VHDL 91

EXPERIMENT NO 10.

Dolph-Tchebyshev Array Antenna

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 & Simlating	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: Dolph-Tchebyshev Array Antenna

Objectives: Model the Dolph Tchebyshev array to analyze the performance parameters

Aim:

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

· To compute performance parameters

Tool used: MATLAB.

Theory:

Plot (AF)_dB Vs , polar ( ,(A)_dB) Another array, with many practical applications, is the Dolph-Tschebyscheff array. 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 Tschebyscheff polynomials. A Dolph-Tschebyscheff array with no side lobes (or side lobes of −∞ dB) reduces to the binomial design.

The recursion formula for Tschebyscheff polynomials is

It can be used to find one Tschebyscheff polynomial if the polynomials of the previous two orders are known. Each polynomial can also be computed using

The following properties of the polynomials are of interest:

1. All polynomials, of any order, pass through the point (1, 1).

2. Withinthe 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 an d−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.

Algorithm for Dolph Tchebyscheff Antenna:

1. Read the values of n and f

2. Calculate λ, β.

3. Read the value of ‘d’ such that d< λ/2.

4. Calculate

5. Calculate Tchebyscheff polynomials using Chebwin(column vector of N size).

6. Take transpose of column vector.

7. Check the condition whether N is even or odd using MOD operation.

8. Calculate coefficient A(x) of AF using Tchebyscheff polynomials (1 to N/2).

9. Calculate AF.

10. Plot AF Vs , polar( ).

11. Calculate AF in dB.

12.

MATLAB program:

% Dolph-Tschebyshev Antenna Array design for 10 elements, major to minor

% ratio 26 dB

clc;

clear all;

close all;

theta=0:pi/200:2*pi;

lambda=.5;

d=(lambda);

u=((pi.*d)/lambda).*cos(theta);

%AF=2.798.*cos(u)+2.496.*cos(3.*u)+1.974.*cos(5.*u)+1.357.*cos(7.*u)+cos(9.*u);

%AF=2.0860.*cos(u)+2.8308.*cos(3.*u)+4.1184.*cos(5.*u)+5.2073.*cos(7.*u)+5.8377.*cos(9.*u);

AF=5.8377.*cos(u)+5.2073.*cos(3.*u)+4.1184.*cos(5.*u)+2.8308.*cos(7.*u)+2.0860.*cos(9.*u);

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

polar(theta,U);

Results:

Conclusion: