Study of Backfire Antennas

The study presented in this article is dedicated to the backfire disk-on-rod antennas fed by a dipole or crossed dipole. For short, these are herein called backfire antennas. Backfire antenna constructions with different configurations of the big reflector are considered. The influence of the feed location in the backfire antenna construction upon the antenna characteristics is also examined. The studies were carried out with a corrugated-rod (disks attached to a metal rod) surface-wave structure. The results obtained may be applied to other types of surface-wave structures, such as dipole array, dielectric rod or dielectric-covered metal rod. The lengths of the investigated antennas ranged between 2λ and 4λ. The design carried out in these investigations may be used for creation of high efficiency backfire antennas.

the backfire antenna in comparison with the end-fire antenna should be 4 times (or 6 dB): 3 dB due to the length of the antenna L e = 2L (the directivity of the relatively short surface-wave antenna is proportional to its length) and 3 dB due to the presence of the big reflector which assures a radiation from the antenna in only one hemisphere.It is found in practice that a bigger directivity increase (6 times or approximately 8 dB) may be obtained by the backfire antenna using a phase corrected big reflector and accurate tuning of the surface-wave structure.This result may be explained only by means of more rigorous model of the backfire antenna radiation mechanism.Consistent with this model the surface wave is reflected multiple times between the reflectors R 1 and R 2 of the semitransparent open cavity R 1 R 2 before be radiated from the virtual antenna aperture VV'.The diffraction effects on the both reflectors and the direct radiation from the feed dipole should be also taken into account [7]- [10].Our experiments with backfire antennas have shown that L e equal to 6L gives the best result in regard to the optimum value of the phase velocity of the surface wave.This model corresponds to six forward and backward travels of the surface wave along the surface-wave structure or to a triple wave reflection from the big reflector.
Because of its uncontestable advantages (simple and compact construction, reduced length and good radiation performance) the backfire antennas have been widely used in various wireless systems, mostly military, earth and spacecraft.Now they may be used for long-range point-to-point applications, say WLAN, WISP and satellite links and in those cases where a gain between 15 dB and 25 dB and a bandwidth less than 10 % are required.

II. OPTIMUM PHASE VELOCITY AND DIMENSIONS OF THE BACKFIRE ANTENNA
In order to obtain maximum directivity and efficiency from the backfire antenna the phase velocity of the surface wave and the dimensions of the antenna should have optimum values.

A. Phase velocity
According to the Hansen-Woodyard condition [11], [12] the optimum value of the phase velocity delay factor of an uniformly illuminated end-fire antenna is where c is the free-space wave velocity, v is the phase velocity of the surface wave, and λ 0 corresponds to f 0 -the design (central or resonant) frequency.
The directivity of the end-fire antenna above an isotropic radiator in these conditions is If the design is based on the optimum phase velocity and taper dimensions of the surface-wave structure (non-uniformly illumination) the expressions ( 1) and ( 2) become where the coefficient q starts near 6 for L = λ 0 and diminishes to approximately 3 for L between 3λ 0 and 8λ 0 and to 2 at 20λ 0 .The formulas (3) and ( 4) proposed by Ehrenspeck and Poehler [12], [13] are based on the experimental investigations on Yagi-Uda antennas.
According to the Hansen-Woodyard condition and based on the simplified model of the backfire antenna radiation mechanism [4], [6], [14] the optimum value of the phase velocity delay factor and the directivity are given by The change of the phase velocity delay factor c/v as a function of the backfire antenna length in wavelengths L/λ 0 is shown in Fig. 2(a) with a dotted line.Better results can be obtained using Ehrenspeck and Poehler experimental results [4]: The variation of the phase velocity delay factor c/v consistent with the expression (7) is presented in above figure with a dashed line.Finally, consistent with the model of the backfire antenna radiation mechanism proposed herein (L e = 3L) the optimum value of c/v (Fig. 2(a),solid line) and the directivity can be defined as follows D = 60L/λ 0 , 1.5λ 0 < L < 4λ 0 (10)  In order to verify the validity of the proposed model of radiation mechanism the both curves of the phase velocity delay factor, the solid line according to the proposed model and the dashed line consistent with the experimental results obtained by Strom [5] are presented in Fig. 2(b).In the same figure our experimental results for two types of backfire antennas: an antenna with a feed near the big reflector (dashed line coinciding with the Strom's results) and an antenna with a feed near the small reflector (dotted line) are also shown.A good agreement between the proposed model and the measurement is found.

B. Feed location
The feed located between the two reflectors acts directly on the backfire antenna characteristics.
There are only two feed locations which assure normal work of the antenna.In the first manner of feed the feed dipole F is located near the small reflector R 1 .The backfire antenna with this feed location is preferable in the practice because of its good radiation characteristics.In the second manner of feed the feed dipole F is located near the big reflector R 2 .The use of the backfire antenna with this feed location is limited because of its lower gain (with 3-4 dB) compared to the antenna with the first feed location.In the both cases the distance between the feed point and respective reflector is λ 0 /4.Other points of feed location along the length of the backfire antenna are not suitable and are not recommended [10].

C. Big reflector
The diameter of the big reflector R 2 is related to the quantity of the reflected energy and to the phases of the reflected waves.In fact, the big reflector reflects two types of waves: a surface wave SW 1 with phase velocity v and a spherical wave with velocity c.In the plane of the big reflector, in the limits of so-called critical angle 2ψ cr (or 2ψ < 2ψ cr ), the wave has a quasi-plane phase front and effective radiation aperture of diameter D e1 (Fig. 1): where Having in mind ( 5) and ( 12) the diameter D e1 is defined as a function of L/λ 0 as follows The value 2ψ cr divides the big reflector R 2 into two regions.In the first region with 2ψ < 2ψ cr the surface wave is predominant, while in the second one with 2ψ > 2ψ cr the spherical wave plays essential role in the wave distribution.Thus, the minimum diameter D 2 of the backfire antenna big reflector R 2 should be equal to the constant-phase effective aperture, or D 2 = D e1 .If the diameter D 2 increases (the second region with 2ψ > 2ψ cr ) the phase front becomes spherical and a quadratic phase distortion on the big reflector plane occurs.In the case where a tolerable phase distortion of π/2 rad at the disk edge is assumed, the dimension of its diameter is given by [4] diameter D 2R is shown in Fig. 3(b).The rim decreases the levels of the backlobe and sidelobes and leads to an improvement of the antenna gain and directivity.The diameter D 2R is calculated by the expression ( 14) and the rim width w 1 is equal to a quarter-wave length w 1 = 0.25λ 0 (15) Further increase of the antenna directivity and efficiency can be obtained using a phase correction in big reflector R 2 .Thus, the reflected wave will involve and the energy of the peripheral spherical waves with a minimum phase shift [4], [10].In this manner the ideal big reflector should consist of which are in good agreement with the results of the experimental studies.

D. Length of the antenna
The backfire antenna can be considered as a parallel-plane resonator antenna with a standing surface-wave field excited inside.In the virtual antenna aperture VV' (Fig. 1) two basic phenomena take place: multiple partial reflections from the small reflector R 1 and multiple intensive radiations from the open aperture area.The length of such radiating cavity must satisfy equation where λ S0 = v/f 0 is the surface wave wavelength, ∆L is the length correction due to the radiation, and n is a real integer called standing-wave number.The experimental results show that where n have the same integral values as in (19).
On the other hand, the antenna length depends directly on the required directivity (gain).It can be approximately calculated by the expression where the values of the coefficient A are given in a Table I.
The accurate length of the backfire antenna can be defined by the mutual solution of equations ( 20) and (21).The most often used in practice are the backfire antennas with lengths between 2λ 0 and 6λ 0 .If a higher directivity is required an use of backfire antenna arrays is recommended.

E. Small reflector
The dimension of the small reflector R 1 acts essentially on the amplitude and phase field distribution in the antenna aperture.In addition it is related to the feed efficiency in the case where the feed is set near the small reflector.The very small values of this reflector transform the backfire antenna into an ordinary end-fire antenna and decrease the directivity.On the other hand the high values of the small reflector diameter close to the big reflector diameter also decrease the antenna directivity because of a reduction of the aperture area (the antenna transforms in a high quality-factor resonator).
The optimum value of the small reflector diameter increases with an increase of the antenna length and can be found by [10] The experimental studies show that for a backfire antenna with a length between 2λ 0 and 6λ 0 the optimum value of the small reflector diameter ranges between 0.35λ and 1.1λ 0 .

III. DESIGN PROCEDURE FOR BACKFIRE ANTENNAS
There are only a few references dedicated to the backfire antennas design [4], [10].It is not considered even in some recently published books on an antenna design [12], [15]- [17].A design procedure for backfire antennas with circular reflectors and a corrugated-rod surface-wave structure, fed by a dipole, is described here.It is based on studies in [10], and some new results obtained by the authors.The results presented here may be applied to other types of surface-wave structures, such as dipole array, dielectric rod, or dielectric-covered metal rod.The lengths of the antennas studied ranged between 2λ 0 and 4λ 0 , which are the most-used lengths, in practice.However, the range of the proposed design may be extended by a simple extrapolation in the range of the antenna lengths from 2λ 0 to 6λ 0 .
Three constructions of backfire antennas are considered in this design: -a backfire antenna fed by a dipole located near the big reflector R 2R , an antenna A1 (Fig. 4); -a backfire antenna fed by a dipole set near the small reflector with a big reflector R 2R , an antenna A2 (Fig. 5);  -a backfire antenna fed by a dipole located near the small reflector with a big reflector R 2C , an antenna A3 (Fig. 6).The antenna A1 has the most simple construction but its gain is the lowest while the antenna A3 provides the highest gain with relatively more complex construction.The new antenna elements and dimensions in Fig. 4 -Fig.6 are denoted as follows: P is a metal rod (a rigid feed coaxial line), Q -a half-wavelength slot balun used to feed the symmetrical dipole by the coaxial line, D 1 -a small reflector diameter, D P -a metal rod diameter, D S -a disks diameter, d S and d R -distances between the dipole and the surface-wave structure, and the nearer reflector, respectively, T -a period of the surface-wave structure, and ∆ -a disks thickness. IV. V. VI.
The directivity, D, the central frequency of the antenna's bandwidth, f 0 , and the type of the surfacewave structure, S, are assumed known in this design.The design goal is to determine the basic dimensions of the backfire antenna.The design procedure involves the following steps:

A. Length of the backfire antenna
The approximate length of the antenna is defined by the required directivity  I for the values of the coefficient A.
The final length of the antenna is defined according to the requirements of ( 20) and (21).

B. Optimum phase velocity of the backfire antenna
The optimum value of the phase velocity delay factor c/v is calculated by the expression (9).For backfire antennas with lengths between 2λ 0 and 4λ 0 more accurate values obtained experimentally by the authors are given in Table II.

C. Dimensions of the big reflector
The diameter D 2R for the backfire antennas A1 and A2 is defined by formula ( 14) and the rim width w 1 is given by (15).
The diameter of the plane part of the big reflector D 20 for the backfire antenna A3 is calculated by (16) and the big reflector diameter D 2C is given by (17).The rim width w 1 and the step width w 2 are defined by (18).

D. Diameter of the small reflector
The optimum values of the small reflector diameter (obtained experimentally by the authors) are given in Table III.Antenna 1 (Fig. 4) 0.295D 2R Antenna 2 (Fig. 5) 0.170D 2R Antenna 3 (Fig. 6

F. Surface-wave structure
Based on the optimum value of the ratio c/v found above the surface-wave structure dimensions D S , D P , T and ∆ may be defined using the well known design procedure described in [18] or [16].In the case where a dielectric rod is used as a surface-wave structure the design procedure should be accomplished consistent with the methods described for example in [16] or [12], [17].

G. Feed dipole
The design of the half-wavelength dipole (or crossed dipole) is classic and may be found in many references [12], [15]- [17].

IV. PRACTICAL EXAMPLES
In order to verify the validity of the proposed design procedure, three backfire antennas were designed, fabricated and tested.A photograph of a backfire antenna with a corrugated-rod surface-wave structure fed by a dipole set near the small reflector with a big reflector R 2C and length L = 4λ 0 , λ 0 = 13.6 cm, is shown in Fig. 7.This antenna construction (an antenna A3) was chosen as a basic antenna configuration because of its high performance characteristics.The radiation patterns in E-(solid line) and H-plane (dashed line) of the fabricated antennas with lengths L = 2λ 0 , 3λ 0 , and 4λ 0 were measured and shown in Fig. 8 -Fig.10, respectively.The directivities of the antennas were defined by an integration of their radiation patterns and the results obtained are illustrated in Fig. 11 for lengths L = 2λ 0 , f 0 = 2.2 GHz (dotted line), L = 3λ 0 , f 0 = 2.25 GHz (dashed line), and L = 4λ 0 , f 0 = 2.2 GHz (solid line).Fig. 12 illustrates the input match bandwidth of the backfire antenna A3 with length L = 4λ 0 , λ 0 = 13.6 cm.The bandwidth for a 2:1 VSWR is 12 % and for a 1.5:1 VSWR is 8.6 %, respectively.The influence of the antenna length on the bandwidth is insignificant.The dimensions of the backfire antennas designed according to the above described design procedure are summarized in Table IV.In the last row of the table the measured and theoretical directivity, calculated by means of (10), D m , are shown for comparison.Good agreement between the designed, measured and theoretical values was found.The results obtained showed that the proposed design procedure can be used for creation of high efficiency microwave communication antennas.
two parts: a first plane part and a second parabolic one.In practice because of technological reasons the simplified stepped and conically corrected big reflectors are mostly used.Fig.3(c) shows a rimmed stepped-corrected disk reflector R 2S of diameter D 2S with a inner diameter D 20 and step width w 2 .A rimmed conically-corrected disk reflector R 2C of diameter D 2C is shown in Fig.3(d).The corresponding dimensions of the reflectors R 2S and R 2C are given by the expressions[4],[10]

Fig. 4 .
Fig. 4. A backfire antenna fed by a dipole located near the big reflector R 2R (Antenna A1).

Fig. 5 .
Fig. 5.A backfire antenna fed by a dipole set near the small reflector with a big reflector R 2R (Antenna A2).

Fig. 6 .
Fig. 6.A backfire antenna fed by a dipole located near the small reflector with a big reflectorR 2C (Antenna A3).
) 0.150D 2C E. Distances from the dipole to the surface-wave structure, and the respective reflector The both the distance d S and the distance d R are defined by d S = d R = 0.25λ 0 (24)

TABLE I .
THE VALUES OF THE COEFFICIENTA FOR A BACKFIRE ANTENNA, L = 2 Λ 0 TO 4 Λ 0

TABLE III .
THE DIAMETER OF THE SMALL REFLECTOR OF A BACKFIRE ANTENNA, FOR L = 2 Λ0 TO 4 Λ0