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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:

Dolph-Tchebysheff Array is based on Tchebysheff polynomials. It has narrowest main lobe for the given side lobe sides. The current distribution reduces the pattern which is similar to Tchebysheff polynomials.

Upon completion of experiment students will be able to :

Students will able to model the Dolph Tchebyshev, compute the performance parameters and compare the performance parameters with standard parameters

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