Investigation of Binomial & Chebyshev Distribution on Dielectric Resonator Antenna Array

Nipun K Mishra Soma Das Asst. Professor Asst. Professor

mishranipun@gmail.com soma.iitkharagpur@gmail.co.in Department of Electronics & Communication,IT, Guru Ghasidas Vishwavidyalay,Bilaspur

Abstract: For wireless communication systems, the antenna is one of the most critical components for transmission as well as reception point of view. Good design of the antenna can relax system requirements and improve overall system performance. In addition to receiving or transmitting energy, an antenna in an advanced wireless system is usually required to optimize or accentuate the radiation energy in some directions and suppress it in others. Thus the antenna must also serve as a directional device in addition to a probing device. Many applications require radiation characteristics that may not be achievable by a single element. It may, however, be possible that an aggregate of radiating elements in an electrical and geometrical arrangement (an array) will result in the desired radiation characteristics [1]. The arrangement of the array may be such that the radiation from the elements adds up to give a radiation maximum in a particular direction or directions, minimum in others, or otherwise as desired. In this paper we concentrated on the electrical and geometrical properties of array elements that give a radiation maximum in a particular direction and minimum in others. We investigate the binomial and chebyshev distribution for linear and rectangular dielectric resonator antenna array. Key words: Antenna, Array, Directivity, lobes, efficiency. I - INTRODUCTION Antenna array is defined as “A radiating system consisting of several spaced and properly spaced phased radiator to get greater directivity in a desired direction” [2]. By controlling the Progressive phase between the elements of the array, maximum radiation of the array can be oriented in any direction to form a phased or scanning array. The system should be capable of continuously varying the progressive phase between the elements. This is accomplished, in practice, electronically by use of ferrite phase shifters. The phase shift is controlled by the magnetic field within the ferrite, which in turn is controlled by amount of current flowing through the wires wrapped around the phase shifters. Various types of antenna array like uniform linear array (ULA) [3, 4], uniform rectangular array (URA) [5]

and uniform circular array (UCA) [6] have been proposed for collecting more information. Later on, the research was more focused on the various issues of antenna array such as mutual coupling effect [7] and multiplexing of antenna elements or spatial multiplexing of local elements (SMILE) [8]. Bidirectional patterns of antennas, in addition to main lobes, are also having secondary or minor lobes. These minor lobes are usually undesirable, because not only considerable amount of power is wasted in the directions of minor lobes but even unnecessary interference is also caused in those areas. Although directional antenna provides a higher gain in the desired direction but at the same time it all becomes necessary to minimize the radiation towards undesired direction or reception from that direction. The minor lobes just adjacent to the main lobe are called side lobes. It is found that with uniform linear array, as the array length is increased to increase the directivity, the minor lobes also appear. At certain application like RADAR, Mobile Communication, Smart Antenna etc, these minor lobes are undesirable and creates the problem of false target indication or undesired reception. The technique used in reduction of side lobe level is called tapering which means amplitude in the sources of linear array is non uniform. Experimentally it is found that minor lobes are reduced if the centre source radiates more strongly than the end source.

II- CLASSIFICATION OF ARRAY

Binomial array: Array of non uniform amplitudes is also possible and a binomial array is one of them. In this, the amplitudes of the radiating sources are arranged according to the coefficients of successive terms of the following binomial series and hence the name. In uniform array secondary lobes appear but main lobe is sharp and narrow. In binomial array width of main lobe beam widens with lesser number of secondary lobes. Binomial array suffers the problem of extreme tapering i.e. ratio of amplitude between centre and end element is very high. Generation of such high amplitude compared to lower one, for larger array is practically tough situation.

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Where the positive coefficient of the series expansion for different values of m are given by Pascal triangle

Dolph-Tschebysheff Array: Dolph-Tchebyscheff array produces narrowest beam width for given side lobe level and vice versa. Since for a specified side lobe level ,narrowest beam width is achieved by this distribution and hence it is considered to be optimum. The method was originally introduced by Dolph and investigated afterward by others. It is primarily a compromise between uniform and binomial arrays. Its excitation coefficients are related to Tchebyscheff polynomials. The array factor of an array of even or odd number of elements with symmetric amplitude excitation is nothing more than a summation of M or M + 1 cosine terms [1]. The following properties of the polynomials are of interest: 1. All polynomials, of any order, pass through the point (1, 1). 2. Within the range �1 � z � 1, the polynomials have values within �1 to +1. 3. All roots occur within �1 � z � 1, and all maxima and minima have values of +1 and �1, respectively. Since the array factor of an even or odd number of elements is a summation of cosine terms whose form is the same as the Tschebyscheff polynomials, the unknown coefficients of the array factor can be determined by equating the series representing the

cosine terms of the array factor to the appropriate Tschebyscheff polynomial. The order of the polynomial should be one less than the total number of elements of the array. Dolph –Tchebyscheff distribution is that it provides a minimum rather optimum beam width for a specified degree side lobe reduction. It results in side lobes are all of the same amplitude unlike distribution in which side lobes near adjacent to the main lobe is largest and others progressively decreases as angle increases from main lobe.Tapering is not extreme i.e. ratio of amplitude between centre element and end element is small which provides ease in feeding design.

Micro- strip patch antenna (MPA) and dielectric resonator antenna (DRA) both share the advantages of low profile, lightweight, ease of fabrication and are easy to excite by different methods [1]. Both antennas are viable candidates for numerous applications, either as individual elements or in an array environment [1]. However, the radiation efficiency of the DRA is better than MPA due to the conduction losses in MPA. The bandwidths and antenna gain of DRA is also higher than MPA. Keeping this in mind, it was planned to implement DRA as an Antenna element in linear array and Rectangular array.

III- SIMULATION RESULTS

In this work first we implemented uniform linear and rectangular array and we find that some side lobe are comparable to main lobe. As we discussed earlier in some application like smart antenna and mobile communication besides narrow main lobe beam, side lobe reduction is also very important. Initially we optimize the single DRA antennas which give the main lobe magnitude of just .1dbi and side lobe level of-10.2dbi.

Figure:1 Radiation pattern for 7*1 binomial array

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More number of elements in array increases the directivity of system and array of 7 elements which provides the main lobe magnitude of 13.44dbi and side lobe of -14Dbi is showing better performance compared to single antenna .

Figure:2 Return loss for 7*1 binomial array

S11 parameter curve for 7*1 binomial array, showing least return loss at 3.85GHz of 16db down.

Figure: 3- 7*1 Chebyshev array

Figure: 4 Return loss for 7*1 Chevyshev array

Figure 3& 4 are showing the radiation pattern and return loss for 7*1 chebyshev array , performance of this array

is almost same as binomial array except chebyshev distribution shows better side lobe rejection performance.

Figure: 5- 7*7 binomial array

Figure: 6- Return loss for 7*7 binomial array

Lesser Angular width is also very important far field parameter for antenna system. 7*1 linear array yielding radiation pattern which have better return loss behaviour but angular width is also very large like 94.70 so resolution of antenna system is poor . It find suitable for broadcasting but for certain application its larger angular width limits its application. 7*1 linear array with both binomial and chebyshev array shows radiation pattern with large angular width. For better resolution of antenna system we used rectangular array of 7*7 elements with binomial and chebyshev distribution. Figure 5 & 6 are showing output for binomial distribution and figure 7 & 8 showing for chebyshev distribution. Binomial distribution provides main lobe magnitude of 23.5 dBi with small angular width of 15.9 degree, it reduces the number of side lobe and amplitude of back lobe is also small but side lobe have different amplitude i.e. some side lobe have larger magnitude compared to other side lobe.

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Figure:7- 7*7 Chebyshev array

Figure: 8- Return loss for 7*7 Chevyshev array

7*7, Chebyshev distribution provides excellent radiation pattern. Amplitude of main lobe is larger, side lobe are smaller as compare to binomial distribution. All side lobes remain below certain level and for that level it provides optimum radiation pattern. Only drawback of chebyshev distribution is more number of side lobes and level of back lobe is larger compare to binomial array.

No. of antenna

Type of distribution

Directivity (dBi)

Main lobe(dB)

Side lobe level( dB)

Beam width (degree)

1 Normal 6.899 .1 -10.2 60.5 7*1 binomial 13.44 13.4 -14.0 91.1 7*1 chebyshev 14 14 -15.3 94.7 2*2 uniform 11.17 9.1 -5.7 21.2 7*7 binomial 23.53 23.5 -21.2 15.9 7*7 chebyshev 24.77 24.8 -30.9 14.2

Table-1Comparision of linear & rectangular array

IV: CONCLUSION

Uniform array of antenna suffer the problem of larger side lobe level and larger angular width. In certain applications like Radar, mobile communication it yields false target due to larger value of side lobes. Tapering of array to reduce side lobe level is obtained through binomial distribution and cheychev coefficient distribution to array element excitation. In this work we simulate the 7*1 linear array with binomial and chebyshev distribution. We also applied binomial and chebyshev distribution for 7*7 rectangular array which is showing superior performance as compared linear array. Chebyshev distribution provide significant side lobe reduction as compare to uniform and binomial distribution. Size of array is important issue in antenna design. Better directivity and side lobe reduction is obtained at the cost of larger size of array, trade off should be done according to applications and requirement. DRA is viable candidates for numerous applications, either as individual elements or in an array environment because of low profile, lightweight, ease of fabrication and are easy to excite by different methods.

ACKNOWLEDGMENT We are thankful to Amit Sharma, Akash Gupta, Akshay Khandelwal, for their support and contribution to our work.

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