1026 PH~~~~~~~~~~.JGCE2YIiHIV1G3 G.F Tum ' r ecmoe

Chairman of the U. S. Committeefor Study, Gr(oup ,Y- T-A. G. Jensen, Bell Telephone Laboratories, MurrayHill, N. J.

More complete information on the technical subjectsunder study by the CCIR, i.e., its program of work forthe next three years, may be found in Volume I of theresults of the Warsaw Assembly which contains thetexts of all recommendations, reports, questions, studyprograms, and resolutions adopted or reaffirmed atWarsaw. This volume may be obtained from the GeneralSecretariat of the International TelecommunicationUnion at Geneva, Switzerland. Payment for the publi-cation should accompany this order and should be madein Swiss francs. The price of the volume is 37.25 Swissfrancs.

Information in more detail on the United Statesactivities for the Warsaw Assembly on technical ques-tions under study is available in the report of the U. S.Delegation to the Assembly and may be obtained, freeof charge, by writing to Mr. Francis Colt de Wolf, Chief,Telecommunications Division, Department of State,Washington 25, D. C.The coordination of the preparatory work in the

United States for the Ninth Plenary Assembly, both onthe technical studies under consideration and on or-ganizational planning for the Assembly in the United

States, is certt-alized in the Telecommunications Divi-sion of thie Deoartment of State. Mr. de Wolf is Chair-man of the over-all U. S. Preparatory Committee andthe U. S. Executive Committee for the CCIR. The mem-bers of the Executive Committee and of the U. S. Com-mittees for the various Study Groups are, for the i. ostpart, representatives of government agencies and pri-vate telecommunication companies or organizationshaving an interest in the work. The Department ofState welcomes the participation of any person wishingto contribute to the studies. If further information onthe United States committee structure is required, itwill be furnished in response to written requests to Mr.de Wolf. On the other hand, any company or personnot already participating in the work of the variousStudy Group Committees and wishing to do so, shouldget in touch with either Mr. de Wolf or with the UnitedStates chairman of the appropriate Study Group Com-mittee whose name and address is shown herein.As a further item of interest, the Institute of Radio

Engineers is represented in the CCIR preparatory com-mittee work by A. G. Jensen, by Professor ErnestWeber of the Brooklyn Polytechnic Institute, and byL. G. Cumming, Technical Secretary of the IRE, whowill be able to provide further detailed informationabout the participation of the IRE in the technicalstudies.

A New Wide-Band Balun*WILLMAR K. ROBERTSt, MEMBER, IRE

Summary-This paper describes a form of balun which is usefulfor matching a balanced circuit to an unbalanced circuit of nearly thesame impedance over a wide frequency range. The bandwidth in-crease is obtained by the use of a quarter-wave transmission linesection which is placed inside one of the balanced arms, therebymin'imiing the over-all physical length. It is shown that a practicalbalun of this type, designed to match a 50-ohm unbalanced line toa balanced 70-ohm antenna, has a voltage standing-wave ratio of 1.4or better over a frequency band of about 2.8 to 1. The wide band-width, simplicity, and reasonable physical dimensions make thebalun particularly useful in connection with the adjustable-lengthdipole antennas which are generally used for vhf and uhf field-strength measurement.

INTRODUCTIONA BALUN is a device intended to act as a trans-

former, matching an unbalanced circuit to abalanced one, or vice versa. The balun de-

Original manuscript received by the IRE, June 17, 1957; re-vised manuscript received September 17, 1957.

t Federal Communications Commission, Laurel, Md.

scribed here was developed to meet a need for a low-loss impedance-matching device to connect a balanceddipole antenna to an unbalanced coaxial transmissionline. It was desirable that the balun have a wide-bandcharacteristic so as to make unnecessary any adjust-ments on the balun over a range of frequencies coveredby adjusting the telescoping elements of the dipole an-tenna. Certain previously described wide-band trans-formers," 2 require a considerable amount of space be-cause of the use of the frequency-compensating effectsof one or two quarter-wave transmission line sectionsconnected between the balun and the balanced load.The balun described here employs a single quarter-

1 Radio Res. Lab. Harvard Univ., "Very High-Frequency Tech-niques," vol. 1, 1st ed,, McGraw-Hill Book Co., Inc., New York,N. Y., pp. 85-91; 1947.

2 E. G. Fubini and P. J. Sutro, "A wide-band transformer froman unbalanced to a balanced line," PROC. IRE, vol. 35, pp. 1153-1155; October, 1947.

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Roberts: A New Wiade-JJnd 13c!un

wave length of transmission line for compensation overa wide band, but the construction is arranged to allowthis line to be housed inside one of the arms of the balun.Thus, the over-all physical length is only one-quarterwavelength.

DESCRIPTION OF THE BALUN

A diagram of the balun is shown in two forms in Figs.I and 2. The sketches represent two variations of thesame arrangement. The device is composed of twolengths of coaxial transmission line, a and b, suitablyconlnected. The symbols Z. and Zb represeInt the charac-teristic impedances of liines a and b, respectively, con-sidering the waves propagated within each line. Zab iSthe characteristic impedance of the balanced transmis-sion line ab composed of the outer conductors of trans-mission lines a and b.

where 0b and Gab are, respectively, the electrical lengthsof transmission lines b and ab, taking into account theirrespective physical lengths and velocities of propagation.From the equivalent circuit,

RNZ = ++M

R+NX

jRZab tan Gabz = jZbtnb- -jZb cot O3bR + jZab tan Gab

R+ jR2Zab tan Gab

R2 R2 + Zab2 tan2 Gab.+1

Zab2 tan2 Gab

- jZb cot Gb.

(2)

(3)

(4)

Let the electrical lengths of line segments b and ab beequal, making Gb = ab =0, and let characteristic imped-ance Zab=R and Zb=Za=S. Then

Z = R sin2 + j(cot G)(R sin2 0 - S). (5)

Fig. 1 -The new balun. The balanced terminals are at F and G,and the unbalanced connection is made at H.

JL

b

IFI

E bt- - -

r- - -- -

HC Zab D

_-_- r-X~~~~~~ Zs - _____

(abF

G

Fig. 2-A slight variation of the balun for the purpose ofdescription.

The coaxial terminal H is the connection for the ex-ternal unbalanced source (or load), while the terminalsF and G are the points of attachment of the balancedload (or source). Center conductors of lines a and b areconnected at D, while outer conductors of a and b areconnected at C. The center conductor of line b ends at E.

IMPEDANCE ANALYSIS

Fig. 3 shows an equivalent circuit of the balun for thepurpose of studying the impedance. The terminals F, G,and H are the same as in Figs. 1 and 2. S and R areexternal impedances which may be connected to thebalun. M is the impedance looking into coaxial line btoward the open circuit at E. N is the impedance lookingfrom FG along the open transmission line ab toward theshort-circuit at C.

If the transmission line losses are neglected,

M - jZb Cot Gb

N = iZab tan Gab,

KzFig. 3-An equivalent circuit of the balun for the purpose of studying

its impedance characteristics. The lettering is the same as thatof Fig. 2.

The reactive component of the impedance is zerowhen cot 0=0, (for which Z equals R) and also whensin2 0=SIR (for which Z becomes S). Fig. 4 is a sketchof the variation of resistance and reactance in theneighborhood of the lowest-frequency band of interest.The physical lengths being fixed, 0 varies directly withfrequency. The region 02 -61 locates a frequency bandf2-fl over which the balun has impedance matchingcharacteristics of a desirable nature. Cot 0=0 estab-lishes the center of the band and corresponds to anelectrical length of 90°. From Fig. 4 it appears that thebalun serves to transform from a resistance R to anotherresistance S with a perfect impedance match at fre-quenciesfi and f2. There is an approximate match in theband of frequencies within this interval and also atfrequencies somewhat outside. The midband staindingwave ratio increases with the ratio of R/S, hence thebalun is particularly interesting for balanced to un-balanced transformations where the desired impedancetransformation ratio is low.

I Y-i

PROCEEDINGS OF THE IRE

An example is a balun for matching a 70-ohm bal-anced source to a 50-ohm unbalanced load. In this caselet Za=Zb=50 ohms, Zab=70 ohms, and 9ab =Ob. Thevalues of 6 for which a perfect match is expected aregiven by

S 50sin2 0 = - = -

R 700 = 580, 1220

70 obnis in the parallel transmission line composed ofthe two lengths of cable held together by a wrapping ofplastic tape. Because of variations in composition, di-ameter, or eccentricity of the outer insulation, the char-acteristics of parallel lines formed from certain coaxialcable samples may differ appreciably from the desiredvalue. It is generally necessary, therefore, to determinethe characteristic impedance and velocity of propaga-tion by testing sample parallel line sections made of theintended material.

Since 0 is linearly proportional to frequency, the fre-quency band between points of perfect match has aratio of 2.1. The mismatch at the worst point in thisband (namely, at the center frequency) corresponds toa voltage standing wave ratio of 1.4.

z

cr

w0 +

w-

fl f2 f

Fig. 4-The input resistance and reactance at the point Z of Fig. 3.

PHYSICAL DETAILS OF CONSTRUCTIONA number of baluns have been made in the form

shown in Fig. 5. In practice, this balun is mounted in-side a bakelite tube supporting a dipole antenna used infield strength measurements. The balun shown is madeof two lengths of RG-58/U coaxial cable, whose shieldbraids form a 70-ohm parallel transmission line ab. Thelength of the parallel section, measured from the pointC, where the two braids are connected together, to thepoints F and G, where the balanced circuit is to be con-nected, is made one-quarter wavelength at the centerfrequency of the operating range. For the determinationof this length, it is necessary to take account of thepropagation velocity, which is somewhat higher thanthat of the waves moving along the inside of the coaxialcables. The center conductor of the coaxial line b is cutby drilling a hole into the cable at the point E, which(considering the velocity of propagation inside thecable) corresponds to a quarter wavelength from thebalanced terminals F and G at the center frequency ofthe band.The construction of this version of the balun is based

upon the realizationi of a characteristic impedance of

Cable b cut off on angle,cut surface placed nextto cable a

Center conductor cutby drilling hole

Plastic tape

-Outer jacket O

0Braid 0 Perforated metalCenter conducto s0 strip for soldering

cable braids

L Balancedterminals

Fig. 5-The construction of a balun for matching a 50-ohm Voaxialcable to a 70-ohm balanced load. The balun is made of two lengthsof RG-58/U cable, held together by a wrapping of plastic tape.In use, this balun is housed inside an insulated tubing whichsupports the center of a half-wave dipole antenna. Alternatively,a metal housing could be employed to shield the balun.

PERFORMANCE OF THE BALUN

Fig. 6 shows the measured vswr looking into the un-balanced connector of a practical 70- to 50-ohm balun,made according to Fig. 5, when the balanced terminalswere terminated by a 70-ohm noninductive resistor.This same figure gives the measured loss. The loss wasmeasured through two identical baluns, their balancedterminals being joined through a 70-ohm balanced re-sistive attenuator for isolation. The loss of one balun isconsidered to be one-half the total attenuation, sub-tracting first the loss of the attenuator. The baluns haveexcellent symmetry, in that no appreciable change inmeasured values resulted from reversal of the balancedterminals of either balun. The curves in Fig. 6 are typi-cal of those which have been measured on other balunsof the same construction covering frequencies as high as1000 mc.To verify the performance of the balun when associ-

ated with a dipole antenna, two identical balun-dipoleassemblies were constructed to cover the range 400 to1000 mc. Signals at a number of frequencies across thisrange were fed to one assembly, radiated, and picked upby the other. The attenuation through this path wascompared with that obtained when the coaxial trans-mission lines were disconnected from the baluns andconnected to each other. The propagation path betweenthe antennas was approximately equivalent to free-space conditions. On the assumption that the resoniant

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Roberts: A Yew Wiade-JJnd 13c!un

1.0

Loss, db

0.5

30 40 50 60 70 20Frequency, mc/s

30 40 50 60 70

Frequency, mc/s

Fig. 6-The measured performance of the balun of Fig. 5 when the balanced terminals are connected to a 70-ohm noninductive resistance.

dipole antennas had a power gain over isotropic an-

tennas of 1.64 (the theoretical value for an infinitely-thin dipole), and taking into account the distance be-tween the dipoles, the loss attributable to the sum ofdipole loss and balun loss for one assembly was foundto be 0.6 db +0.4 db at the frequencies of test. This isconsidered to be an acceptable verification of the loss ofthe balun.

CONCLUSIONA new form of balun has been described. It has low

loss and excellent impedance characteristics over almosta 3 to 1 frequency band, without any adjustments. Thedimensions of the balun make it suitable for use at vhfand uhf, particularly in association with the adjustabledipole antennas widely used for field strength measure-

ments in these frequency ranges.

CORRECTIONDr. Janis Galejs, of the Applied Research Laboratory,

Sylvania Electric Products, Inc., Waltham, Mass., hascalled the following to the attention of the editor.The comments of Strom' on the recent remarks by

Goldstein2 appear to be incorrect. In deriving (11) from(10) Strom states that the second integral on the right-hand side of (10) vanishes. Following Goldstein,3 theband-pass filter output of the radiometer v(t) is a sum

of a periodic and of a random voltage

v(t) = A cos coqt + Bm(t),

where m(t) is a random voltage. Substituting v(t) in (10)the term proportional to A2 in the second integral

lim- (Tv(t)v(t+r) cos Wq(2t + r)T-oo T 2

1 L. D. Strom, "The theoretical sensitivity of the Dicke radi-ometer," PROC. IRE, vol. 45, pp. 1291-1292; September, 1957.

2 S. J. Goldstein, Jr., "A comparison of two radiometer circuits,"PROC. IRE, vol. 45, pp. 365-366; March, 1957.

3 S. J. Goldstein, Jr., private communication.

gives a contribution to the constant term of R3 (r), thatis, equal to the contribution of the term proportional to

A2 in the first integral

liT Cos

qT di.lim - w v(t) v(t + Tr) dt.T-oo T 2

The sum of these two terms is equal to the constant

term in the R3 (r) expression of Goldstein,4 but is twicethe constant term in (12) of Strom.Strom considers his (8) to (12) as a special case of a

more general treatment.5 With the special case in error,

a similar error may be expected in the developmentleading to (5) and (7). In order to make (5) and (7) com-patible with the revised (12) and with the results ofGoldstein,2 a constant 16 should be substituted for theconstant 32 in (5) and (7) of Strom.'

4 S. J. Goldstein, Jr., "A comparison of two radiometer circuits,"PROC. IRE, vol. 43, pp. 1663-1666; November, 1955.

6 L. D. Strom, "The theoretical sensitivity of the Dicke radi-ometer," dissertation, University of Texas; February, 1957.

VSWR

19157 J. 't;