US 3748601 A Abstract A cascade of two identical quadrature hybrid couplers, whose coupling coefficients vary as a function of frequency, are converted to an all-pass network by the inclusion of a 180 DEG phase shifter in one of the two interconnecting wavepaths. Recognizing that the incident signal is coupled primarily to one of the interconnecting wavepaths at the higher frequencies, and to the other wavepath at the lower frequencies, a phase shifter of limited bandwidth, placed in the appropriate wavepath, provides all-pass characteristics over a band of interest which is much broader than that of the phase shifter.
Description (OCR text may contain errors) United States Patent 1 Seidel July 24, 1973 COUPLING NETWORKS HAVING Primary Examiner-Paul L. Gensler BROADER BANDWIDTH THAN INCLUDED A torney-W. L- Keefauver et al. PHASE SHIFTERS [75] Inventor: Harold Seidel, Warren, NJ. ABSTRACT 73 i Bell Telephone L'bontories, A cascade of two identical quadrature hybrid couplers, Incorporated, Murray Hill, NJ. whose coupling coefi'lcients vary as a function of frequency, are converted to an all-pass network by the in- [22] led: 1971 clusion of a 180 phase shifter in one of the two inter- 21 App] 208,305 connecting wavepaths. Recognizing that the incident signal is coupled primarily to one of the interconnect- 7 ing wavepaths at the higher frequencies, and to the [52] US. Cl. 333/10, 333/24 R, 333/31 R other wavcpath at the lower frequencies a phase [51] Int. Cl. "01p 5/14, 01p l/18 Shifter of li i bandwidth, placed i the appropriate [58] Field of Search 333/10, 11, 24, 31 R, wavcpath, provides albcass characteristics over a band 333/32 of interest which is much broader than that of the phase [56] R r r n C'ted shifter e e e ees This technique is also employed to obtain broadband UNHED STATES PATENTS 180 phase shifters and transformers. By a 3,444,475 5/ 1969 Seidel 333/ 11 X boot-strapping technique, the band of interest can be 3,514,722 5/1970 Cappucci. 333/10 further extended 3,037,175 5/1962 Ruthroff 333/32 1 9 Claims, 7 Drawing Figures 40 42 4 E M t I HYBRID I80 HYBRD COUPLER g #3 COUPLER l 0 HYBRID HYBRID --o' E E COUPLER PAIENIED 3. 748.601 SHEET 1 0F 3 I80 DEGREE I fiFI/IsE SHIFTER I -(t +k )*-I IO i HIXJ I I INPUT SIGNAL 31 i 3 -t f I HYBR|D HYBRID 2 LE 4 COUPLER 2 -itk+itk=0 HIGH FREQUENCY Z P TRANSFORMER 2 PASSBAND T k U LT. '0 I t: I I 8 I LOW FREQUENCY TRANSFORMER E I PASSBAND I 3 I l t 0 l O I I I 0 I8 2 0 I h FREQUENCY t k =l OUTPUT IO FIG. .3 INPUT 3 t 3| t I] I HYBRID HYBRID 2 COUPLER X COUPLER m 4 -Ik g iktikt =0 HIGH FREQUENCY TRANsFORMER q I80 DEGREE PHASEIjH I FTER PATENTED 3.748.601 SHEEI 2 OF 3 FIG. 4 4o 42 4| E g t HYBRID I80 HYBRID COUPLER C A COUPLER 2Q 3| T t I E e HYBRID v HYBRID L COUIPLER i 0 COUPLER 43 45 44 FIG. 5 HYBRID HYBRID COUPLER COUPLER o T T I |a0+e Q "L I 52 54 HYBRID HYBRID "-3. HYBRID HYBRID 0- c COUPLER? COUPLER H 2 COUPLER COUPLER so 51 g SHEEI 3 BF 3 FIG. 6 FIG. 7 FREQUENCY COUPLING NETWORKS HAVING BROADER BANDWIDTH THAN INCLUDED PHASE SHIFTERS This invention relates to broad band coupling circuits such as phase shifters and transformers. BACKGROUND OF THE INVENTION In the design of broadband coupling circuits, the con flicting requirements at the opposite extremes of the pass-band are often impossible to reconcile. For example, at the lower end of the band, relatively large inductances are called for, requiring relatively large coils or magnetic cores of an appropriate kind. At 'the upper end of the band, the large coils are plagued with parasitics, or the magnetic core material is inappropriate at these frequencies and is lossy. It is, accordingly, the object of the present invention to obtain broadband coupling circuits using bandlimited transformers. It is known that a power division ratio of a hybrid coupler varies as a function of frequency. However, as was noted by E. A. J. Marcatili in U.S. Pat. No. 3,184,691, a cascade of two frequency sensitive couplers can be converted to an all-pass network by the introduction of 180 degrees of relative phase shift between the signals in the two interconnecting wavepaths. The all-pass characteristic, however, is no broader than the band over which the 180 degrees of relative phase shift can be maintained between the two signals. It is thus a more specific object of the present invention to obtain broadband 180 phase shifters. Since a transformer is simply an all-pass network with an impedance transformation, it is also an object of the invention to obtain broadband impedance transformations. SUMMARY OF THE INVENTION The present invention is based upon the recognition that in a hybrid coupler, the incident signal is coupled primarily to one of the coupled branches at the higher frequencies, and to the other of the coupled branches at the lower frequencies. Accordingly, a 180 phase shifter of limited bandwidth, placed in the appropriate branch of two interconnected hybrid couplers, provides all-pass characteristics for the network over a band of frequencies that is considerably greater than that of the phase shifter itself. It is further shown that the obtainable passband can be further extended by means of a boot-strapping arrangement wherein two such networks are used to obtain a broader band 180 phase shifter. In this embodiment of the invention, the desired 180 of phase shift for one of the two networks is obtained by means of a high frequency, 1:1 turns ratio transformer located in the interconnecting wavepath that carries the higher frequency signal components. While this transformer is essentially ineffectual at the lower frequencies of inter est, essentially no signals at these frequencies are coupled through this wavepath. In the other network, the 180 of phase shift is obtained by means of a low frequency, 1:1 turns ratio transformer located in the interconnecting wavepath that carries the lower frequency signal components. Here again, while the transformer is essentially ineffectual at the higher frequencies of interest, essentially no signals at these higher frequencies are coupled through this wavepath. Because the phase shifters are located in different wavepaths of the two networks, the coefficients of transmission through the two networks are identical over the entire band of interest, but differ by 180. Using a similar technique, a broadband impedance transformer can be realized using two, band limited transformers interconnecting two identical hybrid couplers. 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 an all-pass network in accordance with the present invention; FIG. 2 shows the frequency characteristic of the coupler coefficients t and k; FIG. 3 shows an alternate embodiment of the invention; FIG. 4 shows the embodiments of FIGS. 1 and 3 used as a 180 relative phase shifter; FIG. 5 shows the manner in which the invention can be employed to further extend the bandwidth of an allpass network; FIG. 6 shows a broadband transformer in accordance with the present invention; and FIG. 7 shows the frequency characteristic of the coupling coefi'icients of a cascade of couplers. DETAILED DESCRIPTION In the discussion that follows, a number of different circuits will be considered. These are identified at the head of each section of the discussion. a. All-pass networks Referring'to the drawings, FIG. 1 shows an all-pass network, in accordance with the present invention, comprising a cascade of two identical hybrid couplers l0 and 11, interconnected by means of two wavepaths l2 and 13. Branch 1 of coupler 10 is the network input port. Branch 1' of coupler 11 in the network output port. Branches 2 and 2' are resistively terminated. One of the wavepaths 12 includes a 180 phase shifter 14 which, in this illustration, is simply a 1:1 turns ratio transformer. Typically, each of the couplers has four branches 1, 2, 3 and 4, and 1', 2, 3' and 4', arranged in pairs 1-2 and 2-4, and l-2' and 3'4', where the branches of each pair are conjugate to each other and in coupling relationship with branches of the other of said pair. More particularly, a first coupling coefficient t defines the coupling between branches l-3, 2-4, l'-3' and 2'4', and a second coupling coefficient It defines the coupling between branches l-4, 2-3, 1'4 and 2'-3'. While these are generally complex quantities whose magnitudes and phases vary as a function of frequency, they are related, at all frequencies such that In addition, the coupled signals bear some fixed relative phase relationship, depending upon the nature of the coupler. For purposes of discussion, couplers l0 and 11 are considered to be quadrature couplers, in which case the coupled signals have a relative phase shift of The two wavepaths l2 and 13 connect one pair of conjugate branches 3-4 of coupler 10, to one pair of conjugate branches 3-4' of coupler 11. If, for the purposes of the present discussion the phase shift common to both 2 and k is abstracted, both coefficients are real, and a unit input signal, applied to branch I of coupler 10, produces a signal t at branch 3 and a signal ik at branch 4, where i is the imaginary number 1, and indicates the quadrature relationship between the two signals. The t signal at branch 3, undergoes a 180 phase shift as it traverses wavepath 12, and appears as a t signal at branch 3 of coupler 11. Signal ik experiences no relative phase shift along wavepath 13, appearing as a signal ik at coupler branch 4. Since the two couplers are identical, signal t produces a signal component -t at branch I and a signal component ikt at branch 2'. Simultaneously, signal ik, in turn, produces a signal component (ik) equal to ---k at branch I, and a signal component +ikt at branch 2'. Adding the signal components at the respective branches we obtain for branch I and for branch 2 ikt ikt 0. From equation (2) it is noted that all of the incident signal is coupled to output branch I, and while each of the couplers is frequency sensitive, the output signal is independent of the coupling coefficients t and k. Thus, the circuit illustrated in FIG. 1 is an all-pass network. However, it is an all-pass network only over the frequency band for which the phase shifter provides 180 of phase shift. For relatively narrowband applications, this is generally not a problem. The difficulty resides in extending the passband. The problem is that a transformer designed to operate well at the lower end of an extended band of frequencies, will generally not function well at the higher end because of parasitics which convert the simple transformer to a more complex network having a different phase shift. In addition, the core materials which are needed at the lower frequen cies are generally lossy at the higher frequencies. Conversely, a transformer designed to operate at the higher frequencies will, because of inadequate core reactance, not operate well at the lower frequencies. The present invention is based upon the recognition that a properly designed, band-limited transformer, properly placed, can be used to obtain an all-pass network that is operative over a band of frequencies that is greater than that of the transformer. This is so because of the manner in which the coupling coefficients vary as a function of frequency. For example, FIG. 2 shows the frequency characteristics of the coupling coefficients for a lumped-element quadrature coupler of the type described in U. S. Pat. No. 3,506,932. As shown, the t coefficient is unity at zero frequency and decreases with increasing frequency. Conversely, the k coefficient is zero at zero frequency and increases with frequency. The coefficients are equal at the crossover frequency f,,. Assuming the all-pass network is to operate over the frequency rangef to fl,, it will be noted that there is a region betweenf andf where the k component of signal is negligibly small and the t component dominates, (i.e., k s 0.25t). Similarly, at the higher end of the band there is a region between frequencies f and f,, where the t component is negligibly small and the k component dominates, (i.e., t s 0.25k). Accordingly, a transformer designed to operate over the band between f and f placed in wavepath 12, will provide of phase shift for the t component of signal over the band of frequencies for which there is a significant 1 signal component. While the transformer no longer provides the necessary phase shift above frequency f the 1 signal is negligible at these frequencies such that the effect upon the operation of the all-pass network is likewise negligible. In the circuit just described, a low frequency transformer was placed in the circuit of the network. Alternatively, a high frequency transformer can be placed in the k circuit of the network. Such an arrangement is illustrated in FIG. 3. This embodiment is in all respects identical to the embodiment of FIG. I with the exception that a phase shifter 14' is located in wavepath 13 between coupler branches 4 and 4. If, as previously, a unit signal is applied to input branch I, it can readily be shown that a unit output signal +1 is obtained at output branch 1. Since branch 13 is the k signal branch, from FIG. 2 it is apparent that the k signal is negligibly small over the lower portion of the band of interest and, hence, all-pass operation between frequencies f, and f, can be realized using a high frequency transformer designed to operate over the band of frequencies from f to f,,. Thus, locating a low frequency, band-limited 180 phase shifter in the t signal path, or a high frequency, band-limited 180 phase shifter in the k signal path results in networks having all-pass characteristics that are greater than the bandwidth of either phase shifter. Obviously, this greatly reduces the problems incidental to the design of very broadband all-pass networks of the type described. b. Broadband 180 phase shifter Thus far we have discussed only the relative phase shift between the t and k signal components. There is, however, an absolute phase shift associated with both I and k. In addition, there is an additional phase shift experienced by the signals as they traverse the interconnecting wavepaths. Thus, the output signals for the two networks described above are more accurately given by l 1180+0 and I Q, where 0 is also a function of frequency. It will be noted, however, that while the phase of the two signals vary over the band, their difierence remains a constant 180. Accordingly, the networks of FIGS. 1 and-3, when used in combination, provide a broadband 180 relative phase shift. This property of these networks can be used in a variety of ways, as will now be illustrated. FIG. 4 illustrates the use of two all-pass networks 30 and 31 to generate two out-of-phase signals. Network 30, of the type illustrated in FIG. 1, comprises two cascaded hybrid couplers 40 and 41, including a low frequency 180 phase shifter 42 located in the t signal wavepath connecting couplers 40 and 41. Network 31, of the type illustrated in FIG. 3, comprises two cascaded hybrid couplers 43 and 44, including a high frequency 180 phase shifter 45 located in the k signal wavepath connecting couplers 43 and 44. In operation, a signal E LOsimultaneously applied to the input branches 1 of couplers 40 and 43 will produce an output signal F. (180+!) at the output 1' of coupler 41, and an output signal E Mat the output branch I of coupler 44. These two signals remain 180 out of phase over the entire band of frequencies for which both networks retain their all-pass characteristic. 0. Boot-strapping networks It is a feature of the present invention that the abovedescribed networks can be used in boot-strapping arrangements to produce all-pass networks and 180 phase shifters of even greater bandwidth than either of the individual networks employed, just as either network has a bandwidth that is greater than the transformer it employs. This use of two all-pass networks to obtain a broadband 180 phase shift as a means of forming an all-pass network of greater bandwidth is illustrated in FIG. 5 which comprises two cascaded hybrid couplers 50 and 51, interconnected by means of wavepaths 52 and 53. The first wavepath 52 includes a first all-pass network 54, of the type described in connection with FIG. 1. The second wavepath 53 includes a second all-pass network 55, of the type illustrated in FIG. 3. Network 54, being in the t signal wavepath connecting couplers 50 and 51, is designed to operate over the lower portion of the frequency band of interest, just as the transformer in the t signal wavepath of FIG. 1 was designed to operate over only the lower portion of the band. Similarly, network 55, being in the k signal wavepath is designed to operate over the upper portion of the band of interest. In operation, a unit signal, applied to port 1 of input coupler 50, is divided into a t signal component at coupler port 3 and a k signal component at coupler port 4. The two signal components traverse, respectively, allpass networks 54 and 55, wherein the t signal component undergoes a 180 phase shift relative to the k signal component, appearing as t at port 3' of output coupler 51. Upon recombination with the k signal compon en t at eoupler port 4, an output signal of l 1 180 6 is produced at the output port 1' of the allpass circuit. In the above discussion it was assumed that all-pass networks 54 and 55 were such that the t signal underwent l80 of relative phase shift. However, the circuit can, alternatively, be arranged so that the k signal is shifted 180, in which case an output signal of 1 LOis produced. Thus, two such broadband all-pass networks can be used, as explained in connection with FIG. 4, to produce a broader band l80relative phase shifter. It will be noted that in the applications described hereinabove, the overall bandwidth of interest in each instance is greater than the portion of the band for which each element or each network is designed. Thus there is a progressive extension of the operative frequency range, making it possible for relatively narrowband transformers to be used in a boot-strapping arrangement to produce networks of much broader band. Clearly, the process can be iterated to obtain even broader band all-pass networks and broader band 180 phase shifters. However, as the frequency increases, equal increments in bandwidth represent decreasing fractions of the total bandwidth. In some cases, therefore, it may be more conveneient to combine conventional phase equalization techniques with aspects of the present invention, rather than confine the bootstrapping method described herein solely to the type of arrangement disclosed. d. Broadband transformer Another use of the all-pass networks described hereinabove is as a broadband transformer. A transformer is simply an all-pass network which couples between two different impedance levels. A transformer, in accordance with the present invention comprises, as illustrated in FIG. 6, two cascaded hybrid couplers 60 and 61, having substantially identical frequency characteristics, but different characteristic impedances, Z and N 2,, interconnected by means of wavepaths 62 and 63. Each of the wavepaths includes a lzN turns ratio transformer 64 and 65. One transformer 64, located in the t signal wavepath 62 covers the lower frequency portion of the band of interest, as explained hereinabove in connection with FIG. 2, while the other transformer 65, located in the k signal wavepath 13, covers the higher frequency portion of the band of interest. Depending upon the desired phase of the output signal, one or the other of the two transformers is connected to provide a 180 phase shift. For purpose of illustration, this phase shift is provided by transformer 64. Alternatively, the phase shift could have been provided by transformer 65 in which case there would be a difierence in the phase of the output signal. Because of the IN turns ratio of transformers 64 and 65, there is an overall impedance transformation of l:N between the input ends and output ends of the two wavepaths. Since the all-pass characteristic of the network is greater than that of either of the transformers, the impedance transformation is likewise obtained over a greater band than could be realized by means of either of the transformers used individually. The frequency characteristic illustrated in FIG. 2 suggest a considerable overlapping of the bandwidth covered by the higher frequency transformer and the lower frequency transformer. While this might be the case for a single input and a single output coupler, for many applications each of the couplers identified, respectively, as the input coupler and the output coupler are themselves a complex cascade of couplers such that the overall k and 1 characteristics are'more generally as given by the two curves shown in FIG. 7. As can be seen, the crossover region is much narrower so that the lower frequency transformer, which includes the band between f, and f,, and the higher frequency transformer, which includes the band between f, and f,,, only overlap over the relatively narrow frequency range between f and f,. In either case, the use of narrowband transformers to obtain broadband coupling networks is realized. In all cases it is understood that the above-described arrangements are illustrative of but a small number of the many possible specific embodiments which can represent applications of the principles of the present invention. 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. I claim: 1. A network, having an all'pass transmission characteristic over a specified frequency band of interest AF comprising: two substantially identical hybrid couplers, each havi'ng two pairs of conjugate branches; one branch of one pair of conjugate branches of one coupler being the input port of said network; one branch of one pair of conjugate branches of the other coupler being the output port of said network; first and second wavepaths, each of which connects one branch of the other pair of branches of said one coupler to one branch of the other pair of branches of said other coupler; transmission between said network ports and said first and second wavepaths being defined, respectively, by a pair of coupling coefficients t and k, each of which varies as a function of frequency; and means for introducing an additional 180 of relative phase shift located in one of said wavepaths; characterized in that: the coupling coefficient t is significant over the lower portion of said band of interest and is negligibly small at the higher end of said band of interest; the coupling coefficient k is significant over the upper portion of said band of interest and is negligibly small at the lower end of said band of interest; and in that said phase shift means introduces 180 of relative phase shift over a portion of said band of interest that is at least coextensive with the portion of said band for which the coupling between the wavepath wherein said means is located and said input and output ports is significant, but less than said band of interest. 2. The network in accordance with claim 1 wherein said phase shift means is a 1:1 turns ratio transformer located in said first wavepath; and wherein said transformer provides 180 of phase shift over the portion of said band for which coupling coefficient t is significant. 3. The network according to claim 1 wherein said phase shift means is a 1:1 turns ratio transformer located in said second wavepath; and wherein said transformer provides 180 of phase shift over the portion of said band for which coupling coefficient k is significant. 4. A phase shifter, for introducing 180 of relative phase shift between signals in two transmission paths comprising: a first all-pass network in accordance with claim 1 disposed in one of said transmission paths wherein said phase shift means is a 1:1 turns ratio transformer located in said first wavepath for providing 180 of phase shift over the portion of said band for which coupling coefficient t is significant; and a second all-pass network in accordance with claim 11 disposed in the other of said transmission paths wherein said phase shift means is a 1:1 turns ratio transformer located in said second wavepath for providing 180 of phase shift over the portion of said band for which coupling coefficient k is significant. 5. A circuit, having an all-pass transmission characteristic over a specified frequency band of interest AF comprising: one coupler to one branch of the other pair of branches of said other coupler; transmission between said circuit ports and said first and second signal paths being defined, respectively, by a pair of coupling coefficients t and k, each of which varies as a function of frequency; said coefficient t being significant over the lower portion of said band of interest AF, and negligibly small at the upper end of said band of interest AF; said coefficient k being significant over the upper portion of said band of interest AF, and negligibly small at the lower end of said band of interest AF; and means for introducing 180 of relative phase shift between signals in said two signal path comprising: a first all-pass network in accordance with claim 1 l0- cated in one of said signal paths wherein said phase shift means is located in said first wavepath and provides 180 of phase over a portion of said band for which coupling coefficient t is significant; and a second all-pass network in accordance with claim 1 located in the other of said signal paths wherein said phase shift means is located in said second wavepath and provides 180 of phase shift over a portion of said band for which coupling coefficient k is significant. 6. The circuit according to claim 5 wherein said first signal paths wherein said first network is located and said input and output ports is significant, but less than said band of interest AF; and wherein said second network has an all-pass characteristic over a frequency band of interest that is at least coextensive with the portion of said band of interest AF for which the coupling between the signal path wherein said second network is located and said input and output ports is significant, but less than said band of interest AF. 7. A broadband transformer comprising: two hybrid couplers, each having two pairs of conjugate branches; one branch of one pair of conjugate branches of one coupler being the input port of said transformer; one branch of one pair of conjugate branches of the other coupler being the output port of said transformer; the other branch of said one pair of branches of each of said couplers being resistively terminated; first and second wavepaths, each of which connects one branch of the other pair of branches of said one coupler to one branch of the other pair of branches of said other coupler; transmission between said input port and said first and second wavepaths, and between said first and second wavepaths and said output port being defined, respectively, by a pair of coupling coefficients t and k, each of which varies as a function of frequency; said coefficient I being significant over the lower portion of a frequency band of interest, and negligibly small at the upper end of said band of interest; said coefficient k being significant over the upper portion of said band of interest, and negligibly small at the lower end of said band of interest; a first l:N turns ratio transformer located in said first wavepath and designed to operate over at least that wherein one of said transformers is connected so as to introduce of phase shift relative to the phase shift introduced by the other of said transformers. 9. The transformer in accordance with claim 7 wherein said couplers have substantially the same frequency characteristics, but different characteristic impedances. Disclaimer 3,748,60L-H0W0Z0Z Sez'del, Warren, N .J. COUPLING NETWORKS HAV- ING BROADER BANDWIDTH THAN INCLUDED PHASE SHIFTERS. Patent dated July 24, 1973. Disclaimer filed Sept. 13, 1973, by the assignee, Bell Telephone Labomtom'es, lncwpomted. Hereby enters this disclaimer to claim 1 of said patent. [Ofiicial Gazette June 10, 1975.] Patent Citations
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