VHDL 91

EXPERIMENT NO 9.

Binomial array

Practical Session Plan

Time ( min)	Content	Learning Aid / Methodology	Faculty Approach	Typical Student Activity	Skill / Competency Developed
10	Relevance and significance of experiment	Chalk & Talk , Presentation	Introduces, Facilitates, Monitors	Listens, Participates, Discusses	Knowledge, Communication, intrapersonal
20	Explanation of experiment	Chalk & Talk , Presentation	Introduces, Facilitates, Explains	Listens	Knowledge, Communication, intrapersonal, Application
10	Calculations	N/A	Explains, Monitors	Participates, Discusses	Knowledge, Communication, Intrapersonal, Application
50	Programming	Demonstration	Explains, Monitors	Participates, Discusses	Debate, comprehension, Hands on experiment
10	Debugging & Simulating	Demonstration	Explains, Monitors	Participates, Discusses	Hands on experiment
10	Results and conclusions	Keywords	Lists, Facilitates	Listens, Participates, Discusses	Knowledge, Communication, intrapersonal, Comprehension
10	Oral Question Discussion	Discussion	Discussion	Identifies & Participates	Knowledge Intrapersonal

Title: Binomial array antenna

Objectives: Model the Binomial array to analyze the performance parameters

Aim:

· To sketch the radiation pattern of Binomial array with uniform spacing & amplitude

• To compute performance parameters

Tool used: MATLAB.

Theory:

Binomial Array

Binomial array are conceptually very simple. Also, binomial array doesn’t have any side-lobes in general. But, these arrays suffer from very poor aperture efficiency and highly tapered distribution. So, binomial arrays are not preferable for large arrays. Array excitation corresponding to binomial array of N elements is given by

Array factor corresponding to the above excitation is given as,

Reasons for choosing the above array factor are:

· Array factor should be a periodic function in k_x domain with a period of 2π/a.

· Array factor should have an order of N-1 in domain.

· All the zeros should present at one single location, i.e., k_x = k_x0, so that array factor will not have any side-lobes

For synthesizing such an array, one can apply either the Fourier transform or the definition of array factor itself. The method to evaluate the array coefficients corresponding to binomial array is explained by using the following example.

The array factor for the binomial array is represented by

where the a_n’s are the excitation coefficients which will now be derived.

Excitation Coefficients

To determine the excitation coefficients of a binomial array, J. S. Stone suggested that the function be written in a series, using the binomial expansion, as

The positive coefficients of the series expansion for different values of mare

The above represents Pascal’s triangle. If the values of m are used to represent the number of elements of the array, then the coefficients of the expansion represent the relative amplitudes of the elements. Since the coefficients are determined from a binomial series expansion, the array is known as a binomial array.

The amplitude coefficients for the following arrays are:

1. Two elements (2M = 2)

a₁ = 1

2. Three elements (2M + 1 = 3)

2a₁ = 2 âž± a₁ = 1

a₂ = 1

3. Four elements (2M = 4)

a₁ = 3

a₂ = 1

4. Five elements (2M + 1 = 5)

2a₁ = 6 âž± a₁ = 3

a₂ = 4

a₃ = 1

The coefficients for other arrays can be determined in a similar manner.

Design Procedure

One of the objectives of any method is its use in a design. For the binomial method, as for any other non-uniform array method, one of the requirements is the amplitude excitation coefficients for a given number of elements. This can be accomplished using either (5)

Algorithm:

1. Read the values of n, f and d.

2. Calculate λ,β,ψ.

3. Read array coefficients(at least 5) in matrix.

4. Calculate x=modulus(N,2)

5. If x=0 then used

6. If not,

Where,

7. Calculate absolute value AF.

8. Also calculate normalized value AF.

9. Plot ϕ vs ω.

10. Calculate d₀ value of ω and also get it absolute value and take the average of Ha

11. Plot ϕ vs new ω.

12. Then calculate HPBW and directivity D₀.

Software program:

clc;

clear all;

a=[126 84 36 9 1 ]; % excitation coes.

theta =0:1:2*pi;

lambda=0.5;

d=(lambda)/4; % chnage the spacing to lambda/2 ,lambda see the effect

Nelem =10,Ncoef=Nelem/2;

theta =0:pi/200:2*pi

k=2*pi/lambda;

u=k*d*cos(theta);

AF=0;

for i=1:Ncoef;

AF=AF+a(i).*cos((2.*i-1).*u);

end

U=(abs(AF)./max(abs(AF))).^2;

polar(theta,U);

Results:

Conclusion:

In binomial array, array is arranged in such a way that broadside array radiate more strongly at centre than that from the edges. In order to reduce minor lobe as compared to main lobe i.e. in binomial array no side lobe are present.

Oral Question Bank

Theory Question Bank

Q. No	Description
1.	What is an “array factor”?
2.	What is a binomial array?
3.	What is the disadvantage of a binomial array?
4.	What are the types of antenna arrays?
5.	Define the length of an array
6.	What are the applications of arrays?
7.	Define antenna
8.	Define Radiation pattern
9.	What are the two types of radiation pattern
10.	What is the direction of maximum radiation is maximum only in one direction that is in the direction of array axis.
11.	What are the advantages of binomial array?
12.	What is the need for the Binomial array?
13.	How to convert broad side array radiation pattern into unidirectional?
14.	Define antenna array.
15.	What is an array and mention the various forms of antenna arrays?
16.	What is array factor or space factor?
17.	What is the relationship between effective aperture and directivity?
18.	Write the principle of pattern multiplication?
19.	Define Beam solid angle or beam area?
20.	Define beam efficiency?