1118 IEEE TRANSACTIONS ON AhTTENNAS AND PROPAGATION, VOL. AP-33, NO. IO, OCTOBER 1985

j l

Theoretical and Experimental Study of Monopole Phased Array Antennas

Abstract-A theoretical and experimental investigation of the mutual coupling in large two-dimensional periodic planar phased arrays of thin cylindrical monopoles is addressed. A plane wave representation of the active input impedance is used to analyze an infinite array of monopoles. A finite array analysis is used to compute the center element gain pattern and input impedance as a function of the array size and element position. The center element gain pattern is shown to have omnidirectional vertical polarization with a null on-axis and peak gain in the vicinity of 50” from broadside. Measurements of the element gain pattern and mutual coupling for a 121-element passively terminated monopole square lattice array are shown to be in good agreement with the theory. The results of the infinite array analysis are compared to theoretical and experimental data in the literature for hexagonal lattice arrays.

I. INTRODUCTION

P ERIODIC PLANAR phased array antennas are generally designed to provide close to uniform element gain over a

portion of a hemisphere. The “ideal” element gain pattern for many applications has a cosine variation from broadside. Peak gain occurs at broadside and wide angle scanning out to 60” is possible with many array element designs [l].

The present study considers an element design for wide- angle scanning phased arrays in which a pattern null rather than a pattern maximum is formed at broadside. For certain phased array antenna applications, maximum gain is desirable away from broadside with minimum gain or a null occuring at broadside [2]. A two-dimensional periodic monopole array provides this type of pattern coverage. Phased arrays of monopoles with sinusoidal current distribution have been investigated in [3j and good wide-angle scanning properties were shown. An infinite array analysis and waveguide simulation were used to obtain the active-array scan impe- dance. The infinite array scan impedance for monopoles has also been computed in [4] using a pulse basis point matching moment method approach.

In this paper, both finite and infinite array analyses are used to investigate the behavior of periodic monopole phased arrays. An expression for the active impedance of an infinite array of monopoles, expressed as a plane wave summation, is given in Section 11. Section III contains a brief description of the finite array formulation which is an application of the method of moments. The finite array analysis is used in Section IV to show how the element gain pattern and input impedance are affected by the array size and by element

Manuscript received November 15, 1984: revised May 28, 1985. This

The author is with the Lincoln Laboratory. Massachusetts Institute of work was sponsored by the Department of the Air Force.

Technology, P.O. Box 73, Lexington, MA 02173.

position for “ideal” thin-wire monopoles. Section V considers two monopole array designs (square and hexagonal lattices) with comparisons of measured and calculated data.

11. ANALYSIS OF INFINITE ARRAYS OF MONOPOLES

The analysis used in this paper is an application of a general theory developed in [5] and [6j, in which the infinite array is formulated as a periodic surface with arbitrarily shaped identical linear elements. An array of vertical monopoles with a skewed lattice on a ground plane, shown in Fig. 1, can be analyzed as a periodic surface in free space, by use of image theory. Each monopole element has a vertical image in the ground plane. The ground plane can be removed and an equivalent free-space periodic dipole array results. The input impedance of the dipole array is twice that of the monopole array and the element gain of the dipole array is one-half that of the monopole array.

The details of the input impedance derivation are given in [7]. First, the field radiated by a periodic infinite array of Hertzian dipoles is determined utilizing the Poisson sum formula. Next, an assumed piecewise sinusoidal transmitting current distribution is imposed on the Hertzian element, and the total radiated field is found by single integration. An exterior element identical in shape to the reference element of the infinite array is exposed to the field of the infinite array, and the induced voltage is determined by a second integration. The active input impedance of a reference element of the array is found by displacing the exterior element one wire radius (denoted r,J from the reference element and computing the ratio of the induced voltage to the terminal current. The result for the active array input impedance is

cos /3l+COS2Plj (1)

where

P = 27r/x,

A the lattice skew parameter, 1 the monopole length,

d,, d,, the element spacings,

0018-926X/85/1000-1118$01.00 0 1985 IEEE

1 FEKN: MONOPOLE PHASED ARRAY AKTENNAS 1119

INFINITE GROUND PLANE

(-1. 01

Fig. 1. Two-dimensional monopole phased array arranged in a general skew-symmetric lattice.

2 0 the impedance of free space, X = rw cos 4, Y = r,*. sin 4, 4 is the observation angle about the axis of the

sx = sin 0, cos 4,, SY = sin 0, sin r$s,

monopole,

(Os, &) the scan angles,

The above equation is a rapidly converging series requiring terms up to Ikl I 20, In I I 20. For a wire diameter (d) greater than approximately 0.002 X it is necessary to compute an average value of the input impedance for a series of observation angles. Ten uniformly spaced observation angles are sufficient for wire diameters up to about 0.02 X.

III. ANALYSIS OF FINITE ARRAYS OF MONOPOLES

A method commonly selected for the analysis of thin-wire antennas is the method of moments [8]. A sinusoidal- Galerkin's version of the method of moments formulation was used to analyze periodic monopole arrays on an infinite ground plane. A similar analysis for parallel dipoles assuming sinusoidal basis functions and point matching is given in [9].

The currents In1, m = 1, 2, . , N induced in the monopole array elements are given in matrix form as

I = Z - ' V (2)

where Z is the open-circuit mutual impedance matrix and V is the voltage excitation matrix. Note: for rectangular grid arrays, block-Toeplitz symmetry [8] is used in reducing the cpu time and computer storage required to solve (2).

The input impedance of the mth array element is computed from

The array radiated field is given by the product of the single isolated element pattern and the array factor using the moment method currents.

The scattering matrix of mutual coupling coefficients is computed from the normalized impedance matrix by using the following relation [ 101:

S=[z- f ] [z+f] - ' (4)

where

In ( 3 , 2, is the feed-line characteristic impedance and f is the identity matrix. In the matrix S, the element represents the ratio of the signal received at the nth array element to the signal transmitted by the kth element. If the center element is chosen as a reference, then the active reflection coefficient is given by [ l l ] , [12], [13]

where (xn, y,) are the coordinates of the nth array element.

Iv. THE EFFECTS OF A R R A Y SIZE FOR IDEAL ONE-QUARTER WAVELENGTH MONOPOLES

To better understand the electrical behavior of a large phased array of monopoles, it is of interest to show some results for finite arrays of various sizes. The examples given are for one-quarter wavelength monopoles with one-half wavelength spacing on a square grid. The monopoles are assumed to be electrically thin, with a wire radius of 0.001 X. The finite array formulation is utilized to compute the element gain pattern and input impedance. Finite arrays up to size 25 rows by 25 columns are treated here. Additionally, the infinite array analysis is used for comparison and good agreement is shown. A listing and description of the Fortran computer program used to analyze finite and infinite arrays of mono- poles can be found in [7].

Consider first the radiation pattern (Eo component) of a single monopole antenna on an infinite ground plane. As shown in Fig. 2 (solid curve) there is a null on axis ( 0 = 0") and the elevation pattern peak occurs as expected at 0 = 90". Now, consider the radiation patterns of the center element of the five row by five column passively terminated monopole array shown in Fig. 3. The elevation pattern (4 = 0") for this array is shown in Fig. 2. The principal plane peak gain occurs at 0 = 38". Successive elevation radiation patterns for the center monopole of 9 x 9, 11 x 11, and 25 x 25 arrays are included in Fig. 2. The peak element gain occurs close to 0 =

50" as the array size grows. For the 11 x 11 array, the element gain pattern has only small differences when com- pared to the results obtained for the 25 X 25 array. The element gain pattern for the infinite array of monopoles is also shown in Fig. 2 . The peak gain is 2.7 dBi and occurs at 0 = 50". This compares quite closely to the element gain pattern peak computed for the 25 x 25 array which is 2.9 dBi. For the

1120 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. AP-33, NO. 10, OCTOBER 1985 @

Fig. 2. Theoretical

5 . 5 9'9

. _...- T -30 f __ . 1 1 ' 1 1

-35 ,L - -- 25 T 25 1; . . . . . . .. INFINITE I 1 -40 I I I I I I

-90 -60 -30 0 30 60 90

19 (deg)

center element gain pattern (@ = 0" cut) as a function of monopole array size. wire radius is 0.001 X, and element spacing is N2.

Monopole ]en,& is X/4,

INFINITE GROUND PLANE

\

J

Fig. 3. 5 x 5 monopole aray with center element excited and surrounding elements passively terminated.

11 X 11 array the azimuthal pattern variation at 0 = 55 O is approximately -+ 0.3 dB as shown in Fig. 4.

Also, the center element input impedance versus array size is summarized in Table I. The input impedance of the h/4 monopole with W 2 element spacing tends to be purely resistive as the number of surrounding loaded monopoles increases, and the resistance is insensitive to m a y size.

The behavior of elements near the edge of the monopole array is of general interest. Consider, for example, the 11 X 11 array shown in Fig. 5. The principal plane gain patterns for

.- 5 - - PEAK GAIN = 3.1 1 dBi - rn 2 - 1

CENTER ELEMENT 1 -10 I I I I I I

0 60 120 180 240 300 360

4 Fig. 4. Conical pattern cut for the center monopole of an 1 1 X 11 array. Monopole length is M4, wire radius is 0.001 A, and element spacing is h/2.

#

, FENN: MONOPOLE PHASED ARRAY ANTENNAS 1121

TABLE I THEORETICAL INPUT IMPEDANCE FOR THE CENTER ELEMENT OF

PASSIVELY TERMIh'ATED MONOPOLE ARRAYS

ARRAY SIZE NO. OF INPUT IMPEDANCE

NO. ROWS (ohms) ELEMENTS NO. COLUMNS

1

38.6 + j 2.1 81 9 9

38.7 + j 2.4 49 7 7

38.8 + j 3.2 25 5 5

38.0 + j 5.9 9 3 3

36.5 + j 21.0 1 1

11 11 121 38.5 + j 2.0

25

Monopole length is AM, wire radius is 0.001 X, and element spacing is x/2 on a square

38.4 + j 1.8 625 25

grid.

Y

t 5. . . . . . . . . . . I I I I I

4 . . . . . . . . . . . 3 . . . . . . . . . . . 2. I

I . . . . . . . . . .

l . . . . . . ' (121 . . - .

! l l . - l l - 2 . . . . . . . . . .

I I

121-ELEMENT MqNOPOLE ARRAY

I I

-5 -4 -3 -2 - 1 0 1 2 3 4 5

-3. . . . . . . . . . . I

-4. . . . . . . . . . . -5 . . . . . . . . . . .

? CENTER COLUMN

Fig. 5 . 11 x 11 array numbering convention.

the elements along the center row are shown in Fig. 6. Approximately 2.2 dB of asymmetry occurs between the two (left and right) peak values of the edge element pattern. The edge-adjacent element (-4, 0) has about 1.2 dB of pattern asymmetry. For monopoles two or more elements away from the edge element, the pattern peak asymmetry is less than 0.5 dB.

Next, the input impedance of a few elements of the 121 element array is given in Table 11; the center element, a comer element, and an edge element of the center row. The real part of the input impedance is seen to be relatively insensitive to element position in the array and the imaginary part varies by less than 10 W.

The active input impedance of the monopole array is now considered. For an infinite array of monopoles the active input impedance as a function of scan angle 8, is shown in Fig. 7.

- J a .20t

-25 t -301 -35

ELEMENT POSITION (-5.0) (edge) - - - - - - (-4.0) - - - - (-3.0) - - - - (-2.0) -- (-1,O) (0.0) (center) - i

-40 I I I f I I 1 -90 -60 -30 0 30 60 90

0 (deg)

Fig. 6. Theoretical element gain patterns as a function of element position along the center row of an 1 1 X 11 monopole array. Monopole length is A/ I 4, wire radius is 0.001 h, and element spacing is X/2.

The active input impedance for the 11 x 11 array compares quite closely to the infinite array data. The magnitude of the reflection coefficient for the 11 X 11 and infinite arrays is shown in Fig. 8 for the principal and diagonal planes scans. The reflection coefficient minimum is seen to occur in the vicinity of Os = 60".

One of the conclusions that can be made from the above data is that a large array of monopoles has good wide-angle scanning capability. Based on the theoretical element gain pattern, scanning with low gain loss is possible from approxi- mately 30" to 60" from broadside. In reference to the infinite array data and 25 x 25 array data, it is apparent that the center element in an 11 row by 1 1 column array behaves very similar to that in a much larger array.

,

1122 IEEE TRANSACTIONS ON ANTEhWAS AND PROPAGATION, VOL. AP-33, NO. 10, OCTOBER 1985 @ ,

TABLE II THEORETICAL INPUT IMPEDANCE AT VARIOUS ELEMENT POSITIONS IN

AN 1 1 X 1 1 MONOPOLE ARRAY

ELEMENT POSITION IN 11 X 11 ARRAY

CENTER ELEMENT (0.0)

EDGE ELEMENT OF CENTER ROW (-5.0)

CORNER ELEMENT ( -5 , -5)

ISOLATED ELEMENT (Reference)

INPUT IMPEDANCE (ohms)

38.5 + j 2.0

39.7 + j 7.0

39.7 + j 11.7

36.5 + j 21.0

Monopole length is W4. wire radius is 0.001 X, and element spacing is A12 on a square grid.

1.00

9 - I- 2 (II

075 I- z 0 U 2 05C 0 V

1 00 n

5 3 t-

(3 2 0 7 5

t- a Lu U

0 2 0 5 0

V

0 I- U 0 2 5 W

CENTER ELEMENT I \ bs = 0 \ \

- 1 1 s 11 ARRAY -- - INFINITE ARRAY

- 0 1

I I I I I V L I 0

I I I I I I I I I

- 1 1 X 11 ARRAY v0 \

a - - - INFINITE ARRAY

- 1 1 X 11 ARRAY v0

- - - INFINITE ARRAY

.\ '

i

4

I I I I I I I I I O 0 10 20 30 40 50 60 70 80 90

SCAN ANGLE Os ldegl

(b) (b) I Fig. 7. Theoretical active input impedance as a function of scan angle for Fig. 8. Theoretical center element reflection coefficient magnitude as a

infinite and finite arrays of monopoles. Monopole length is M4, wire radius function of scan angle for infinite and finite m a y s of monopoles. Monopole is 0.001 X, and element spacing is M2. (a) principal plane (b) diagonal length is M4, wire radius is 0.001 X, and element spacing is M 2 . (a) plane. Principal plane. (b) Diagonal plane.

I FENN: MONOPOLE PHASED ARRAY ANTEiiNAS

v. 121-ELEMENT SQUARE GRID MONOPOLE ARRAY: EXPERIMENT AND THEORY

Based on the thin-wire monopole array data given in the previous section, a 121-element square grid array is consid- ered well representative for demonstrating the element per- formance in a large array. To verify the theory, it was decided to build an array at L-band operating over the frequency range 1.2 to 1.4 GHz. Assuming an interelement spacing of 4.2 inl this yields a 42 in by 42 in array. At a center frequency of 1.3 GHz the element spacing is 0.462 X. The diameter of the monopole elements was chosen to be 0.125 inches which is 0.0148 X at the high frequency 1.4 GHz; hence, the thin wire formulation is applicable.

The monopole element length can be optimized theoretically by computing the center element active array reflection coefficient over the desired scan sector and frequency band- width. After running a number of cases, a length of 2.5 in (0.275b) was deemed appropriate.

Each monopole element was constructed by soldering a 1/8 in diameter brass rod to the center pin of a type-N panel connector. A photograph of one of the array elements is shown in Fig. 9. A 4 ft by 4 ft square sheet of aluminum was used for the array ground plane. The element mounting holes were machined such that the base region of each monopole is flush with the ground plane. A sketch of the overall array configuration is given in Fig. 10 and a photograph of the assembled 12 1 -element array is shown in Fig. 1 1. For far-field pattern measurements, the center element is driven and the surrounding elements are terminated in 5 0 4 resistive loads.

The measured center element gain elevation patterns (4 = 0") from 1.2 GHz to 1.4 GHz are given in Fig. 12. Included are the corresponding finite array theoretical gain patterns which compare quite closely to the measured data. The differences between the calculated and measured peak gains can be attributed to the assumption of an infinite ground plane in the theoretical model and small experimental measurement crrors. Fig. 13 shows measured conical pattern cuts from 1.2 to 1.4 GHz for 0 = 5 5 " . The E 8 (principal) polarized pattern is seen to be nearly omnidirectional. The cross-polarized component (E d) is down by more than 30 dB. These patterns confirm that wide-angle scanning is practical with a monopole element.

Next, to measure the complex mutual coupling in a passive array, the center element is connected to the transmitter and the received voltage is measured at each of the surrounding elements. Except for the transmitting element and the receiv- ing element, all elements are terminated in 50-ohm resistive loads. Fig. 14(a) shows a plot of the amplitude of the coupling coefficients along the center row at 1.3 GHz. Fig. 14(b) is the corresponding phase received at each element. The measured amplitude is in good agreement with the theory. However, there is a noticeable shift in phase between the measured and theoretical data. This is likely due in part to two approxima- tions in the analysis. One is that a delta gap model is used for the feed region rather than the actual coaxial aperture. Second, the analysis assumes a one mode sinusoidal current distribu- tion on the monopole which is not exact. It is useful to note that the received amplitude is down by 40 dB at the edge

1123

Fig. 9. Cylindrical monopole element.

Fig. 10. 121-element monopole array layout.

Fig. 11. 121-element monopole array on antenna positioner in anechoic chamber.

elements. Thus, little change in the results would be expected by increasing the array size.

Using the measured coupling coefficients in (6), the active input impedance as a function of scan angle can be computed. This is done for the principal plane scan (4,=0") in Fig. 15 for 1.2, 1.3, 1.4 GHz. The three curves are measured data, finite array theory, and infinite array theory. Other than a slight phase displacement, there is good agreement between theory and experiment.

The data in Fig. 15 may be useful in further optimization of the input impedance by applying standard impedance matching techniques [ 141. The optimization would be with respect to a selected bandwidth and scan sector.

VI. HEXAGOKAL LATTICE INFIKITE ARRAY RESULTS

The results of the present analysis are compared now to calculated and measured data in the literature for hexagonal lattice infinite arrays. Herper and Hessel [3] performed a similar infinite array analysis (combination unit cell and variational impedance technique) which also assumed a

1124 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. AP-33, NO. 10, OCTOBER 1985 * 5 - MEASURED PEAK GAIN = 2 30 dBi - MEASURED PEAK GAIN = 2.70 d8i - -

" ELEMENT

0 - 2 0 -

-25 -

a

-30 - - - ,, THEORY -

MEASURE0 -35

I I I I - 40

- " THEORY -

MEASURED - - THEORY - MEASURED -

-90 -60 -30 0 30 60 90 -90 -60 -30 0 30 60 90 -90 -60 -30 0 30 60 90

ANGLE FROM BROADSIDE 8 (degl ANGLE FROM BROADSIDE e (deg) ANGLE FROM BROADSIDE 0 (deg)

(a) (b) (C)

Fig. 12. Measured and theoretical center element gain pattern for the 12lelement monopole array. Elevation cut at 6 = 0". Monopole length is 2.5 in. wire radius is 0.0625 in. and element spacing is 4.2 in. (a) 1.2 GHz. (b) 1.3 GHz. (c) 1.4 GHz.

r

E, (Principal Polarization)

CENTER ELEMENT

w 5 -10-

' E, (Principal Polarization) -

2 - 2 0 - z t CENTER ELEMENT

1.3 GHz E, (Cross Polarization) CONICAL CUT

W

I- 2 -30

- e = 55'

CENTER ELEMENT

1.4 GHz -20 p6 (Cross Polarization) CONICAL CUT -30 / e = 55O

-40 -180 -108 -36 36 108 180

[ C') 6, ANGLE ABOUT BROADSIDE (deg)

Fig. 13. Measured center element radiation pattern for the 12lelement monopole array. Conical cut at 0 = 5 5 " . Monopole length is 2.5 in, wire

GHz. (c) 1.4 GHz. radius is 0.0625 in, and element spacing is 4.2 in. (a) 1.2 GHz. (b) 1.3

sinusoidal current distribution. They used the waveguide simulation technique to verify the theoretical active array input impedance for a few scan angles. The array parameters used were monopole length = 0.25 A, monopole diameter = 0.02 X, and element spacing = 0.55 X at the center frequency. Their results are reproduced in Fig. 16 along with a comparision of the present theory. The 45 O scan angle data are all in good agreement. For the 65 O scan angle the agreement is not as good, but this is likely attributed to the single sinusoid current distribution assumption and the delta-gap model previously mentioned. Even with the simple model, however, the correct scan angle dependence and frequency behavior are

Q O z S E

S-l,O s1.0

(4 ~,SZ.O O W I' so.0 '1

i! -10- / --?-+\ A.

I

O I - LL 2 -20-

u o 3& t o --s

\

0 LL -30-

5 0 -40':

,d' 1.3 GHz 'h:3.0 - , . \

A THEORY s4.0'p'~L

2 - 5 0 , 1 1 1 1 1 1 ~ ~ MEASURED s5.0

-5 -4 -3 -2 -1 0 1 2 3 4 5

ELEMENT POSITION RELATIVE TO CENTER (a) -

m

'0 360 c 2

300 u U U w 240 0 0 0 180 z -I n 3 120 0 0 U. 60 0

v ) o X

W

a n

- 5 - 4 -3 -2 -1 0 1 2 3 4 5

ELEMENT POSITION RELATIVE TO CENTER

@) 5 Fig. 14. Coupling coefficient as a function of position for the 121element

monopole array. Center element is transmitting and elements along the center row (row # 0 in Fig. 7) are receiving. Monopole length is 2.5 in, wire radius is 0.0625 in, and element spacing is 4.2 in. (a) Magnitude. (b) Phase.

predicted. Agreement is expected to improve with the use of multiple overlapping sinusoidal expansion fimctions and the magnetic frill voltage generator model [SI.

An example of an infinite monopole phased array has also been given in [4] by Schuman, Pflug, and Thompson. They chose as parameters; I = 0.3 X, d = 0.02 X, spacing = 0.577 X (hexagonal lattice), and computed the active array scan impedance in a single plane. They modeled the monopole current with four pulse basis functions and used a plane wave expansion to obtain the scan impedance. Their results are

i

4

4

1 FENN: MONOPOLE PHASED ARRAY ANTENNAS 1125

(C)

Fig. 15. Measured and theoretical center element active input impedance of monopole arrays. Monopole length is 2.5 in, wire radius is 0.0625 in, and element spacing is 4.2 in. (a) 1.2 GHz. (b) 1.3 GHz. (c) 1.4 GHz.

1.0 \

1 .o Fig. 16. Theoretical and measured active array impedance as a function of

scan angle for infinite arrays of monopoles with hexagonal lattice.

I I I I I b 75 - - SCHUMAN. PFLUG, THOMPSON [4] -

v) 0 THIS THEORY

E 2 . . 8 50 z

-

W

5l 2 P IMAGINARY

w 25 - > I- o 4

-

- - 0 10 20 30 40 50 6 0

SCAN ANGLE (deg)

Fig. 17. Theoretical active array impedance as a function of scan angle for infinite arrays of monopoles with hexagonal lattice. Monopole len,@ = 0.3 A, wire radius = 0.01 X, and element spacing is 0.577 X.

presented in Fig. 17 along with those obtained by the present theory and good agreement is indicated.

VII. CONCLUSION

This paper has described the theory and experimental results for two-dimensional periodic monopole phased array anten- nas. An infinite array plane-wave representation of the active impedance was given for monopoles; with sinusoidal current, arranged on a general skewed grid. A sinusoidal-Galerkin's version of the method of moments was used to analyze finite arrays. Element gain patterns and active input impedance were computed both for finite and infinite arrays of thin cylindrical monopoles. The effects of the array size and element position on the element gain pattern and input impedance were shown.

Good agreement for element gain patterns, mutual coup- ling, and input impedance was obtained between theory and measurements for a 121-element monopole array. The center element gain pattern indicates good pattern coverage at wide angles from broadside. The radiation pattern is vertically polarized and nearly omnidirectional at a fixed angle from broadside. Wide angle scanning out to 60" with peak gain occuring near 50" from broadside is possible with this antenna configuration. Natural sidelobe suppression would occur in the vicinity of broadside because of the monopole element pattern null. Good agreement between the present infinite array analysis and calculated and measured data for hexagonal lattices was shown.

Finally, there is the issue of blind spot occurrence in thin- monopole phased arrays. As is well-known, blind spots are often due to the presence of higher-order modes within the array unit cell [ 11. The above analysis has assumed that the transmitting current distribution is a single piecewise-sinusoi- dal function. The assumption of a symmetric current distribu- tion on the equivalent dipole is valid because the monopole image current is always symmetric with the current on the monopole. The current vector direction is essentially parallel to the orientation of the thin monopole and the azimuthal (phi) component of current is negligible. Thus, higher-order modes are not provided for in the model. However, since the

1126 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. AP-33, NO. 10, OCTOBER 1985

monopole length is close to M4, the fundamental resonance, it is very unlikely that higher order modes would exist to any appreciable degree. Based on these considerations and the presented theoretical and experimental results, blind spots are not expected to occur for phased arrays of thin monopoles.

ACKNOWLEDGMENT

The author wishes to express his gratitude to Mr. W. Rotman, Dr. A.J. Simmons, Dr. A.R. Dion, and Dr. G.N. Tsandoulas for technical discussions. The construction and RF measurements of the 121-element monopole array were organized by Mr. R.J. Burns. Computer programming was performed by Ms. D.L. Washington and Mr. D.S. Besse. Technical discussions with Professor B.A. Munk of The Ohio State University ElectroScience Laboratory are sincerely appreciated.

REFERENCES

R. J. Mailloux. “Phased array theory and technology,” Proc. IEEE, vol. 70. pp. 246-291, Mar. 1982. E. J. Kelly and G. N. Tsandoulas, “A displaced phase center antenna concept for space based radar applications,” in IEEE Eascon, Sept. 1983, pp. 141-148. J. C. Herper and A. Hessel, “Performance of X14 monopole in a phased array.” IEEE Antennas and Propagat. SOC., 1975 Symp. Digest. pp. 301-3M. H. K. Schuman, D. R. Mug, and L. D. Thompson, “Infinite planar arrays of arbitrarily bent thin wire radiators,” IEEE Trans. Anrenna Propagat., vol. AP-32, no. 3, pp. 364-377, Apr. 1984.

[5] B. A. Munk and G. A. Burrell. “Plane-wave expansion for arrays of arbitrarily oriented piecewise linear elements and its application to determining the impedance of a single linear antenna in a lossy half- space.” IEEE Trans. Antennas Propagat., vol. AP-27, no. 3, pp. 331-343, May 1979.

[6] T. W. Korbau. “Application of the plane-wave expansion method to periodic arrays having a skewed grid geometry,“ Ohio State Univ. ElectroSci. Lab. Tech. Rep. AFAL-TR-77-112 (Oct. 1977). 4

[7] A. J. Fenn, “Monopole phased array antenna evaluation for a low altitude space based radar,” MIT Lincoln Lab. Project Rep. SRT-2, Aug. 1983.

[8] W. L. Stutzman. and G. A. Thiele, Antenna Theory and Design. New York: Wiley. 1981.

[9] 0. C. Williams and C. E. Hickman. “Computer determination of current distribution on arbitrarily located parallel center-fed dipoles with terminals in a common ground plane.” IEEE Tram. Antennas Propagat., pp. 540-541. July 1972.

[lo] C. G . Montgomery, R. H. Dicke and E. M. Purcell, Principles of ”icowave Circuits, Massachusetts Inst. Technol., Radiation Lab. Series, 8. New York: McGraw-Hill, 1948. pp. 147-149.

[ 111 R. C. Hansen, Ed.. Microwave Scanning Antennas, Vol. II: Array Theory and Practice. New York: Academic, 1966, pp. 213-216.

[12] N. R. Brennecke and W. N. Moule, ”Uses of fences to optimize operating impedance of phased arrays. using an improved measuring technique,” IEEE Antennas Propagat. Soc. Int. Symp. Dig., 1964,

[13] N. Amitay, V. Galindo, and C. P. Wu, Theory and Analysis of # [14] R. L. Thomas. A Practical Introduction to Impedance Matching.

pp. 134-142.

Phased Array Antennas. New York: Wiley. 1972, p. 22.

Dedham. MA: Artech House, 1976.

Alan J. Fenn (S’74-M’78), for a photograph and biography please see page 564 of the Joly 1982 issue of this TRANSACTIONS.

Q