IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 41, NO.1, JANUARY 1993 Novel Schiffman Phase Shifters JosC Luis Ramos Quirarte, and J. Piotr Starski, Member, IEEE Abstract- In a standard Schiffman phase shifter a coupled section and a uniform transmission line are used to give a differential phase shift. In order to achieve larger bandwidth it is necessary to use tight coupled sections which are difficult to reaIize. This paper shows how different configurations of coupled lines or parallel connected coupled lines can be used together with a uniform transmission line, another coupled lines or parallel connected coupled lines in order to obtain a differential phase shifter with loose coupled lines and the same performance as for the standard case. The measurements confirm the calculated results leading to a more realizable structure. Index TermsDhase shifters, Schiffman sections, coupled transmission lines. (4 ( b) (C) (d 1 Fig. 1. Some altematives to obtain a differential phase shifter: (a) Standard Schiffman phase shifter, (b) Double Schiffman phase shifter, (c) Schiffman phase shifter with cascaded sections, and (d) Parallel Schiffman phase shifter. The characteristic impedance and the phase response are SCHIFFMAN phase shifter [ l ] is a differential phase obtained from following equations: shifter that consists of two transmission lines, one of [VI = [Zl[II (1) them folded (coupled section) to be dispersive, Fig. l(a). By the proper selection of the length of these lines and the degree of coupling, the phase difference between them can be made where [ Z ]is the general impedance matrix given as [4]: to be almost constant over a broad bandwidth. j 211 = ~ ~ 2 = ~ 3 3 = ~ ~ ~ = - - ( Z o e f Z o o ) C O t ~ Other method to design the phase shifter is by using two 2 coupled sections instead, as shown in Fig. l(b) or by using j Z 1 2 = 221 = Z34 = 2 4 3 = --(Zo, - Zoo) cot 8 two cascaded coupled sections and a transmission line [2], [3], 2 (2) shown in Fig. l(c). In this case the phase shift is determined j 2 1 3 = 2 3 1 = 224 = Z42 = - - (Z,, - Zoo) csc 8 by the choice of the length and coupling of each section. 2 Unfortunately, there are several cases where the phase j shifter can not be realized given the desired performance, 2 1 4 = 241 = 2 2 3 = 2 3 2 = - -( zoo) CSC 0 2 particularly in those cases when low relative dielectric constant is used. A method to reduce this problem is to design the Using ( 2 ) in (1) for the special case when two ends of coupled sections for higher input impedances and connect the coupled lines are interconnected, the impedance matrix expressed in terms of the even- Z,,, and odd-Z,,,-mode them in parallel. This altemative is presented in Fig. l(d). Another application of the parallel configuration is the case impedances of the coupled lines and their lengths is obtained as when the performance is poor due to the fact that the width [Z’I = of the transmission lines in the coupled section is too wide compared to its length. cot o tan 0) - 2 cot 6 tan 0) I. INTRODUCTION A z , , + I S( z , ~ + z,, (z,, + zoo 1 1 . A SINGLE COUPLED SECTION - ~ ( ~ , , c o t ~ + ~ ~ -~ ~ 2( t~ a ,n , c~o ) ttl-~,,tan~) The coupled section used in the Schiffman phase shifter (3) consists of two parallel coupled lines of equal length connected at one end. Expressions for the characteristic impedance 21, From (3) the characteristic impedance, ZI and the transfer and phase response for the coupled section as well as for other constant ( a j $ ) are obtained [5] as coupled lines were given by Jones and Bolljahn [4] in terms of the even and odd mode characteristic impedances of the I - 2 ’ 11 2 = (4) lines and their lengths. I ( - 2’2~2)1’z Ja Manuscript received December 17, 1991; revised April 21, 1992. The authors are with Chalmers University of Technology, Gothenburg, Sweden. IEEE Log Number 9204036. and 0018-9480/93$03.00 0 1993 E E E ~ 1.e. - (7) As explained before. 3 some cases giving the maximum bandwidth when 5 ' . We assume that the length of the coupled section in the even 8.e. 2. An unsymmetrical response is observed there since at least one of the coupled sections has 8 # 90' at the center frequency.k0. We see also that the double Schiffman phase shifter gives little narrower bandwidths but require considerably weaker coupling coefficients when compared to the standard Schiffman phase shifter [8]. Schiman Phase Shifter (. f 0 . VOL. zoo (1 1) 1 ' . i. zoo is the impedance ratio that determines the degree of coupling of the coupled section. The four element admittance matrix for a single coupled section in terms of the even and odd mode impedances is obtained from ( 3 ) as [Y'] = (Zoe. f0. 41. In Fig. f 2 " .5".e.10 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. 81. and odd 8. f 2 " . 3.Zootan2 8 ) cot 8 . KO is the transmission phase of the uniform line and the transmission phase of the coupled section as given by (5).5". In Fig. 5:). + zoo tan2 8) cot 8 2Zoe~oo 2z0ez00 +3 .Z00 (zOe + zoo tan2 0) cot 8 220. l ' . &0.. the phase shift response is antisymmetric in respect to the center frequency and broad band characteristics are obtained for these cases [SI. modes is equal. Double S c h i f f " Phase Shifter If instead of the uniform transmission line another coupled section is used as shown in Fig. is: t = k5". [71 c = -2Olog A. fl".1' are shown. TWO SECTIONS IN PARALLEL where 8 is the electrical length of the coupled section. Response of 90' Schiffman phase shifters. The desired shift is obtained from (8) by the proper choice of 8 : K and p. i. the allowed phase deviation t. JANUARY 1993 Fig. Fig. p2 and 8 2 . i. the total four element admittance matrix [q'] is equal to the addition of the four element admittance matrix of each section [ 5 ] . The coupling C? in dB is defined as [61. = 8 in all cases.: Any desired phase shift is obtained from (9) by choosing properly PI. Also we can see that when 8 is chosen to be a/2 or T at center frequency. 2 the responses of 90" phase shifters are plotted when the phase deviation E. is: t = f and.j (zOe + zoo tan2 8) cot 8 2Zo. Response of 90' double Schiffman phase shifters. the differential shift z. k l o . de = 8. and. the phase shift (A#) of a Schiffman phase shifter is obtained as the transmission phase difference between an uniform transmission line and a coupled section.. When two coupled sections are connected in parallel. where a lossless network ( a = 0) has been considered and p=- (A4) is obtained as 20. 111. NO. B. l(b). l(d). a mismatch and a drastic change on phase exist at those frequencies. . When ZIt. We note that (19) has the same kind of symmetry as the standard Schiffman phase shifter has (8). In Fig.RAMOS QUIRARTE AND STARSKI: NOVEL SCHIFFMAN PHASE SHIFTERS 11 In the general case when both coupled sections are different we use (1 1) in (10) to get the four elements of the admittance matrix in terms of the even and odd mode impedances for the two coupled sections connected in parallel as The phase constant given by (14) reduces in this case to COS$ = ppl ppl - + tan2 81 + tan’ 81 where Ppl = P1P2 zoo1 Zoel + Zoo2 Zoea Using (12) the total characteristic impedance ZIt is obtained as By using (1 5)-( 17) new versions of Schiffman phase shifters can be designed. pz and p3 and on the input impedance of each parallel connected section. Any desired shift is obtained by the proper choice of the parameters 81 and K and the performance of the shifter will depend on the coupling and the input impedance of each section. Parallel Double S c h i f f ” Phase Shifter If the uniform line in the parallel Schiffman phase shifter is replaced by a coupled section. do not cancel each other. B. 3 . From (13) we observe that the total characteristic impedance is a function of 81 and Qz and thus the circuit is not matched for all frequencies. . In the following some cases are presented. When the length of both coupled sections is the same (81 = (13) reduces to where ppl is given by (17). and so the same bandwidths are expected. when the differential phase shifter is made by using two parallel connected coupled sections and a uniform transmission line. Parallel SchifSman Phase Shifter If the single coupled section in the standard Schiffman phase shifter is replaced by two parallel connected coupled sections having the same length as shown in Fig. several different altematives have been analyzed. where p p l is given by (17).. among others. n = 1 .! PI and p 2 are known 212 is found from (15) as shown in (18) at the bottom of the page. then the differential shift is expressed as e. 5 . Equations (13) and (14) are the general expressions for design of the parallel connection of two coupled sections. ZI. some examples given the same phase deviations as those for the double Schiffman phase shifter are presented. 4.). Since (15)-( 17) can be simplified under some conditions.. a single coupled section and another two parallel connected coupled sections.11 where Pee = Zoez/Zoei. A possible solution is to place the poles outside of the bandwidth of interest but this solution gives a much narrower bandwidth than that obtained by letting the length of both coupled sections be the same (01 = 02). then the differential shift is expressed by using (8) and (16) as The transfer constant is obtained when cos$ = q 1 2 Q = 0 from (12) as y. A . Since the poles produced by 01 = nn/2 and 02 = nn/2. . The desired phase shift is obtained by proper choice of O1 = 02 and 83 and the performance depends on p1. For practical reasons in a system with 50 R characteristic impedance we want to keep Yo. Fig. Again as with the double Schiffman phase shifter (Fig. = 8. Yo. Yo. 6. 3) the unsymmetrical response is observed.0 f/f.~ 12 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. = 2700 8. which corresponds to the capacitance between the parallel lines.1" are shown. as low as possible because large Yo. For coupled sections with 100 R characteristic impedance Yo. and f0. Response of 90" parallel Schiffman phase shifters. Fig. p3 and p4 and on the input impedance of each parallel connected section. 6. some cases giving maximum bandwidth when the allowed phase deviation E. VOL.. f1".. above 10 mS and to have Yo. is: E = f 5 " . The calculated results for Yo. = 900 +=83dB e. as low as possible..5 1. Response of 90" parallel double Schiffman phase shifters IV. then the differential shift is expressed by using (16) as A 4 = c0s-l pp2 pp2 + tan2 83 - tan2 83 ) -cos-l( p p l . 41. In Fig. The difference between the even and odd mode characteristic admittances is Yo. NO. values of coupling coefficients and input impedances that give similar responses as those presented for the other cases are shown. f 2 " . COMPARISON BETWEEN DIFFERENT CASES To obtain 90" phase shift (A$ = 90') the relation between the lengths of the coupled sections is found from (20) to be The comparison between analyzed cases can be done as follows. Response of 9O0 double parallel Schiffman phase shifters. The conclusion is that all cases shown in Figs. 5.5 Pp2 = P3P4 zoo3 Zoe3 + zoo4 + zoe4 The desired phase shift is obtained by proper choice of 81 = 8 2 and 83 = 84 and the performance depends on p2. 5.5". Double Parallel Schiffman Phase Shifter If each coupled section in the double Schiffman phase shifter is replaced by a parallel section having the same length. 1. JANUARY 1993 lie. Thus we can write In Fig. C . 1. should be above 5 mS and again Yo. is difficult to realize. Fig. and t = f 2 " are shown in Table I. f0.tan2 81 p p l tan2 81 + (22) where ppl is given by (17) and. 0. 3-6 are considerably easier to realize than the standard case shown . 4. 03 4.5. The agreement is good. V.RAMOS QUIRARTE AND STARSKI: NOVEL SCHIFFMAN PHASE SHIFTERS 13 TABLE I COMPARISON OF THE DIFFEREhT CONFIGURATIONS Case lLo (mS) 32. and K = 3.06 6. The results show that the proposed differential phase shifters have larger range of the feasibility compared to the standard Schiffman phase shifter since equivalent responses are obtained with considerably weaker coupling coefficients.46 10.86 13.06 6.02 13.2 5. (mS) 25.03 13. 45.58 7.35 14.75 17..06 17.41 6.32 7. (mS) (mS) yoc (mS) Yo. MEASUREMENTS To show the larger range of application for the proposed circuits.95 18.58 Yo. coupled sections or parallel connected sections has been presented. 2 Fig.05 L . The photographs of the circuits are shown in Fig. = p2 = 2. As a comparison the standard Schiffman phase shifter as shown in Fig. Theoretical and measured responses for the parallel Schiffman phase shifter (p) and the double parallel Schiffman phase shifter ( d ) shown in Fig. (mS) yoe (mS) Yoc (mS) 23. = 02 = 90". 2.6 mm and t .61 13. 7. The circuits were design on Diclad 522 with H = 1. since the input impedance of each parallel connected coupled section is about twice that for a single coupled section.06 Y o ' (mS) 20. The measured and theoretical phase responses of these circuits are presented in Fig. = 2. (mS) 12.64 13. 5 Fig.'s are close to each other maintaining the same phase performance.09 6.03 Yo. in Fig. the same coupling is even easier to realize. 8. = 2 1 2 = 100R. 7. . Using (15)-( IS) and (19) we get for the parallel Schiffman phase shifter with t = *lo: 01 p1 VI.49 7.. Fig. (mS) 15.54 12.25 8. (mS) 10. 3 Fig. . Using (15)-(18) and (22)-(23) we get for the double parallel Schiffman phase shifter with t = f2': ( b) Fig.41 14.47 z .38 27. CONCLUSIONS In this paper the theory needed to design differential phase shifters by using two coupled sections or parallel connected sections together with uniform lines.36 6. Photographs for: (a) The parallel Schiffman phase shifter and (b) The double parallel Schiffman phase shifter. we have selected a parallel Schiffman phase shifter and a double parallel Schiffman phase shifter as examples. . In addition for the configurations in Figs.29 6.12 (43') Fig. 6 Yo. 2 can not be realized with edge coupled lines for those phase deviations on this substrate.45 6.58 7. 4-6 we have the possibility to choose the coupling coefficients for different sections in such a way that Yo. 7.64 13.93 Yo.64 I. Moreover. 8. 4 Fig.99 8. Norwood. in 1973 and 1978. He received the Tekn.Y. Reading. 131 B. 1958. Microwave Theory Tech. Poland on October 19. Microwave Engineering. The thesis dealt with the design of digital microwave systems of medium capacity.S. He received the M. Levy. Bolljahn. Nov. 8. M. Scanlan and R. [6] J. 75-81. 666-671. no. Chalmers University of Technology. His research interests include microwave devices and systems and electromagnetic radiation and scattering.. Licentiat (Licentiate of Engineering) degree in 1992 from the School of Electrical and Computer Engineering of Chalmers University of Technology. MCxico in 1980. Jones and J. 1956. 1. 1966. Edinburgh: Oliver and Boyd. vol. 39. From 1978 to 1979 he was employed as a Design Engineer at Anaren Microwave. vol...S.. Sweden. 462473. Microwave Theory Tech. A. P. Semiconductor Control. Circuzr Theory. Schiffman. Schiek and J. 25. Jalisco.S. Piotr Starski (S’7f%M’78) was bom in Lodz. Microwave Theory Tech.” IEEE Trans. “Synthesis of Schiffman phase shifters. F. 1970. In 1983 he was appointed to Associate Professor at the Chalmers University. in 1956. Jose Luis Ramos Quirarte was bom in Ameca. pp. Syracuse. Starski has been Chairman of IEEE Sweden Section since 1987. 1I. Kohler. MCxico D.F. 1. vol. His Licentiate thesis dealt with broadband microwave amplifiers and phase shifters. Gothenburg.. From 1972 to 1978. pp. Pozar. Shelton and J.” IEEE Trans. 1885-1889. pp. White. no.14 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. pp. Jalisco. “A method for broad-band matching of microstrip differential shifters. T. pp. Gothenburg. He received the M. 41. degree in Electric Engineering Speciality in Telecommunications from the Centro de Investigacion y de Estudios Avanzados del Instituto PolitCcnico Nacional (CINVESTAVIPN). and Ph. [8] JosC Luis Ramos Quirarte and J. no. [4] E. Since 1979 he has been employed as a Researcher at the Division of Network Theory. 1977. 1990. JANUARY 1993 REFERENCES [ I ] B. 1977. He received the B. In 1985 he was awarded with a scholarship from the Concejo Nacional de Ciencia y Tecnologia (CONACYT) in MCxico to continue his studies at Chalmers University of Technology in Sweden and in 1989 he got financial support from the Swedish Institute. [2] J. N. degree in Communications and Electronic Engineering from the Universidad de Guadalajara. VOL. Microwave Theory Tech. 1991. 415-430. Apr. pp. “Synthesis and design of wide-band equal ripple TEM differential couplers and fixed phase shifters.” IRE Trans. Microwave Theory Tech. J. Piotr Starski. Aug. MA: Addison-Wesley. Dr. in Electrical Engineering from Chalmers University of Technology. Sweden. [7] D. In 1978 he was awarded a Fellowship from the SwedenAmerica Foundation for postdoctoral studies. in 1985. MTT-14. “A new class of broad-band microwave 90-degree phase shifters. pp. [5] J. Chalmers University of Technology. Oct.” IEEE Trans. T. “Coupled-strip-transmission-line filters and directional couplers. MA: Artech House. Guadalajara. vol. Inc. 10. 1947. 0.’’ IRE Trans. The thesis dealt with the design of a transmitter-receiver antenna for earth stations which operate according to the mexican domestic satellites. 232-237. he was associated with the Division of Network Theory. M. MCxico. 474482.D. Apr. Mosko. . NO. His current research activities are in the areas of microwave circuits and devices. M. respectively.