US 3761843 A Abstract A circuit building block for simulating quarter wave length four-port devices is disclosed. The building block includes two sections each made from a pair of coupled lines which are substantially equal in length and have substantially equal phase velocity in the even and odd modes of excitation. The pairs of coupled lines each have an even mode impedance of Ze and an odd mode impedance of Zo. The characteristic impedance of the line Zt is equal to 2ROOT ZeZo. A pair of uncoupled lines interconnects the pairs of coupled lines in series. The uncoupled lines each have a characteristic impedance of Zt. Another pair of uncoupled lines is connected to each unconnected end of the pairs of coupled lines to provide phase correction. The disclosure also teaches how to use the basic circuit to provide functions normally provided by other structures. The disclosure also teaches the use of a four-port device for impedance matching and phase shifting.
Description (OCR text may contain errors) United States Patent [1 1 Cappucci Sept. 25, 1973 [75] Inventor: Joseph D. Cappucci, Wayne, NJ. [73] Assignee: Merrimac Industries, Inc., W. Caldwell, NJ. [22] Filed: May 16, 1972 [21] Appl. No.: 253,862 [52] US. Cl 333/10, 333/31 R, 333/35 [51] Int. Cl. HOlp 5/14 [58] Field of Search 333/10, 11, 20, 31 R, [56] References Cited UNITED STATES PATENTS 3,452,301 6/1969 Cappucci et al 333/10 3.6143572 10/1971 Newboulcl v 333/10 3621,4178 11/1971 Johnson et al 333/10 FOUR PORT NETWORKS SYNTHESIZED FROM INTERCONNECTION OF COUPLED AND UNCOUPLED SECTIONS OF LINE LENGTHS Primary Examiner-Paul L. Gensler Att0meyLawrence I. Lerner et a1. [ 5 7] ABSTRACT A circuit building block for simulating quarter wave length four-port devices is disclosed. The building block includes two sections each made from a pair of coupled lines which are substantially equal in length and have substantially equal phase velocity in the even and odd modes of excitation. The pairs of coupled lines each have an even mode impedance of Z, and an odd mode impedance of Z,,. The characteristic impedance of the line Z, is equal to Z Z A pair of uncoupled lines interconnects the pairs of coupled lines in series, The uncoupled lines each have a characteristic impedance of Z,. Another pair of uncoupled lines is connected to each unconnected end of the pairs of coupled lines to provide phase correction. The disclosure also teaches how to use the basic circuit to provide functions normally provided by other structures. The disclosure also teaches the use of a four-port device for impedance matching and phase shifting. 43 Claims, 19 Drawing Figures PATENIEU 3.761 .843 SHEET 30F 4 Lfdb F/G. l0 , T Freq. (MC) 200 300 400 500 97 f 93 9 IO! INPUT POWER DIVIDER F/6.// PRIOR ART Q T r 93 'NPUT POWER DIVIDER I07 lO8 I09 POWER DIVIDER 6 INPUT PATENTEDSEP25|975 3.761.843 SHEET h 0F 4 SIG. GEN. FOUR PORT NETWORKS SYNTHESIZED FROM INTERCONNECTION OF COUPLED AND UNCOUPLED SECTIONS OF LINE LENGTHS FIELD OF THE INVENTION This invention relates to electrical networks and particularly to electrical networks generated from the interconnection of four-port devices. BACKGROUND OF THE INVENTION Electrical signals can be modified by the transfer function of networks through which they pass. As a result, various systems for synthesizing networks have been developed which enable network designers to construct signal shaping and modifying networks. Each system of theory of network synthesis results in certain basic network components which are interconnected in accordance with the cicuts theory to result in particular wave shaping or modifying networks. With the advent of four-port quadrature hybrid couplers, the quadrature coupler has begun to be looked upon as a circuit element for interconnection into wave shaping networks. U.S. Pat. No. 3,452,300 which issued to J. D. Cappucci, et al. on June 24, 1969 and is entitled Four Port Directive Coupler Having Electrical Symmetry with Respect to Both Axes discloses a four-port quadrature hybrid coupler suitable for interconnection in accordance with the teachings of, for example, U.S. Pat. No. 3,514,722 which issued to J. D. Cappucci on May 26, l970and is entitled Networks Using Cascaded Quadrature Couplers, Each Coupler Having a Different Center Operating Frequency into networks for wave shaping. Attempts have been made to develop printed circuit microwave networks using interconnections of fourport quadrature couplers. These systems employ interconnected quarter wave length couplers of different impedances to provide the various transfer characteristics necessary for network design; In order to change impedance in a printedcircuit environment, the dielectric spacing must be changed, or if the spacing is constant then either the ground plane spacing or the separation between conductors must bealtered. This results in parasitic effects at the interface between impedance systems which generally cannot be made to be dual in both modes of excitation and therefore provide actual solutions which are far from ideal. BRIEF DESCRIPTION OF THE INVENTION In accordance with the teachings of this invention, a network theory is provided which results in new circuit networks with repeatably comp'ensatable impedance interfaces. The basic building block which results from this invention includes first and second lines electromagnetically coupled to each other. The first line provides first and second terminals at opposite ends thereof while the second line provides third and fourth terminals at opposite ends thereof. The electrical length of the first and second line are equal. The first and second lines exhibit an even mode impedance of Z, when the first, secnd, third and fourth terminals are terminated in an impedance of 2,. These first and second lines exhibit an odd mode impedance of 2,, when the first, second, third and fourth terminals are terminated in the impedance of 2,; Z, is equal to V 2,2,. The first and second coupled lines exhibit equal phase velocity in the even and odd modes of excitation. The basic building block also includes third and fourth lines electromagnetically coupled to each other. The third line provides fifth and sixth terminals at opposite ends thereof while the fourth line provides seventh and eighth terminals at opposite ends thereof. The electrical length of the third and fourth lines are equal. The third and fourth lines exhibit the even mode impedance of 2 when the fifth, sixth, seventh and eighth terminals are terminated in the impedance of 2, while the third and fourth lines exhibit the odd mode impedance of 2, when the fifth, sixth, seventh and eighth terminals are terminated in the impedance of 2,. The third and fourth coupled lines exhibit equal phase velocity in the even and odd modes of excitation. The basic building block further includes a fifth line for connecting the second terminal to the fifth terminal and a sixth line for connecting the fourth terminal to the seventh terminal. The basic circuit building block can be made to function as a four-port quadrature coupler by including four uncoupled lengths of line attached to the first, third, sixth and eighth terminals to provide an overall length of a quarter wave at the center operating frequency thereof. Four-port quadrature couplers constructed from the basic circuit building block as above described can be interconnected to provide various circuit networks. In each case the additional four uncoupled lengths of line can be deleted from the end sections resulting in foreshortened four-port quadrature structures. In accordance with this invention it has been discovered that a four-port quadrature coupler a quarter wave length long can be employed for impedance matching purposes as well as for performing its normally intended function. It has further been discovered that differential phase shifters of the Schiffman variety can be substantially improved by employing a shorting device a quarter wave length long. DESCRIPTION OF THE DRAWINGS For a more complete understanding of the invention, reference should be made to the following detailed description and drawings in which: FIG. 1 is a schematic diagram of the basic building block which results from this invention; FIG. 2 is a schematic diagram of an equivalent to a quarter wave length four-port quadrature coupler constructed in accordance with the teachings of this invention; FIG. is a schematic diagram of a prior art cascaded coupler system; FIG. 4 is a schematic diagram showing a network constructed in accordance with the teachings of this invention which provides a similar transfer function to the conventional prior art structure shown in FIG. 3; FIG. 5 is a schematic diagram showing an alternate way of constructing a network in accordance with the teachings of this invention which includes a mix of quarter wave and foreshortened devices; FIG. 6 is a graphic illustration of the comparison of loss functions for a structure as shown in FIG. 3 with a structure shown in FIG. 4 or 5; FIGS. and 7b are graphic representations of two different forms of loss functions which can 21st by networks 22nd accordance with the teachings of this invention; 23rd 24th FIG. 8 is a schematic diagram of a network constructed in accordance with the teachings of this invention which provides the transfer function as shown in FIG. 7b; FIG. 9 is a schematic diagram of another network constructed in accordance with the teachings of this invention which provides a transfer function of the form shown in FIG. 7b; FIG. 10 is a graphic showing of the response ofa coupler constructed as in FIG. 8 in accordance with the teachings of this invention both actual and calculated; FIG. 1 1 is a schematic diagram of a prior art 90 fixed differential phase shifter as defined by Schiffman; FIG. 12 is a schematic diagram of a 90 fixed differential phase shifter constructed in accordance with the teachings of this invention; FIG. 13 is a schematic representation of a differential phase shifter constructed in accordance with the teachings of this invention; FIG. 14 is another defined of a fixed in phase shifter constructed in accordance with the teachings of this invention; 22 FIG. 15 is a schematic diagram of a quarter wave coupler terminated in accordance with the teachings of this invention; FIG. 16 is a schematic diagram of the circuit of FIG. 15 rearranged for mathematical analysis; and FIGS. 17 and 18 are schematic representations of even and odd mode bisections respectively of FIG. 16. DETAILED DESCRIPTION OF THE INVENTION Referring now to FIG. 1 we see a two-section structure 30 constructed from first and second coupled lines 31 and 32 (represented by a pair ofparallel lines), both having the same electrical length, and a pair of uncoupled lines 33 and 34 (represented by a pair of curved lines). It should be clear that the coupled lines can be formed each from a pair of conductors held in registration with each other between a pair of ground planes, not shown. Of course, the coupled lines can be constructed in any fashion so long as the even and odd mode impedances of the system are dual to the characteristic impedance of the generator and terminations. The overall length of this structure 30 is always less than a quarter wave length at its center frequency. Applying duality conditions to both the coupled lines 31 and 32 and the uncoupled lines 33 and 34, we find that because of the distributed nature of the elements, and in order to satisfy duality requirements over a wide frequency range, it is necessary to make the phase velocity in each mode of the coupled lines 31 and 32 alike, the phase velocity of each of the uncoupled lines 33 and 34 alike and the characteristic impedance of the coupled lines 31 and 32 and the characteristic impedances of the uncoupled lines 33 and 34 equal to the characteristic impedance of the system. In each of the structures constructed from coupled and uncoupled line lengths as taught by this invention, common impedance systems of coupled and uncoupled lines are employed throughout so that the transistions from coupled to uncoupled lines are similar at each junction. This enables easy fabrication and easy parasitic compensation of the structure. The lengths of the coupled lines 31 and 32 and the uncoupled lines 33 and 34 and the impedance thereof can be derived by employing equations defining the above-mentioned conditions of duality and in addition constructing an equation which sets the amplitude response of the section coupler 30 equal to a desired amplitude function. In Appendix I, will be found a mathematical treatment of the development of the structures shown in FIGS. 1 and 2. In FIG. 2 the two-section coupler 30 is modified by adding four uncoupled lines 36, 37, 38 and 39 thereto to provide an overall electrical length from a first input port 41 to a first output port 42 of a quarter wave length long at the center operating frequency thereof. Similarly the electrical length from a second input port 43 to a second output port 44 is one quarter wave length at the center operating frequency. The structure shown in FIG. 2 is substantially an electrical equivalent to a quarter wave length four-port hybrid quadrature coupler. Thus the section 30 is substantially the electrically equivalent in amplitude, but not in phase of a quarter wave length coupler. Section 35 is the electrical equivalent of a quareter wave length coupler which contains the phase compensation to make it substantially equivalent in both amplitude and phase. FIG. 3 shows a prior art structure which interconnects quarter wave length devices 46, 47 and 48 asdescribed by Crystal and Young in Theory & Tables of Optimum Symmetrical TEM-Mode Coupled- Transmission-Line Directional Couplers, Vol. MMT-I3, September 1965, pgs. 544-558. Each of the quarter length devices 46, 47 and 48 has its impedance variable solely by the geometry of the section. In FIG. 4 we see a system of interconnected line lengths which has been synthesized to provide a response substantially equal to the response of the structure shown in FIG. 3. It should be noted that sections of the structure in FIG. 4 are formed from units 35 shown in FIG. 2. A section 35 similar to section 35 of FIG. 2 is placed in the system in a position similar to section 47 of FIG. 3. Section 35' has substantially the same amplitude and phase response as section 47. On opposite ends of section 35' there are coupled amplitude equivalent sections and 45, with section 45 on one end consisting of a pair of coupled lines 49 and 51 interconnected by uncoupled lines 52 and 53 with uncoupled lines 38' and 39 joining coupled lines 51 to section 35'. The other section 45' consists of coupled lines 54 and 56 joined by uncoupled lines 57 and 58. Uncoupled lines 36' and 37' join coupled lines 54 to the other end of section 35'. It will be noted that section 45 is a section structurally similar to section 35 of FIG. 2, but electrically equivalent to section 46 of FIG. 2. Similarly, section 45' is structurally similar to section 35 but electrically equivalent to section 48 of FIG. 2. Both sections 45 and 45 differ from section 35 in that a pair of uncoupled lines 36 and 37 of section 35 in the case of section 45, and 38 and 39 of section 35 in the case of section 45, have been removed from their respective sections. This has been done because the lengths of the generator and the termination can be eliminated as they do not affect either the amplitude response or the phase quadrature at the outputs, but affect only the transfer phase of the network, reducing it from that of the original. FIG. 5 shows a hybrid type system which employs both conventional quarter wave structures and structures synthesized with coupled and uncoupled lines which were described in detail with respect to FIGS. 1 through 4. In FIG. 5 a center section 59 is a quarter wave length structure while the two end sections 61 and 62 are structures constructed from coupled and uncoupled line lengths. It should be appreciated that the quarter wave section 59 is equivalent to the quarter wave section 47 in FIG. 3 while the synthesized sections 61 and 62 of FIG. 5 are identical to sections 45 and 45 of FIG. 4 and are equivalent to the quarter wave sections 46 and 48 of FIG. 3. FIG. 6 shows the comparison between the response of the structure in FIG. 3 and the structure of FIGS. 4 and 5. The dotted line represents the response of FIG. 3 and the second line represents the amplitude response of FIGS. 4 and 5. It should be noted that the deviation between the two responses is insignificant. The graph in FIG. 6 shows the loss function in db as a function of frequency for one class of the networks. FIGS. 7a and 7b represent loss functions of networks as functions of normalized frequency w. The prior art has described networks which are even functions of'w as shown in FIG. 7a which can be synthesized by networks as shown in FIGS. 3, 4 and 5. FIG. 7b employs a network response which is an odd function ofm which is obtained through the use of networks of the form of FIG. 8. As an even function of w, the loss function is symmetrically displaced about w=l with either a maximum or a minimum (depending on the order of the function) located at m=l. As an odd function of w, the loss functions is antisymmetrically displaced about m=1 with a mean value of coupling (an inflection point) located at aF-l. FIGS. 7a and 7b depict both forms of the loss function. In FIG. 8 there is shown a network form which will produce the odd function of m as shown in FIG. 7b. The network of FIG. 8 including two identical sections 70 and 72 (similar to section 30 of FIG. 1 but having a different center operating frequency than section 30) joined by a coupled line 74. The coupled impedance of section 74 is the same as the coupled impedance of sec-. tions 70 and 72. FIG. 9 shows a five-section coupler having an odd function of response. Sections 76 and 78 on opposite ends of the coupler are identical to each other. Section 76 is joined to another section 80 by a coupled line 84. Section 78 is joined to a section 82 by a coupled line 86. Coupled lines 84 and 86 are identical. Sections 80 and 82 are identical to each other but have a different operating frequency than sections 76 and 78. Sections 80 and 82 are connected together by a coupled line 88. It should be noted that sections 76, 78, 80 and 82 are similar structurally to section 30 of FIG. 1 but have different operating frequencies than the operating frequency of section 30. The coupled impedance in all the sections can be equal. FIG. is a graphical showing of the loss function L of a form of the network of FIG. 8 plotted against frequency. The lower curve represents the calculated response of the networks and the upper curve represents the response achieved from fabricating the networks. It should be noted that there is a substantially minimal loss differential between the two curves which can be attributed to the copper losses in the network. Thus it has been shown that various graphical forms of loss versus frequency curves can be synthesized utilizing the techniques and sections of the present invention. FIG. 11 is a prior art differential phase shifter 89 of the class developed by Schiffman. The differential phase shifter 89 is driven by a power divider 90 which provides signals having fixed phase relationships therebetween to terminals 91 and 92. The terminal 91 is an input terminal of a reference line 93 which has a length determined by the differential phase shift desired. The terminal 92 is an input terminal of a quarter wave coupler 94 shorted by a conductor 96 at its unconnected end. The differential phase shifter 89 as above described phase shifts the signals applied to terminals 91 and 92 so that a constant differential phase shift is imposed therebetween when the signals arrive at terminals 97 and 98. In FIG. 12, elements similar to those shown in FIG. 11 have been given like numerals. The shorted coupler 94 in FIG. 11 is replaced with a structure 99 which includes the basic building block of this invention shown in FIG. 1 and a shorting line 101 connected thereto. It should be noted that the structure 99 is less than a quarter wave length long so that the reference line 93 can be shorter than heretofore to provide the same differential phase shift. It should be noted that the refer-' ence line 93 is shortened by twice the amount that the structure 99 is less than a quarter wave length long. FIG. 13 shows another differential phase shift in which the power divider 90 drives a reference line 93 and a structure 102. In this case the structure 102 includes a quarter wave length coupler 103 and a half wave length loop 104 of uncoupled line. The uncoupled loop 104 essentially moves the odd mode short a quarter wave length away from the terminal end of the quarter wave length coupler. Other structures can be generated using the twosection coupler algorithm. Any device using a quarter wave coupler can be replaced by a two-section coupler. This would include reflection mode devices such as variable attenuators, variable phase shifters, reflection amplifiers, etc. In addition, power distribution and collection networks (arrays) and devices such as mixers can be fabricated from the two-section coupler. In almost all of the instances stated above, the end-section phase compensation (All!) is not necessary for proper performance, since the device performance is dependent on relative phase and not absolute phase. In other devices such as fixed differential phase shifters, the absolute phase through the device is critical and the end-section phase compensation must be used. In a differential phase shifter such as proposed by Schiffman (B. W. Schiffman, A New Class of Broad- Band Microwave 90 Phase Shifters Vol. MTT-6, April 1958, pgs. 232-237), the algorithm described in Appendix I is directly applicable with the following improvements: l. The end section phase compensation Ail: required at the input and output (ports 1 & 3) legs are not required, shortening the reference path by 2M1, and 2. The short circuit in the odd mode necessary at ports 2 & 4 is well defined leading to less parasitic compensation. The basic Schiffman phase shifter is shown in FIG. 11, and the two-section coupler equivalent in FIG. 12. Schiffman has described a number of phase shifters in his paper. which are defined as Type A-F phase shifters. In every instance, the quarter wave and/or three-quarter wave couplers with varying impedance 7 8 can be replaced with the appropriate two-section coualso gained. plers with end section compensation (A104 This The reference line length in this structure is always form of solution as in the multiple section couplers of shorter than the length of the coupled section. The de- Appendix I allows the use of a common geometry sysviation over an octave band is less than i 0.4". Ninety tern leading to simpler construction and smaller paradegree solutions can be found for reference line lengths sitic difficulties. of 39 and 0 as well as for the 56 length shown. In addition, Cristal (E. G. Cristal, Analysis and Exact As before, ea h coup ed s ct n ca b replaced by S nthesis of casc ded C mmensurat Transmissiona two-section coupler to generate a system of constant Line C-Section All-P ss Netwo ks V 1, MMT. 14 impedance sections which are noncommensurate in June 1966, pgs. 285-291) has synthesized threelength, making the device y to P section C-type phase shifters, and this procedure is di- 15 Shows a quarter Wave coupler 63 driven from rectly applicable to this structure. The differential a source impedance 64 and terminated in impedances phase hift proposed by Cristal is a commensurate 66 and 67 which are different from the source impedcascade of varying impedance couplers. These can be anceimpedance 68 equal to the Source impedance replaced, coupler-by-coupler, with the a ro i 15 terminates the isolated port of the coupler 61 3. In accortwmsection couplers (with phase compensation Alp) to dance with the teachings of this invention it has been f a noncommensurate system with a common found that if the impedance of a coupler is equal to the pedance format geometric mean of the source impedance and the ter- Schiffman has shown that wideband differential mmafing impedances the coupler 63 Serve as a phase shifters can be constructed using a shorted coumatihing trfmsforwer with isolation at the fourth port pler (FIG. 11) coupled to a length of line. The phase termmated m the Impedance slope of the shorted coupler is always greater than The coupler 63 can be a conventional quarter wave unity, so that-the comparison line is always longer than 'f constructed 2 heretofore techtI: overall lefigth of the coupler niques or a coupler built in accordance with the teach- If the coupler contains the odd mode short a quarter ings of this invention and outlined in detail in Appendix wave length away from the JUIlCtlOI'lS as shown in FIG. FIGS. 17 and 18 are equivalent circuits of the 13, then the phase slope at center band becomes less structure of FIG. 15 and are referred to in detail in Apthan unity, and the comparison length of line becomes endix II. shorter than the overall length of the coupler. p For a 90 differential phase shift using Schiffman,s It should be understood that while the above inven tion has been described with res ect to articular emmethod, the comparison line IS 270 long at center frep p F th h hfi th th d d bodiments thereof, numerous others will become obvii or 6 same p S I using me o eous to those of ordinary skill in the art in light thereof. scribed above, the comparison line is 90 long. Typical responses for 90 phase shifters show that APPENDIX 1 over an octave band the deviation from 90 over the. band is considerably reduced using the circuit of FIG. THE TWQ'SECTION COUPLER, The basic form of the two-section coupler is shown 13. The Schiffman circuit is 90 i 2.8 over an octave, 0 o in FIG. 1. The coupler is fabricated by connecting two the circuit proposed here is 90 i 1.4 or twice as good v short sections of coupled lines by short lengths of unas the present art. 40 F th th t l b th coupled lines. The overall length of this structure is al- Ur 6 quar er wave coup er m 0 cases can ways less than a quarter wave length at its center frebe reduced to a two-section type to reduce the lengths I t d O t h t of the structures and allow the device to be easily mtequency App ymg dual y con m o eac Sec grated into other systems of couplers without changing we get the geometry of the system. be: 4 4n Referring now to FIG. 14 we see the power divider (1) 5 (1b) 90, the reference line 93 and a structure 106. In this z, 1/z,,, 2 (2a) case the structure 106 includes two tandem quarter 2, a/z.,2= 1 wave length couplers 107 and 108 terminated in a half wave loop 109 which is the same as the loop 104 in Th f r atrix (ABCD) an be expressed a a FIG. 13. function of the even mode matrices becoming: Cos jz Sin 5 Cos j Sin CO m is Sin Me: Sin Cos 1 j Sin & Cos 4: jg Sin Cos (3) The modified phase shifter as shown in FIG. 14 can Normalizing the function in (u, where (b, is the phase either provide more bandwidth for a given deviation, or l th of the first section at w=l, and f), is the phase lc d viat n for th am andw length of the center section at w=l, and multiplying the It, of course, should be understood that multiple seci s, w obtain for the matrix terms: tions in addition to sections 107 and 108 can be added A =D =Cos (,m){ C0 '(1w)- (i to produce the different desired results. It should also (z-l/z)Sin(,m)Sin (4 0) Cos l0) (40) be understood that the structures 102 and 106 in FIGS. B =j 2zCos (,w)Sin (,m) Cos(,m)+Sin (,w){ l3 and 14, respectively, can be simulated by foreshort- Cos'( w)zSin w)}} (4b) ened structures as described heretofore and the results C,=j{ 2/ZCos w)Sin (,w)Cos (4 ,w)+Sin(,m accruing from the structure as shown in FIG. 12 can be Cos(,m)l/Z2Sin (4: 10 (4c) the values of Z8 and P( l) and assuming if), and (1) 11, is Solutions to equations 6 and 7 are found by setting w Sin 9 Cos held constant and 41 is varied until eq. (6) is satisfied and these values substituted in eq. (7). The solution for P(l) is compared to the value of PU) needed and 4a C05 0 q- 0 J M11 adjusted accordingly. This process is iterated until both {R VH eqs. (6) and (7) are satisfied. aia This iterative procedure is done easily with a comjl/lal Si 0 i Sin 9 puter and solutions are always found so long as 1,, is greater than the even mode impedance necessary to Setting up the condition for Directivity, that S S build the equivalent quarter wave coupler. 0 we obtain: The coupler derived in this fashion will always have Z8 R lz z Ry/Z 17 a phase length which is shorter than that of the equivalent quarter wave coupler. Therefore, in order to proand vide a phase equivalency between the two structures, R z z (13) a phase length must be added to all four ports of the two-section coupler. The transfer phase of the two- Expressing equation 16a and 16b in terms of z we section coupler at m=l is, get: so that the phase to be added at each port of the two- V COS 0 U 1 section coupler is, ze "lia( )l) H120: . z 1 bin 6 This completes the algorithm which equates the two- W R1 section coupler to a quarter-wave coupler. The completed circuit is shown in FIG. 2. Sin 0 COS 9 1 (19a) Cos 0 j APPEXDIX ii we. 2. COUPLERS USED AS TRANSFORMERS Maw: 2.. . y-: bin 6 If, bin 0 There has been a use in recent years, whereby quadj i I (19h) rature 3db couplers have been used in arrays to parallel transistor amplifiers. The quadrature array isolates the amplifiers and as such provides the best harnessing medium. The difficulty is that the system impedance of Solving equations 16a, 16b, 19a, and 19b we can obor 75 Q is normally too high for the emitter impedances 50 tain the scattering parameters of the four-port which of the transistor which typically ranges from 1-5 ohms. are; Because of this, compromises are made leading to nonoptimum system performance. One possible solution to this problem is offered here. Couplers have long been analyzed'as though they were 1 C 9 W Rr-m quarter wave filters or transformers functioning be- S hpi 11= tween equal impedance levels. If a quarter wave cou- 1 C 0 0s +J 25 J Sin 0 Sin 0 pler were constructed as in FIG. 15, then the coupler could be identified as the equivalent circuit of FIG. 16 with the terminating resistors R at ports 2 and 3 replaced by ideal transformers. This allows simple matrix 2 analysis of the structure in its even and odd modes. The 512: 1 network bisections are shown in FIGS. 17 and 18, and H. m (km 1 7L) Sin 0 the ABCD matrices in each mode for each pair are: l R1 (31) These equations define the performance of the transforming coupler. For example, for an equal split coupler covering an octave band, 6, =60, 6 120 6,, 90. Therefore, SI 2 i 3 1 a 1 2 (2 Substituting in eq. 24, we get: I z. /Ml 2- W Z: Sin (25) and solving eq. 25, we obtain: The above equations show that couplers with transforming properties can be built by fabricating couplers whose characteristic impedance is equal to the geometric means of the source and load impedances. The analysis shows that the outputs are in phase quadrature, and that the directivity of the coupler can be maintained. The only effect is the change in input VSWR with frequency which would be expected from any transformer. Since this device can be analyzed independently, it then follows that the device can be iterated to produce a binary split into 2" outputs where the transformer action is that of an n-section transformer. In addition, quarter wave transformers can be used at the input and/or outputs to better the VSWR of the device. Finally, the device discussed here can be replaced by the proper two section coupler of Appendix I to produce similar performance and can be iterated in the manner discussed above. What is claimed is: l. A distributive parameter device including in combination: I first and second lines electromagnetically coupled to each other; said first'line providing first and second terminals at opposite ends thereof; said second line providing third and fourth terminals atopposite ends thereof; the electrical length of said first and second lines being equal; said first and second lines exhibiting an even mode impedance of Z, when said first, second, third and fourth terminals are terminated in an impedance of 2,; said first and second lines exhibiting an odd mode impedance of Z when said first, second, third and fourth terminals are terminated in said impedance of Z, where: Z1: V e o said first and second coupled lines exhibiting equal phase velocity in said even and odd modes of excitation; third and fourth lines electromagnetically coupled to each other; said third line providing fifth and sixth terminals at opposite ends thereof; said fourth line providing seventh and eighth terminals at opposite ends thereof; the electrical length of said third and fourth lines being equal; said third and fourth lines exhibiting said even mode impedance of Z, when said fifth, sixth, seventh and eighth terminals are terminated in said impedance of Z,; said third and fourth lines exhibiting said odd mode impedance of Z, when said fifth, sixth, seventh and eighth terminals are terminated in said impedance of Z,; said third and fourth coupled lines exhibiting equal phase velocity in said even and odd modes of excitation; a fifth line for connecting said second terminal to said fifth terminal; and a sixth line for connecting said fourth terminal to said seventh terminal said fith and sixth lines being uncoupled lines. 2. The combination as defined in claim 1 where the electrical length from said first terminal to said sixth terminal is equal to the electrical length from said third terminal to said eighth terminal when said first, third, sixth an eighth terminals are terminated in said imped ance of Z 3. The combination as defined in claim 1 in which said fifth and sixth lines exhibit a characteristic impedance of Z,. 4. The combination as defined in claim 3 where the electrical length from said first terminal to said sixth terminal is equal to the electrical length from said third terminal to said eighth terminal when said first, third, sixth and eighth terminals are terminated in said impedance of Z,. 5. The combination as defined in claim 4 in which said first and third terminals, said second and fourth terminals, said fifth and seventh terminals, and said sixth and eighth terminals respectively are physically adjacent to each other. 6. The combination as defined in claim 1 also includa seventh line having a first and second end thereof; said first end of said seventh line being connected to said first terminal and said second end of said seventh line serving as a first port; and an eight line having a first and second end thereof; said first end of said eighth line being connected to said third terminal and said second end of said eighth line serving as a second port: said seventh and eighth lines being uncoupled lines. 7. The combination as defined in claim 6 in which the electrical length from said first port to said sixth terminal is equal to the electrical length from said second port to said eighth terminal. 8. The combination as defined in claim 7 in which said fifth and sixth lines exhibit a characteristic impedance of 2,. 9. The combination as defined in claim 8 in which said seventh and eighth lines exhibit a characteristic impedance of 2,. 10. The combination as defined in claim 9 also including: means for shorting said first port to said second port. 11. The combination as defined in claim in which said combination has a center operating frequency and said shorting means is a quarter wave Tength long at said center operating frequency. 12. The combination as defined in claim 11 in which said combination has a center operating frequency and said shorting means is connected to said first and second ports by a structure which is a quarter wave length long at said center operating frequency. 13. The combination as defined in claim 11 in which said combination has a center operating frequency and said shorting means is connected to said first and second ports by a structure which is greater than a quarter wave length long at said center operating frequency. 14. The combination as defined in claim 13 in which said combination has a center operating frequency and said means for connecting is a structure which is more than a half wave length long at said center operating frequency. 15. The combination as defined in claim 6 also including: a ninth line having a first and second end thereof; said first end of said ninth line being connected to said sixth terminal and said second end of said ninth line serving as a third port; and a 10th line having a first and second end thereof; said first end of said tenth line being connected to said eighth terminal and said second end of said tenth line serving as a fourth port: said ninth and 10th lines being uncoupled lines. 16. The combination as defined in claim 15 in which the electrical length from said first port to said third port is equal to the electrical length from said second port to said fourth port. 17. The combination as defined in claim 15 in which said combination has a center operating frequency and said electrical length is equal to a quarter-wave length as said center operating frequency. 18. The combination as defined in claim 17 in which said fifth and sixth lines exhibit a characteristic impedance of Z 19. The combination as defined in claim 18 in which said seventh, eighth, ninth and 10th lines exhibit a characteristic impedance of Z 20. The combination as defined in claim 18 in which said seventh and 10th lines exhibit a characteristic impedance of Z, and said eighth and ninth lines exhibit a characteristic impeance of 2,. 21. The combination as defined in claim 19 also including: means for shorting said first port to said second port, 22. The combination as defined in claim 21 in which said combination has a center operating frequency and said shorting means is a quarter wave length long at said center operating frequency. 23. A distributive parameter device including in combination: first and second lines electromagnetically coupled to each other; said first line providing first and second terminals at opposite ends thereof; said second line providing third and fourth terminals at opposite ends thereof; the electrical length of said first and second lines being equal; said first and second lines exhibiting an even mode impedance of Z, when said first, second, third and fourth terminals are terminated in an impedance of 2,; said first and second lines exhibiting an odd mode impedance of 2,, when said first, second, third and fourth terminals are terminated in said impedance of Z,, where: r o said first and second coupled lines exhibiting equal phase velocity in said even and odd modes of excitation; third and fourth lines electromagnetically coupled to each other; said third line providing fifth and sixth terminals at opposite ends thereof; said fourth line providing seventh and eighth terminals at opposite ends thereof; said electrical length of the third and fourth lines being equal; said third and fourth lines exhibiting said even mode impedance of Z when said fifth, sixth, seventh and eighth terminals are terminated in said impedance of Z,; said third and fourth lines exhibiting said odd mode impedance of Z, when said fifth, sixth, seventh and eighth terminals are terminated in said impedance of Z,; said third and fourth coupled lines exhibiting equal phase velocity in said even and odd modes of excitation; a fifth line for connecting said second terminal to said fifth terminal; and a sixth line for connecting said fourth terminal to said seventh terminal: said fifth and sixth lines being uncoupled lines a seventh line having a first and second end thereof; said first end of said seventh lines being connected to said first terminal and said second end of said seventh line serving as a first port; and an eighth line having a first and second end thereof; said first end of said eighth line being connected to said third terminal and said second end of said eighth line serving as a second port: said seventh and eighth lines being uncoupled lines ninth and 10th lines electromagnetically coupled to each other; said ninth line providing ninth and 10th terminals at opposite ends thereof; said lOth line providing 1 lth and 12th terminals at opposite ends thereof; the electrical length of said ninth and 10th lines being equal; said ninth and 10th lines exhibiting said even mode impedance of Z when said ninth, 10th, 1 lth and 12th terminals are terminated in said impedance of 2,; said ninth and 10th lines exhibiting an odd mode impedance of Z when said ninth, 10th, 1 lth and 12th terminals are terminated in said impedance of 2,, said ninth and tenth coupled lines exhibiting equal phase velocity in said even and odd modes of excitation; llth and 12th lines electromagnetically coupled to each other; said eleventh line providing thirteenth and fourteenth terminals at opposite ends thereof; said twelfth lines being equal; said llth and l2th lines exhibiting said even mode impedance of Z when said 13th, 14th, 15th and 16 th terminals are terminated in said impedance of Z said llth and 12th lines exhibiting said odd mode impedance of Z when said 13th, 14th, 15th and 16th terminals are terminated in said impedance of Z said llth and 12th coupled lines exhibiting equal phase velocity in said even and odd modes of excitation; a 13th line for connecting said l2th terminal to said 13th terminal; a 14th line for connecting said l2th terminal to said 15th terminal; and means for connecting said first and second ports to said ninth and llth terminals respectively: 25. The combination as defined in claim 24 in which said fifth, sixth, seventh, eighth, 13th and 14th lines each exhibit a characteristic impedance of Z,. 26. The combination as defined in claim 25 in which the electrical length from said sixth terminal to said fourteenth terminal is equal to the electrical length from said eighth terminal to said 16th terminal. 27. The combination as defined as defined in claim 26 in which said electrical length from said sixth terminal to said 14th terminal is greater than a quarter and less than a half wave length at the center operating frequency thereof. 28. The combination as defined in claim 27 also including four additional lines each having a first and second end thereof, each of said first ends thereof being connected to one of said sixth, eighth, 14th and 16th terminals respectively, the electrical length from said second end of said first additional line to said second end of said third additional line and the electrical length from said second end of said second additional line to said second end of said fourth additional line being one-half wave length at said center operating frequency: said four additional lines being uncoupled lines. 29. The combination as defined in claim 24 also including: 15th and 16th lines electromagnetically coupled to each other; said 15th line providing 17th and 18th terminals at opposite ends thereof; said 16th line providing nineteenth and th terminals at opposite ends thereof; the electrical length of said 15th and 16th lines being equal to each other and to said first line; said 15th and 16th lines exhibiting said even mode impedance of 2 when said 17th, 18th, 19th and 20th terminals are terminated in said impedance of 2,; said 15th and 16th lines exhibiting an odd mode impedance of Z, when said 17th, 18th, 19th and 20th terminals are terminated in said impedance of 2,, said 15th and 16th coupled lines exhibiting equal phase velocity in said even and odd modes of excitation; 17th and 18th lines electromagnetically coupled to each other; said 17th line providing 21 and 22 terminals at opposite ends thereof; said 18th line providing 23 and 24 terminals at opposite ends thereof; the electrical length of said 17th and 18th lines being equal to each other and to said 15th line; said 17th and 18th lines exhibiting said even mode impedance of Z, when said 21st, 22nd, 23rd and 24th terminals are terminated in said impedance of 2,; said 17th and 18th lines exhibiting said odd mode impedance of Z, when said 21st, 22nd, 23rd and 24th terminals are terminated in said impeance of 2,, said 17th and 18th coupled lines exhibiting equal phase velocity in said even and odd modes of excitation; a 19th line for connecting said 18th terminal to said 21st termina; a 20th line for connecting said 20th terminal to said 23rd terminal; means for connecting said 17th terminal to said 14th terminal; and means for connecting said nineteenth terminal to said 16th terminal: said 19th and 20th lines being uncoupled lines. 30. The combination as defined in claim 29 in which said fifth, sixth, seventh, eighth, 13th, 14th, 19th and 20th lines each exhibit a characteristic impedance of 2,. 31. The combination as defined in claim 30 which the electrical length from said sixth terminal to said 22nd terminal is equal to the electrical length from said eighth terminal to said 24th terminal. 32. The combination as defined in claim 31 in which the electrical length from said sixth to said 22nd terminal is less than three-quarter wave length and greater than one-half wave length at the center operating frequency thereof. 33. A distributive parameter device including in combination: first and second lines electromagnetically coupled to each other; said first line providing first and second terminals at opposite ends thereof; said second line providing third and fourth terminals at opposite ends thereof; the electrical length of said first and second lines being equal; said first and second lines exhibiting an even mode impedance of 2,. when said first, second, third and fourth terminals are terminated in an impedance of 2,; said first and second lines exhibiting an odd mode impedance of Z when said first, second, third and fourth terminals are terminated in said impedance of 2,, where: Z, 32 v Z, 2,, said first and second coupled lines exhibiting equal phase velocity in said even and odd modes of excitation; third and fourth lines electromagnetically coupled to each other; said third line providing fifth and sixth terminals at opposite ends thereof; said fourth line providing seventh and eighth terminals at opposite ends thereof; said electrical length of the third and fourth lines being equal; said third and fourth lines exhibiting said even mode impedance of 2 when said fifth, sixth, seventh and eighth terminals are terminated in said impedance of 2,; said third and fourth lines exhibiting said odd mode impedance of Z, when said fifth, sixth, seventh and eighth terminals are terminated in said impedance of 2,; said third and fourth coupled lines exhibiting equal phase velocity in said even and odd modes of excitation; a fifth line for connecting said second terminal to said fifth terminal; and a sixth line for connecting said fourth terminal to said seventh terminal: said fifth and sixth lines being uncoupled lines seventh and eighth lines electromagnetically coupled to each other; said seventh line providing ninth and tenth terminals at opposite ends thereof; said eighth line providing eleventh and twelfth terminals at opposite ends thereof; the electrical length of said seventh and eighth lines being equal; said seventh and eighth lines exhibiting said even mode impedance of 2, when said ninth, 10th, 11th and 12th terminals are terminated in said impedance of 2,; said seventh and eighth lines exhibiting said odd mode impedance of Z, when said ninth, 10th, 11th and 12th terminals are terminated in said impedance of Z,, said seventh and eighth coupled lines exhibiting equal phase velocity in said even and odd modes of excitation; ninth and 10th lines electromagnetically coupled to each other; said ninth line providing 13th and 14th terminals at opposite ends thereof; said tenth line providing 15th and 16th terminals at opposite ends thereof; the electrical length of said ninth and 10th lines being equal; said ninth and 10th lines exhibiting said even mode impedance of Z, when said 13th, 14th, 15th and 16th terminals are terminated in said impedance of Z,; said ninth and 10th lines exhibiting said odd mode impedance of Z when said 13th, 14th, 15th and 16th terminals are terminated in said impedance of Z said ninth and 10th coupled lines exhibiting equal phase velocity in said even and odd modes of excitation; an 1 lth line for connecting said tenth terminal to said 13th terminal; a 12th line for connecting said 12th terminal to said 15th terminal; first means for connecting said ninth terminal to said sixth terminal; and second means for connecting said 11th terminal to said eighth terminal: said 11th and 12th lines being uncoupled lines. 34. The combination as defined in claim 33 in which said fifth, sixth, 11th and 12th lines exhibit a characteristic impedance of Z 35. The combination as defined in claim 34 in which said first means includes a 13th line; said second means includes a 14th line and said 13th and 14th lines are electromagnetically coupled to each other. 36. The combination as defined in claim 35 in which said 13th and 14th lines exhibit said even mode impedances of 2 when terminated in impedances of Z, and said odd mode impedance of Z, when terminated in impedances of Z,. 37. The combination as defined in claim 36 in which the electrical length from said first terminal to said 14th terminal is equal to said electrical length from said third terminal to said 16th terminal. 38. The combination as defined in claim 29 in which said first means also includes 15th and 16th lines for connecting said 13th line of said sixth and ninth terminals, respectively, and said second means also includes 17th and 18th lines for connecting said 14th line to said eighth and l lth terminals, respectively: said 15th, s 16th, 17th, and 18th lines being uncoupled lines. 39. The combination as defined in claim 38 in which the 15th, 16th, 17th and 18th lines each exhibit characteristic impedances of 2,. 40. The combination as defined in claim 39 in which the electrical length of said first, second, third, fourth, seventh, eighth, ninth and 10th lines are equal. 41. In combination: a coupler having first, second, third and fourth ports, said coupler being responsive to a signal applied to said first port through an impedance of Z, for providing signals at said second and third ports in quadrature relationship when said second, third and fourth ports are terminated in said impedance means for applying a signal to said first port through a source impedance of Z and means for terminating said second and third ports in load impedances of Z, and said fourth port in said impedance of Z where: 1 T I so that said coupler in addition to serving as a coupler serves the additional function of matching said source impedance of 2 to said load impedance of Z, wherein Z, and Z are different impedances. 42. The combination as defined in claim 41 in which said coupler has a center operating frequency and said electrical length from said first port to said third port is a quarter wave length at said center operating frequency. 43. The combination as defined in claim 42 in which said coupler includes: first and second lines electromagnetically coupled to each other; said first line providing first and second terminals at opposite ends thereof; said second line providing third and fourth terminals at opposite ends thereof; the electrical length of said first and second lines being equal; third and fourth lines electromagnetically coupled to each other; said third line providing fifth and sixth terminals at opposite ends thereof; said fourth line providing seventh and eighth terminals at oppostie ends thereof; the electrical length of said third and fourth lines being equal; a fifth line for connecting said second terminal to said fifth terminal; a sixth line for connecting said fourth terminal to said seventh terminal; a seventh line having a first and second end thereof said first end of said seventh line being connected to said first terminal and said second end of said seventh line serving as said first port; said seventh line having a characteristic impedance of Z,,; an eighth line having a first and second end thereof; said first end of said eighth line being connected to said third terminal and said second end of said eighth line serving as said second port; said eighth line exhibiting a characteristic impedance of Z ninth line having a first and second end thereof; said first end of said ninth line being connected to said sixth terminal and said second end of said ninth line serving as said third port; said ninth line exhibiting a characteristic impedance of 2,; and 10th line having a first and second end thereof; said first end of said 10th line being connected to said eighth terminal and said second end of said 10th line serving as said fourth port; said tenth line exhibiting a characteristic impedance of Z 1&1 Q 5 UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No; 3,761,843 Dated September 25 1973 Inventor(s) Joseph D. Cappucci It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below: Column 12, line 20, cancel "fith" and insert --fifth therefor. Column 12, line 25, cancel "an" and insert --and-: therefor. Column 14, line 54, after "said" and before "l 2th" insert --llth- Column 14, line 54, after "equal" and before semicolon insert -in electrical length-- Column 16, line 58, after "lines" and-before "seventh" insert a semicolon. Signed and sealed this 6th day of May 1975. (SEAL) Attest C. MARSHALL DANN RUTH C. MASON Commissioner of Patents Attesting Officer and Trademarks Patent Citations
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