Ruthroff_ Some Broad Band Transformers, I

Some Broad-Band Transformers" C. L. RUTHROFFt, MEMBER, IRE Summary-Several transmission line transformers are described which have bandwidth ratios as high as 20,000: 1 in the frequency range of a few tens of kilocycles to over a thousand megacycles. Experimental data are presented on both transformers and hybrid circuits. Typical applications are: interstage transformers for broad-band amplifiers; baluns for driving balanced antennas and broad-band os- cilloscopes; and hybrids for use in pulse reflectometers, balanced modulators, etc. These transformers can be made quite small. Excellent trans- formers have been made using ferrite toroids having an outside diameter of 0.080 inch. SEVERAL transmission line transformers havingbandwidths of several hundred megacycles. are,de-scri bed here. The transformers are shown 111 Figs. 1-9. When drawn in the transmission line form, the transforming properties are sometimes difficult to see. For this reason, a more conventional form is shown .' Original manuscript received by the IRE. February 5. 1959; reVIsedmanuscript received, April I, 1959. t Bell Telephone Labs., lnc., Holmdel, K J. with the transmission line form. Some winding arrange- men ts are also shown, Certain of these configurations ha ve been discussed elsewhere and are included here for the sake of completeness (1-4}. In conventional transformers the interwinding ca- pacity resonates with the leakage inductance producing a loss peak. This mechanism limits the high frequency response. In transmission line transformers, the coils are so arranged that the inter winding capacity is a COIl1- poueut of the characteristic impedance of the line, and as such forms no resonances which seriously limit the bandwidth. Also, for this reason, the windings can be spaced closely together maintaining good coupling, The net result is that transformers can be built this way which have good high frequency response. In all of the transformers for which experimental data are presented, the transmission lines take the form of twisted pairs. In some configurations the high frequency response is de- tennined by the length of the windings and while any type of transmission line can be used ill p;inciple, it is Proceedingsof the Ire August 1959 ),~~P -z-TRmSMISSION UNE FORM Fig. 1-Reversing transformer. T I;'lNSMISSION LINE FORM Fig. 2-Unhnlanced to balanced transformer. quite couveuien r to make very small windings with twisted pairs. The sketches showing the conventional form of trans- former demonstrate clearly that the low Irequencyre- spouse is determined in the usual way, i.e., by the pri- mary inductance. The larger the core permeability, the fewer the turns required for a given low frequency re- sponse and the larger the over-all bandwidth. Thus a good core material is desirable. Ferrite toroids have been found very satisfactory. The permeability of some fer- rites is very high at low frequencies and falls off at high- er frequencies. Thus, at low frequencies, large reactance can he obtained with few turns. When the permeability falls off the reactance is maintained by the increase in frequency and good response is obtained over a large frequcnc y range. It is important that the coupling be 11igh at all frequencies or the transformer action fails. Fortunately, the bifilar winding tends to give good coupling. All of the cores used in the experimental transformers described here were supplied by F. J. Schnettler of the Bell Telephone Laboratories, Inc. POLAR!TY REVERSING TRANSFOR}'lER--FIG. 1 This transformer consists of a single bifilar winding and is the basic building block for all of the transform- ers. That a reversal is obtained is seen from the conven- tional form which indicates current polarities. Both , . ?ll 2"n I, TRANSt-'ISSIOH LJf;t FORM CONVENl"IONAL ~ORM .•••,RIIIIG DIAGRAM Fig. 3-4: 1 Impedance transformer. '- . -'(£ ,"""'~." u~ -::.. ~~r#J. E~ */ t~ -~A\.o\HC(-I.Jof&aa..AMC£ ~tVUlSA.l.. TIUHSfCRM(R I" CONVOIlIONA,L fORM WIRING DI~GR"M Fig. 4-4: I Impedance transformer. Unbalanced-symmetrical. ends of the load resistor are isolated from ground by coil reactance. Ei ther end of the load resistor can then be grounded, depending upon the output polarity desired. Ii the center of the resistor is grounded, rhc output is balanced. A suitable winding consists of a twisted pair of Formex insulated wire. In such a win ding , the pri- mar y and secondary are very close together, insuring good coupling. The interwinding capacity is absorbed ill the charucteristic impedance of the line. At high frequencies this transformer can be regarded as all ideal reversing transformer plus a length of trans .. mission line. If the characteristic impedance of the line is equal to the terminating impedances, the trausrnission is inherently broadband. If not, there will be a dip in the response at the frequency at which the transmission line is a quarter-wavelength IOlJg. The depth of the dip 160 ZR Fig. S-Balanced-lllliJalanced 4:1 impedance transformer. . "~ 3 > "j • , R.'-- I- z R TJ unsymmetrical. where f3 is the phase constant of the line, and l is the length of the line. Thus, the reS}JOIlSC is down 1 db when the line length is >-/4 wavelengths and the response is zero at )../2. For wideband response this transformer must be made small. For a plot of (1) see Fig. 16. Experimental data are given far a trausformcr of this type in Fig. 12. UNrL\LANl.ED-SYM~.IETR!cAL 4:1 h!!'EDANCE TRANSFORMER-FIG. 4 This configuration requires three hifilar windings as shown in Fig. 4. All three windings can be placed 011one core, a procedure which improves the low frequency response.' When winding multiwindi ng transformers the following well-known rule should be followed: wi rh the g-enerator connected and the load open, a completed circuit should be formed by the windings so that the core will be magnetized. The fields set lip by the cur- rents should be arranged so as to aid each other. I Pointed out to the ;nltnor by N. J. Pierce of Bell Telephone Labs .. 11lC.,Holmdel, N. J- BALANCED-TO- UN J3!\I.Al'CEO 4: 1 I~II'ED.\NC" TRANSFORMElb-FJ{; . .'i The circuit of Fig. 5 is quite simple. The single bifilar winding is used as a reversing- transformer as in Fig. 1. The high frequency cutoff is the sa me as that for the transformer of Fig. 3. In some applications it is desirable to omit the phys- ical ground on the balanced end. 1n such cases, Fig. 5(b) can be used. The high frequency cutoff is the same as for the transformer of fig. 3. The low frequency anal- ysis is presented in Appendix B. HVBRID CIRCUITS: FlGS, 6--9 Various hybrid circui ts are developed from the basic form using the transformers discussed previously. The drawings are very nearly self-explanatory. In all hybrids in which all four arms are single-ended, it has been found necessary to use two cores in order to get proper magnetizing currents, Two hybrids have been measured and data included here. The response of a hybrid of the type shown in Fig. S is given in Fig. 13. For this measurement R = 150 ohms. In order to measure the hybrid ill a 75-ohlll cir- cuit, arms B, D were measured with 75-ohm series re- sistances in series with the 75-ohm measuring gear. This accounts for 3 db of the loss. Under these condi lions arms Band D have a 6 db return loss. The transmission of the resistance hybrid of Fig. 9 is given in Fig. 14. This hybrid has been matched using the technique described previously for the reversing transformer. The results of this matching are included in the figure. This hybrid was designed for use ill a pulse reflcctometer , the main part of which is a stroboscopic oscilloscope with a resolution of better than 3 muscc, The oscilloscope was designed by W. M. Goodall. ApPLICATIONS Many applica tions Ior these transformers will occur to the reader. For purposes of illustration, a few of them are listed here. 1) The reversing transformer of Fig. 1 can he used to reverse the polarity of short pulses, all operation which is frequently necessary. I t has also been used ill balanced detectors and to drive flush-pull amplifiers from single-ended generators. 2) The transformers of Fig-s. 2 and 5(b) arc useful for driving balanced antennas, The circuit of Fig. S(b) may find applica tion in COllllCctillg twill lead transmission line (0 commercial television recciv- crs. J) The 1 runsformcr of Fig. 3 has found wide IIS(' ill bro.idba ud amplifier iIlterS!agct;. l t will also be useful in transforming the high output iIllPC" 'RL• R, Fig. IS-Transformer schematic. "L~ !...!I -_...J,I..-- -<-...---1.. " .'1"'( "\ -r FiH:_qUCHCY IN TCfUl\5 or LIN( L(~TH Fig. 16- Theoretical insertion loss vs frequency. From this expression, the conditions for maximum pow- er transmission are obtained by setting 1=0 and setting dPo/dRLI1_O=O. The transformer is matched when RL = 4Rg. The optimum value ior Z« is obtaincd by minimizing the coefficient of sin? f31 in (3). In this man- ner the proper value for Z« is found to be Zo = 2Rg. Now, setting RL =4Rg and Zo = 2Rg, (3) reduces to c2(1 + cos (31)2 Po = --- (4) Rg[(l + 3 cos{3t)2 + 4 ~in2 /3lJ Also, e2 Pavnilaule = -r-r--r r 4Rg (5) (2) and dividing (4) by (3) : Power Available (1 + 3 cos (31)2 + 4 sin" (31 = . (6) Power Output 4(1 -I- cos (31)2 This function is plotted in Fig. 16. The impedances seen at either end of the transformer with the other end terminated in ZL have been derived. They are: Z;,,(low impedance end) ( Z L cos {3t +tz, sin (3l ) = z, 2Zo(1 + cos{3l) +'jZr. sin fJI (7) (3) 163 Proceedingsof the Ire August 1959 and Zin(high impedance end) _ r (2Z L(l + cos (jl) + tz, sin f3l) - Zo . Z« cos (3l + JZL sin {31 ArPENDIX B In the low frequency analysis of the transformer of Fig. 5 the series impedance of each half of the bifilar winding is denoted by Z. The loop equations are: E = (Rg + Z)ft - (2 + kZ)1z E = (Rg - kZ)II + (RD + Z + kZ)Iz, from which 11 RL + 2Z(1 + k) - = ------ = 2 if 2» RI,. 12 Z(1 + k) We now proceed to calculate the voltages from points 1 and 2 to ground When the transformer is matched, E=2hRg and Similady, Vw = hZ -- kZ(l1 - 12). -VVith the aid of (10) th is can be rearranged to _ r [Z(1 + sv - kRr, - 2kZ(1 + k)] Vw - Z11 . • Rr, + 2Z(1 + k) (12) (8) Now let the coupling coeJlicient k = 1, then [ -kRI" ] t.u: Vir. = IIZ RL + 2Z(1 + k) ~ - 4 for Z» RL. When the tr ansf or mer is matched, R/"=4Rg so that (13) (9) and the load is balanced with respect to ground. From (13) it is clear that the center point of RJ- IS at ground potential. This point can therefore be grounded physically, resulting in Fig. 5(a). (10) ACKNOWLEDGMENT. I n addition to those mentioned in the text, the author is indebted to D. II. Ring for many stimulating discus- sions on every aspect of these transformers. REFERENCES III Willmor K. Roberts, "A new wide-band balun," PROC. IRE, vol. 45, pp. 1628-1631; December, 1957. [2] H. Gunther Rudenberg, "The distributed transformer," Raytheon Mfg. Co., Waltham, Mass. l3] G. Guane!la, "New method of impedance matching in radio Ire- queucy circuits," Brown-Boveri Reo., voL 31, p, 327; 1944. f4] A. I. Talkin and J. V. Cuneo, "Wide-band balun transformer," Reuieui of Sci. Inst., vol. 28, No. 10, pp. 808-815; October, 1957. 151 C. A. Burrus, unpublished memorandum.