curve of FIG. 9. Thus, with the prior art branch line 
couplers it has not been possible to obtain a flat power division band 
width over an appreciable band such as up to a 30% band. 
OBJECTS OF THE INVENTION 
One object of the present invention is to provide a branch line directional 
coupler that has an improved broad band coupling performance in comparison 
to known branch line couplers. 
Another object of the present invention is to provide a branch line 
directional coupler characterized by a very flat VSWR curve by providing 
matching at more than one frequency in the operating band. 
Still another object of the present invention is to provide a branch line 
directional coupler characterized by improved power division over a 
relatively large portion of the operating band. In accordance with the 
invention flat power division is possible over bandwidths up to 30% of the 
operating band. 
A further object of the present invention is to provide a branch line 
directional coupler having in addition to improved VSWR, also improved 
isolation and return loss. 
Still another object of the present invention is to provide a four port 
coupler that is relatively simple in construction, easy to fabricate and 
relatively compact in size. 
Another object of the present invention is to provide a branch line coupler 
that can be constructed as a quadrature hybrid with equal coupling at the 
output ports and that can be constructed in many different forms such as 
in strip line microstrip, coaxial, or waveguide construction. 
SUMMARY OF THE INVENTION 
To accomplish the foregoing and other objects of this invention there is 
provided a branch line directional coupler which is comprised of four 
interconnected lossless two port networks interconnected to form four 
ports including an input signal port and a pair of output ports. Actually, 
any port of the coupler can be an input port. In order to provide an 
improved VSWR and flat coupling, in the preferred structure like two port 
matching networks are respectively coupled independently at each port of 
the coupler. For some applications only two matching networks may be used. 
For example, two networks may be used at the output only if matching is 
not critical at the input ports of the device. By the proper selection of 
the admittances of the fundamental networks comprising the coupler the 
coupler functions as a quadrature hybrid with equal power division over a 
relatively wide bandwidth. In the disclosed embodiment wherein the coupler 
is of strip line construction, each of the matching networks comprises a 
stub (strip) and associated quarter wavelength transformer extending from 
the ports of the coupler. The stub may be a shorted stub of quarter 
wavelength or an open stub of half wavelength. Under some conditions 
matching can be accomplished using only a quarter wavelength transformer 
without the stub (stubless version). The concepts of the invention are 
also applicable in the construction of waveguide and coaxial couplers.

EXPOSITION 
As previously discussed, FIG. 1A shows a fundamental prior art coupler of 
strip line construction comprised of four interconnected networks forming 
the ports 1, 2, 3 and 4. As previously mentioned, the performance of this 
coupler can be improved as far as the flatness of the VSWR is concerned by 
a previously known technique of providing additional branch lines or 
strips coupled essentially in parallel with the device. FIG. 1B shows a 
typical branch line coupler provided with additional conductive strips B1 
and B2. Three branches may also be used with all lengths being the same. 
Strip B1 couples between strips 1A and 4A, while strip B2 couple between 
strip 2A and 3A. With any of these prior art branch line couplers, 
although there is an improvement in VSWR the branch line coupler still has 
a parabolic curvature characteristic as far as the coupling is concerned 
with ideal coupling still at the most at only two frequencies. FIG. 9 
shows coupling curves at the output ports indicating the single frequency 
match and still basically parabolic curvature. 
In accordance with the present invention, instead of adding branch lines, a 
two port matching network is connected at each port of the coupler. Each 
of the matching networks is connected independently at the port with no 
interconnections between adjacent matching networks. FIG. 2 shows a four 
port electrical network in two wire form comprised of four networks 
interconnected between the ports 1, 2, 3 and 4. The ports 1 and 4 and the 
ports 2 and 3 are connected by a two port network N whereas the ports 1 
and 2 and the ports 3 and 4 are connected by a different two port network 
N'. The networks N and N' are both lossless, reciprocal and symmetrical 
networks. Because these networks are reciprocal and symmetrical the 
relations Y.sub.22 = Y.sub.11, and Y.sub.21 = Y.sub.12 hold for the 
admittance matrix elements shown in FIG. 2 which specify each of the two 
port networks. Furthermore, the network N' is actually the same as network 
N except for the factor of the admittance level Y. The network N' is equal 
to this level Y times that of the network N. The admittance matrix 
elements of network N' as shown in FIG. 2 are given by; Y'.sub.11 = 
Y.multidot.Y.sub.11 and Y'.sub.12 = Y.multidot.Y.sub.12. FIG. 2 also shows 
the matching network in accordance with the present invention represented 
by the elements of an ABCD matrix connected at each of the ports 1, 2, 3, 
and 4 shown in FIG. 2. 
The device shown in FIG. 2 with its particular symmetry regarding the 
networks N and N' functions as a perfect directional coupler if it is 
matched. It will be matched if no incident power is reflected at the input 
port 1 with port 4 being isolated while power couples out of ports 2 and 3 
in some ratio. However, in accordance with this invention by selecting a 
two port matching network connected at each of the input ports 1, 2, 3 and 
4 matching can occur at a number of frequencies and in particular at two 
frequencies as disclosed hereinafter. 
It can be shown by mathematical derivation that for all the matched 
frequencies the coupling ratio will be the same for a four port network of 
the specified form, and is given by the following equation: 
EQU .vertline.S.sub.12 /S.sub.13.vertline. = .sqroot. Y.sup.2 -1 (1) 
where S.sub.12 is the amplitude of the signal transmitted to port 2 from 
port 1; S.sub.13 is the amplitude of the signal transmitted to port 3 from 
port 1; and Y is the admittance level ratio between the networks N and N'. 
By selecting a matching network which, when connected at each of the ports 
1, 2, 3, and 4, matches the four port network at a number of frequencies, 
then very flat coupling is obtained over a frequency band including these 
frequencies since the coupling will be the same all frequencies at which 
the device is matched. The curve of FIG. 8 gives a clear indication of 
this coupling characteristic. A similar result is not obtained for the 
multi-branch coupler of FIG. 1B (See FIG. 9), as it does not fall into the 
category of network shown in FIG. 2. 
The next step is to determine the equivalent admittance into which the 
matching network (represented by the ABCD matrix in FIG. 2) has to match 
in order to be able to determine an appropriate matching network. If a two 
port matching network represented by the ABCD matrix matches into this 
complete admittance, then the same two port network connected at each of 
the four ports 1, 2, 3, and 4 yields a matched device when looking into 
ports 1', 2', 3' and 4'. The expression for the equivalent admittance is 
given by the general expression: 
EQU Y.sub.eq = G' + jY' 
and more specifically by: 
EQU Y.sub.eq = .sqroot.Y.sup.2 -1 Y.sub.12 + j (1+Y) Y.sub.11 (2) 
where Y.sub.11 and Y.sub.12 are the elements of the admittance matrix for 
the two port network N as shown in FIG. 2. The real part of the equivalent 
admittance is the conductance and the imaginary part is the susceptance. 
If A, B, C and D are the elements of the ABCD matrix of the matching 
network which has been connected at each of the four ports, then the 
matching conditions become: 
EQU 1 = (B.sup.2 + D.sup.2) .sqroot.Y.sup.2 -1 .multidot. Y.sub.12 = (B.sup.2 + 
D.sup.2) G' (3) 
EQU (ab-cd) = (b.sup.2 + d.sup.2)(1+y) .multidot. y.sub.11 = (b.sup.2 + 
d.sup.2) y'. (4) 
the final ABCD matrix is obtained by multiplying the matrix for a 
transformer by the matrix for a stub. 
Equations 3 and 4 may be used to design directional couplers with flat 
coupling in either strip line, microstrip, coax or waveguide transmission 
lines. However, an example may be helpful illustrating a particular design 
procedure. Consider a four port strip line device of the type shown in 
FIG. 2 in which the network N is simply a length of transmission line of 
electrical length .theta. and unit admittance Y.sub.o =1 as in FIG. 1A. 
The network N' connecting ports 1 and 2 as well as ports 3 and 4 is also a 
length of transmission line with the same electrical length .theta. but 
with a characteristic admittance Y. It is further assumed that the coupler 
is a quadrature hybrid with equal coupling at the output ports. There is 
thus equal power division between ports 2 and 3 so that .vertline.S.sub.12 
.vertline.= .vertline.S.sub.13 .vertline.. It follows from equation (1) 
that then Y = .sqroot.2. For the particular structure chosen Y.sub.11 = 
-cot .theta. and Y.sub.12 = 1/sin .theta.. It then follows from equation 
(2) that: 
EQU Y.sub.eq = 1/sin .theta. - j(1 + .sqroot.2) cot .theta. (5) 
It can be seen from equation (5) that when .theta. = 90.degree. 
corresponding to a quarter wavelength, the equivalent admittance is one. 
In the vicinity of .theta. = 90.degree., the equivalent admittance has the 
approximate form of a unit resistance shunted by a short-circuited stub of 
electrical length .theta. and admittance level (1 + .sqroot.2). 
FIG. 3 shows a matching network that may be used with the fundamental 
coupler structure. This network as shown in FIG. 3 comprises a quarter 
wavelength transformer of electrical length .theta. and admittance level 
Y.sub.1 shunted by a short-circuited stub of the same electrical length 
.theta. and characteristic admittance Y.sub.2. As previously mentioned, 
the resultant ABCD matrix is obtained by multiplying together the ABCD 
matrices for the stub and transformer. The resultant matrix elements are 
then substituted into equations (3) and (4). Next, the real and imaginary 
parts of equations (5) are substituted into equations (3) and (4) and the 
following 
matching conditions result: 
EQU sin.sup.2 .theta./Y.sub.1.sup.2 + (1+Y.sub.2 /Y.sub.1).sup.2 cos.sup.2 
.theta. = sin .theta. (6) 
EQU sin .theta./Y.sub.1 - (1+Y.sub.2 /Y.sub.1) (Y.sub.1 sin .theta. - Y.sub.2 
cos.sup.2 .theta./sin .theta.) = -(1+.sqroot.2) (7) 
The equations (6) and (7) can be solved simultaneously to determine the two 
unknown characteristic admittances Y.sub.1 and Y.sub.2. Further, these 
equations are unchanged if the electrical length .theta. is replaced by 
180.degree.-.theta.. There will thus be two frequencies of perfect match 
symmetrically located about the center frequency corresponding to these 
two electrical lengths. If additional matching stubs and quarter 
wavelength transformers are provided at each port, still further 
frequencies exist of ideal match. For example, each port of the device may 
have two matching stubs associated therewith. 
FIG. 4 shows the directional coupler with the matching networks 1B, 2B, 3B 
and 4B coupled to the respective ports 1, 2, 3 and 4 of the branch line 
directional coupler. The curves shown in FIGS. 7 and 8 are associated with 
the embodiment of FIG. 4 and give the theoretical performance (VSWR and 
coupling to ports 2 and 3, respectively) for a strip line matched hybrid 
optimized for the 3.7-4.2 GHZ band by a proper choice of .theta.; 
EQU .theta. .perspectiveto. cos.sup.-1 .sqroot.1/2 cos (.pi./2 (1 + 
.DELTA.f/f)) 
where .DELTA.f/f is normalized bandwidth. 
For Y.sub.1 = 1.026 and Y.sub.2 = 2.39 the VSWR is less than 1.06 and the 
coupling imbalance is about 0.012 db although the theoretical coupling 
imbalance can be made less than 0.006 db maximum over this band. With this 
matching structure there is a flat coupling in comparison with other 
devices of bandwidths up to 30%. The balance is perfect as noted in the 
curves at those frequencies for which the VSWR = 1. Furthermore, the 
coupling to port 2 has a ripple and not the usual parabolic curvature 
characteristic of branch line couplers such as the type shown in FIG. 1B. 
As previously mentioned the coupler of this invention can be constructed as 
a quadrature hybrid by the proper selection of the admittance values of 
network N and N'. For the quadrature hybrid it has been shown that the 
ratio is in the magnitude .sqroot.2. However, by slightly varying this 
ratio the curves of FIG. 8 can be moved essentially relative to each other 
thereby crossing each other so that there are four frequencies at which 
coupling is the same and ideal. Thus, matching frequencies may be, for 
example, at two spaced frequencies about 3.78GHZ and two other spaced 
frequencies about 4.12 GHZ. 
FIGS. 5 and 6 show another embodiment of the present invention. Instead of 
short-circuited stubs as indicated in FIGS. 3 and 4, open circuited stubs 
of electrical length equal to 2.theta. and characteristic admittance 
Y.sub.2 = 1.195 (= 1/2 Y.sub.2 for short-circuit stub) were used thereby 
making the construction simpler. As indicated in FIG. 5 these stubs, 
having a longer length, are folded back to make the construction more 
compact. However, the gap (c) is made sufficiently long to prevent any 
cross talk between the facing stubs. 
FIG. 6 in particular shows in a cross-sectional view the basic components 
of the device. In FIG. 6 the different layers comprising the device can be 
interconnected in a suitable manner. The strip line device is primarily 
embodied on a printed circuit board 10 having clad thereto the conductor 
12 which is constructed in the form clearly depicted in FIG. 5. The device 
also comprises in a sandwich construction ground planes 14 and 16 and a 
blank insulating sheet 18. Connections can be made in a conventional 
manner to the etched conductor 12 at the appropriate ports. 
The network pattern shown in FIG. 5 can be constructed in a well known 
manner. A photoresist is applied to a copper-clad printed circuit board 
and predetermined areas of the board have the copper etched therefrom 
leaving the pattern of FIG. 5. The strips comprising the device can be 
trimmed easily to provide the proper admittance values for the basic 
structure and the matching stubs. 
In the example previously given the operating frequency was about a center 
frequency of 3.95 GHZ. Devices for operation at different frequencies can 
be easily constructed by a simple scaling operation. For a quadrature 
hybrid the ratio between admittances for the basic network would remain 
.sqroot.2 but the electrical lengths would change in a scaled ratio to 
operating frequency. Of course, the previously cited equations would be 
used to calculate admittance values of the stubs for the new frequency 
band. 
Many modifications of the matching network are possible which also will 
provide a low VSWR and very flat coupling over bandwidths up to at least 
30%. For instance, the stub may be replaced by a lump element shunt 
resonant LC circuit with the capacitance C and the inductance L chosen to 
give the same center frequency and susceptance-slope parameter as the 
stub. This is advantageous at the lower end of the microwave spectrum 
where the stub becomes quite long. Likewise, the basic structure of the 
junction may be modified while still remaining with the general structure 
represented by FIG. 2. For example, the admittance Y.sub.0 need not be 
selected at unity but could be some number larger than unity which would 
actually improve the performance after matching over a given bandwidth 
(See solid curve of FIG. 7). 
FIG. 10 shows a schematic diagram similar to that shown in FIGS. 4 and 5 
but for the stubless version of the present invention. This device is of 
strip line construction and has an etched conductor defining the four 
ports 21, 22, 23, and 24. These ports 21, 22, 23 and 24 have associated 
therewith quarter wavelength transformers 21A, 22A, 23A and 24A, 
respectively. It is noted in the version of FIG. 10 that the strips 
defining the ports are of a substantially larger width than the 
embodiments shown in FIGS. 4 and 5. The widths of these strips are 
calculated as being 2w whereas the width as depicted in FIG. 4 is w. 
In the design procedures for the coupler of this invention there are 
actually three variables, namely Y.sub.0, Y.sub.1, Y.sub.2 that must be 
chosen. By assuming that the stub is eliminated, the variable Y.sub.2 is 
therefore eliminated and one can solve the equations such as equations 6 
and 7 for the admittances Y.sub.1 and Y.sub.0. Upon doing this a structure 
like that shown in FIG. 10 is developed. As previously mentioned with this 
arrangement, the width of the strips is twice that shown in an arrangement 
like FIG. 4 and the transformers have a width of 1.414w. The arrangement 
of FIG. 10 may have some applications but there is a problem with this 
arrangement in that the equations show that Y.sub.0 must be quite large 
and consequently this arrangement gives rise to junction effect problems. 
This is apparent from FIG. 10 where the ports are large and relatively 
close together so that the conditions for junction effect problems are 
present. 
FIGS. 11A and 11B show a waveguide version of the present invention as a 
10db coupler. With such a coupler the power division of the output ports 
is in he ratio of one-to-ten. In the arrangement of FIGS. 11A and 11B 
there are two main guide channels defining the ports 31, 32, 33 and 34. 
The two cross channels 35 and 36 connect between the main channels and 
provide the cross coupling for the coupler. It is noted that because this 
is a 10db coupler the channels 35 and 36 are of a substantially lesser 
width than the width of the main through channels. FIG. 11B clearly shows 
the stubs 31A, 32A, 33A, 34A each respectively associated with the ports 
31, 32, 33 and 34. Each of the stubs can be a short section of terminated 
waveguide. In this waveguide version the height of the sections of the 
guide is proportional to the required characteristic admittance levels. 
FIG. 12 shows a coaxial transmission line version of the present invention 
comprising coaxial transmission line sections defining ports 41, 42, 43 
and 44 defining the basic structure of the device. In this particular 
arrangement only two stubs are provided shown in FIG. 12 as terminating 
conductors 45 and 46 associated respectively with output ports 42 and 43. 
The conductors 45 and 46 are terminated to the outer shield by conductive 
plates 45A and 46A, respectively. The arrangement of FIG. 12 may be used 
in an application where one is not concerned with a match at the input 
ports. For example, the structures shown in FIG. 12 may be used as a power 
divider where input match is not as important as flat power coupling out 
of the output ports. 
The use of only two matching networks may also apply in the strip line 
construction where the device may be used as an isolator or a power 
switch, for example. In some of these applications diodes are connected at 
the output ports. These diodes inherently have series and shunt reactance 
which causes some imbalance problems when employed with branch couplers or 
the basic coupler. However, with the structure of this invention 
compensation for these diode parameters can be made quite easily by 
trimming the length of the stubs thereby changing the electrical length 
.theta. to compensate for this diode reactance. Usually, only the stub 
having the diode associated therewith is trimmed. 
The embodiment shown in FIG. 13 is substantially the same as that shown in 
FIG. 5 and thus like reference characters will be used to identify similar 
parts in these two diagrams. The primary difference in the embodiment of 
FIG. 13 is that this coupler has been constructed as a 10db coupler having 
uneven power division at the output ports 2 and 3. In this particular 
arrangement it is noted that the strips 50 and 51 have a width 
substantially less than the other strips comprising the basic structure. 
The equations can be solved to yield the proper admittances for these 
cross strips. With this arrangement the power coupling is in the ratio of 
ten-to-one between the ports 2 and 3, respectively. 
FIG. 14 is a schematic diagram in two wire form illustrating series 
connections of the two port matching networks. This diagram is quite 
similar to the one previously shown in FIG. 2 except that the diagram of 
FIG. 2 was for the preferred connection or parallel connection of the two 
port matching networks. In FIG. 14 the matching networks are still 
represented by the ABCD matrix but the basic network is now represented by 
an impedance matrix rather than an admittance matrix. Each of the four 
ports comprising the basic network is represented by its own impedance 
matrix. The diagram of FIG. 14 may actually be considered as a dual form 
of the diagram of FIG. 2 and is similar to the case of parallel 
connections if admittances are everywhere replaced by impedances. 
The embodiment of FIG. 14 may be practically applied in the waveguide 
coupler version of this invention. For this version the important quantity 
is the equivalent impedance Z.sub.eq which is given by the following 
equation: 
EQU Z.sub.eq = .sqroot.Z.sup.2 -1 Z.sub.12 + j(1+Z) Z.sub.11 
the power division is now determined by the following equation: 
EQU Z = .sqroot..vertline.S.sub.12 .vertline..sup.2 /.vertline.S.sub.13 
.vertline.+1 
having described a limited number of embodiments of this invention, it 
should now become apparent to those skilled in the art that the principles 
herein disclosed can be applied to construct many different versions of 
the invention.