IEEE TRANSACTIONS ON BROADCASTING. VOL. 38, NO. 1, MARCH 1992 27

A VOLTAGE-MATCHING METHOD FOR FEEDING ANTENNA ARRAYS

COSTAS MERTZIANIDIS TEI of Cavala

Ethnikis Antistasis 8r, CAVALA 654 03, GREECE

IOANNA DIAMANDI, MEMBER IEEE JOHN N. SAHALOS, SENIOR MEMBER IEEE

Department of Physics University of Thessaloniki, THESSALONIKI 54 006, GREECE

Abstract: A method for feeding antenna arrays is presented. Each element of the array is connected with transmission line sections. The first two sections are connected to a common point where the voltage from both sections is the same. The common point is connected with a new transmission line which is also doing the same with the third section. The procedure is continued until the last common point will be connected to a single source. A formulation for the antenna currents as a function of the frequency is also given. Some examples show the applicability of the method.

I . INTRODUCTION AND FORMULATION

One of the main problems in the antenna design is the synthesis of the feed system. The antenna is fed by a single source and the terminal voltages on the elements are synthesized by choosing the appropriate length of transmission line sections. Recently two methods for solving the antenna feed problem have been presented. One is the AI Christman's work I ] and the other is the work of Y.W. Kang and D.M. Pozar [A]. In [ I ] the feed system of a two-tower array has been derived while in [2] the pattern synthesis by using reactive loads and transmission line sections has been given. Our method has to do with the antenna array feed system without. using reactive loads. The transmission line sections are not in series or in parallel all together in a common point. They are connected in the form of a parallel corporate feed, which will be shown later. Except of [ I ] and [2] many other studies have been presented in the past for the antenna synthesis. All of them, [3]-(7], make use of reactive loads as in [2]. Our method has common things with [ I ] and generalizes its formulation for any number of antenna elements.

Consider an N-element array antenna connected to an N-port feed network as shown in Fig.1.

[ I I = [ Y l [ V I (1) [ Y ] is the NxN admittance matrix of the array system.

elements is that which in graphical form is given in Fig.2. A method by which we can connect the antenna

- T

'il T

Fig.2 - Our feed configuration.

Using the idea of [ I ] we find the electric lengths 91 and 92 of the transmission line sections for which the common point A has the same voltage. We continue the same procedure for the point B where we suppose that at the point A we have a load equal to the ratio:

The method is continued until we reach the last element. The last common point will give the input impedance of the feed system. It is important to say that the basic equation for the transmission line sections (see Fig.3) is of the following form:

Zi and Zi.1 is the input impedance of two loads and Roi, R0,i-I is the characteristic impedance of the corresponding section of the transmission lines.

Fig.1 - A singly fed antenna array with a transmission line network.

0018-9316/92$03.00 Q IEEE

different kinds of transmission line. One has 50 0 and the other 75 0 characteristic impedance.

The connections of the antenna array are given in Fig.4:

i 0 -

Ro

Fig.3 - Connection of two loads.

1 2 3 4 1 2 3 4 174.72" 183.86" 187.21" 6.22" 162.93" 163.30" 331.30" 174.20"

5 0 0 5 0 0 500 5 0 0 7 5 n 7 5 0 7 5 0 7 5 n

The current Is at the points is

Is = Isi + lsi-1 (4)

where Vi Isi = li cosei + j 7 sinei 01

(5) 1,i-l = Ii-1 cosei-, + j + sinei-1

and the voltage Vs is:

Vs = Vi COSQi + j li Roi sine, (6)

The ratio gives the load Zs which is connected with the next element with input impedance Zi+l by using a similar expression with (3). The electric lengths Bi, 8i.l e.t.c. are given from the expressions (28) and (29) of [l].

I I . ANTENNA DESIGN AND APPLICATIONS

We give two different applications of the antenna design. One has to do with a three wire dipole collinear antenna and the other with a Dolph-Chebyshev end-fire array.

A collinear antenna is applicable to transmiting systems where we need high gain radiation.

For a three element uniformly excited antenna array working at 650 MHz, we choose a mutual distance between the dipoles d=0.346 m and we design the array for two different wire antennas. In the first case we suppose that we have wire radius r=0.004 m, while in the second the radius is r=0.01 m. The length of each wire dipole is chosen to have a self-impedance near to real. So, for r=0.004 m the length is 0.215 m and for r=0.01 m it is 0.2182 m. We use two

i

8 Ro

1-13

1 2 3 4 1 2 3 4 175.48" 184.68" 186.51" 5.48" 90" 90" 264.05" 177.03"

5 0 0 5 0 0 5 0 0 500 7 5 0 7 5 0 7 5 n 7 5 n

Fig.4 - Connection of the three element collinear antenna.

For a uniform array where 1 1 = 12 = 13 = 1 A we have the following input impedances of the dipoles:

r=0.004 m, Zl=Z3=76.15 - j 7.30 0, Z2=76.00 - j 15.27 0

r=0.01 m, Zl=Z3=88.31 - j 7.83 0, Zp88.33 - j 15.88 0

For the above radii we have in general 64 different solutions depending on the transmission line impedance. From all of these we choose two for each case. The details are given in the following tables:

TABLE I r=0.004 m

I T I

TABLE I 1 r=0.01 m

29

Because of the symmetry of the system we could also use a connection in one common point of three transmission line sections. In this case we will have 81=83 and 84=O. So, for 50 f2 transmission lines we have:

r=0.004 m, 81=83=174.72~, 82=183.84O, Z~=25.38 - i 2.43 f2

and for transmission lines of 75 0 we will have:

r=0.004 m, 81=83=162.93~, 82=163.30°, Z~=26.96 - j 1.81 f2

In practice the design of the antenna will be completed when we analyze it in a frequency band around the design frequency. It is evident that since we use a different frequency the electric lengths as well as the Zii parameters of the antenna are changed. This makes the antenna feeder to have different input impedance and different currents. So the pattern of the antenna changes. To find the new currents we use a procedure based on the same quantity of the voltage at the common points. That gives a system of the form:

A X + B Y = C (7 1

D X + E Y = F

12 (X =rT and Y= l3 ri) The parameters A,B,C,D,E and F are given as a function of the impedance parameters and the transmission line lengths. These are:

f 91 = (r, 18,

( fo is the design frequency )

Solving (7) we can find the current of the antenna elements as a function of the frequency. We also can find the input impedances. Matching the impedance for the frequency fo to a 50 f2 load we can derive the VSWR of the antenna as a function of frequency for the above studied cases. VSWR is given in F ig5 where it is clear that the antenna is working in a wide band.

" I I

0.8 0.9 - I I 1.1 1.2

(0

r = O O l m

1, = 650 MHz

1 .1 1.2 0.E 0.9 - i ' lo

Fig.5 ~ VSWR of the collinear antenna as a function of frequency for the four different cases given in Tables I and 11.

520 MHz

637 MHz V S W R = 1 2

663 MHz V S W R - 1 2

780 MHz

650 MHz VSWR = 1

Fig.6 - Pattern of a three elements collinear antenna array for five different frequencies.

30

i 8

R o

For one case of r=0.004 m we show in Fig.6 the radiation pattern in five different frequencies. All the patterns are similar and for VSWR I 1.2 we have a bandwidth Af=26 MHz. The bandwidth increases much more for the wire of radius r=0.01 m, where it becomes Af=117.5 MHz. We must say that because of the geometry (small mutual impedances) and the radius of the wire antennas, the above results were expected.

Another case where the mutual coupling is strong enough gives results which are more sensitive with the frequency. We suppose that we want to design a Dolph- Chebyshev end-fire array with three parallel dipoles in a distance d=z and with SLL=QO db. In this case the array is shown in Fig.7 and the geometry has been designed for 600 MHz frequency.

A

1 2 3 4 1 2 3 4

50 n 50 50 n 50 75 0 75 0 75 75 f2 34.46" 289.04" 272.85" 70.84" 173.33" 330.33" 321.19" 31.70"

--L

i 1 2 3 4 1 2 3 4

8 161.87" 325.34" 309.42" 46.34" 29.81 O 297.21 O 259.15' 53.84" , R o 5 0 n 5 0 0 5 0 0 5 0 n 7 5 0 75 0 7 5 0 7 5 n

f

We can again give results for two different wire radii. In our design case the input currents must be:

I1 = 1 A, 12= 1.6914/ 223.84"A, 13= 1 1 87.62"A

The input impedances are:

r=0.004 m Z1 =27.81 - j 22.05 n, Z2 =33.88 + j 75.95 0 Z3 =43.53 + j 19.35 n r =0.01 m Z1 =36.43 - j 22.03 n, Z2 =42.58 + j 78.46 n Z3 42 .50 + j 20.41

We have in general 64 different solutions for the connection of the dipoles with transmission line sections of 50 n and 75 0.

In Tables I11 and IV two different cases for each wire radius are given.

After matching the antenna to a 50 n load, Fig.8 shows the VSWR of the antenna as a function of the frequency for the above cases.

Since the array is more sensitive it is expected the VSWR to increase faster than in the case of the collinear antenna. We also can see that the pattern of the antenna is changed faster.

Fig.7 - Geometry of a three-dipole end-fire array.

TABLE 111 r=0.004 m, L0.2325 m

7 1

Fig.9 shows the patterns of the antenna for five different frequencies. As we go far from the frequency of 600 MHz the side lobe increases and becomes similar to the main one. However for VSWR I 1.2 we have similar patterns and the bandwidth becomes Af=9 MHz for r=0.004 m. The quantities of Af for r=0.01 m increase to Af=10 MHz. Comparing these values with the others for collinear antennas we conclude that the bandwidth becomes 10 times smaller.

From the 64 possible solutions of the design of the feed system there are many others which can give results with more or less bandwidth and possibly more preferable results. There is not any from which we can in advance select one of the cases. So, the only rule must be the length of the transmission line sections. These sections have to be longer than the mutual distances of the dipoles. That is because otherwise we must extend the sections in multiples of the wavelength.

8 720 MHz

603 MHz

W R = 12

8

6 594 MHz

VSWR. 12

8 480 M H z

6W MHz

VSWR. 1

Fig.8 - VSWR of a three wire dipoles Dolph-Chebyshev end-fire array as a function of frequency for the cases given in Tables I11 and IV.

0.0 0.9 I1 1.1 1.2 f 0

I I

r = 0.01 m I, = 600 MHz

0.0 0.9 - f 1 1.1 1.2

‘0

Fig.9 - Pattern for five different frequencies of a three elements antenna which has been designed to be end-fire Dolph-Chebyshev with SLL=-20 db at f=600 MHz.

AlB=51.89cm c A,C = 44.60 cm A3D = 48.10 cm A& = 34.74 cm A5B = 34.19 cm B D = 36.37 cm

STUB F: 5.24cm STUB G: 11.89 cm

C E = 34.98 cm D E = 22.86 cm E F = 12.36cm F G = 8.24cm

Fig.10 - Geometry of the feed system of an end-fire Dolph-Chebyshev array with SLL=-20 db.

To show the applicability of the method for more than three elements, a five dipole Dolph-Chebyshev end-fire array with SLL=-20 db is presented. The dipoles in mutual distance 3 are designed for f,=600 MHz with radius r=0.004 m and length 0.2325 m. We use transmission line sections of 75 n and we match the system to a 50 load. The geometry of the antenna as well as the transmission line sections are shown in Fig.10. In the above case the maximum number of solutions is 400.

I I I . CONCLUSION

A method for feeding antenna arrays has been presented in this paper. The array is fed by a single source, through a network consisting of transmission line sections. Applications to three and five element array show the applicability of the method. It was also found the frequency bandwidth of the antennas. Using different solutions and different wire radius we can have better design in term of the bandwidth and the antenna specifications.

REFERENCES

[ I ]

[2]

AI Christman, “A Voltage-matching Method for Feeding Two-Tower Arrays”, IEEE Trans. on Broadcastinq, Vol. BC-33, No. 2, pp. 33-40, June 1987. Y.W. Kang and D.M. Pozar, “Pattern Synthesis Using Reactive Loads and Transmission Line Sections for a Singly Fed Array”, IEEE Trans. on Antennas and ProDaaation. Vol. AP-37, No. 7, pp. 835-843, July 1989. R.F. Harrington and J.R. Mautz, “Straight wires with arbitrary excitation and loadings”, IEEE Trans. on Antennas and ProDaaation. Vol. AP-15, pp. 502-515, July 1967.

[3]

32

[41 D.P.S. Seth and Y.L. Chow, “On linear parasitic arrays of dipoles with reactive loading”, IEEE Trans. on Antennas and ProDaaation, Vol. AP-21, pp. 286-292, May 1973. R.F. Harrington and J.R. Mautz, “Pattern synthesis for loaded N-port scatterers”, IEEE Trans. on Antennas and ProDaaation, Vol. AP-22, pp. 184-190, Mar. 1974. R.F. Harrington, “Reactively controlled directive arrays”, IEEE Trans. on Antennas and ProDaaation. Vol. AP-26, pp. 390-395, May 1978. D.H. Sinnott and R.F. Harrington, “Simple lossless feed networks for array antennas”, Electron. Lett., Vol. 8, No.26, pp. 634-635, Dec. 1972.

Costas Mertzianidis was born in Kavala, Greece, on February 2, 1945. He received the B.Sc. degree in Physics from the University of Thessaloniki, Greece, in 1968, the M.S. degree in Meteorology from the University of Athens, Greece, in 1973, the M.S. degree in Electronics and the Ph.D. in Physics from the University of Thessaloniki, in 1975 and 1976 respectively.

From 1972 to 1977 he was with the University of Thessaloniki. From 1977 to 1985 he worked as an engineer of telecommunications at the Hellenic Telecommun,ications Organization. Since 1985 he has been with the Technological Educational Institution (TEI) of Kavala as professor of Electronics. His research interests are in antenna and microwave engineering.

loanna Diamandi was born in Edessa, Greece, in October 1964. She received the B.Sc. degree in Physics and the Diploma of Post-Graduate Studies in electronics from the University of Thessaloniki, Greece, in 1986 and 1989, respectively. Since 1990 she has been working towards the Ph.D. degree in the same university. Her research interests are in appl ied e lect romagnet ics and microwaves.

John N. Sahalos (M175-SM’84) was born in Philippiada, Greece, in November 1943. He received the B.Sc. degree in Physics and the Diploma in civil engineering from the University of Thessaloniki, Greece, in 1967 and 1975, respectively and the Diploma of Post-Graduate Studies in electronics in 1975 and the Ph.D. in electromagnetics in 1974. From 1971 to 1974 he was a Teaching Assistant of Physics at the University of a Thessaloniki and was an Instructor

there from 1974 to 1976. During 1976 he worked at the ElectroScience Laboratory, The Ohio State University, Columbus, as a Postdoctoral University Fellow. From 1977- 1985 he was a Proffessor in the Electrical Engineering Departement, University of Thrace, Greece, and Director of the Microwaves Laboratory. During 1982, he was a Visiting Proffessor at the Departement of Electrical and Computer Engineering, University of Colorado, Boulder. Since 1985 he has been a Professor at the School of Science, University of Thessaloniki, Greece. During 1989 he was a Visiting Professor at the Universidad Politecnica de Madrid, Spain. His research interests are in the area of applied electromagnetics, antennas, high frequency methods and microwave engineering. He is the author of three books and more than 90 articles published in the scientific literature.

Dr.Sahalos is a professional Engineer and a consultant to indusrtry. He has been honored with the Investigation Fellowship of the Ministerio de Educacion y Ciencia (Spain). Since 1985 he has been a member of the Editorial Board of the IEEE Transactions on Microwave Theory and Techniques.