# Antenna Array Questions and Answers – Pattern Multiplications

This set of Antennas Multiple Choice Questions & Answers (MCQs) focuses on “Pattern Multiplications”.

1. Pattern multiplication is the multiplication of single array radiation pattern with ___
a) Array Factor
b) Beamwidth
c) Total Field
d) Directivity

Explanation: The radiation pattern of the single array antenna is multiplied by the antenna factor then it is called pattern multiplication. Array factor is the function of antenna positions in the array and its weights.Total array field is the field generated by the sum of the individual elements in array.

2. Which of the following expression represents the pattern multiplication?
a) Etotal=Eθ × Array Factor
b) Etotal=Eθ × Directivity
c) Etotal=Eall elements × Array Factor
d) Etotal=Eθ × Beamwidth

Explanation: The pattern multiplication is the product of the radiation pattern of the single array antenna by the antenna factor. This helps to sketch the radiation pattern of the entire array. An Array factor is defined as the function of antenna positions in the array and its weights.

3. All the elements must be identical to apply pattern multiplication principle.
a) True
b) False

Explanation: This pattern multiplication principle works only for the identical elements in the array. This is one of the disadvantages of the pattern multiplication. This is used to sketch the radiation pattern of the entire array.

4. Which of the following is the resultant pattern obtained by pattern multiplication principle for the figure shown below?

a)
b)
c)
d)

Explanation:The radiation pattern of the single array antenna is multiplied by the antenna factor then it is called pattern multiplication. At nulls the final pattern will also have same nulls from bath patterns.

5. Which of the following statements is false?
a) Pattern multiplications gives use the radiation pattern of the array
b) All elements must be identical to apply pattern multiplication principle
c) The radiation pattern of the single array antenna is multiplied by the antenna factor then is pattern multiplication
d) Pattern multiplication is also applicable for array with different unequal elements

Explanation: The pattern of the individual array element is multiplied by the array factor. This is pattern multiplication. To apply this principle all elements must be identical. This shows the radiation pattern of the entire array.
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6. Which of the following is the resultant pattern obtained by pattern multiplication principle for the figure shown below?

a)
b)
c)
d)

Explanation: The radiation pattern of the single array antenna is multiplied by the antenna factor then it is called pattern multiplication. At nulls the final pattern will also have same nulls from bath patterns.

7. Which of the following doesn’t applicable for pattern multiplication?
a) It is the product of the individual radiation pattern of the element with the array factor of the array
b) All elements must be identical
c) All elements need not be identical
d) This gives the radiation pattern of the entire array

Explanation: The pattern of the individual array element is multiplied by the array factor. This is pattern multiplication. To apply this principle all elements must be identical. This shows the radiation pattern of the entire array.

8. For two elements array find the radiation pattern of array separated by λ/4 and phase difference is 0?
a)
b)
c)
d)

Explanation: Consider the far field pattern, equation the field pattern to zero to get nulls.
Etotal=Eθ×Array Factor=0
Eθ=0 =>cosθ=0,θ=±π/2
Or
⇨ Array Factor=0
⇨ AFn=0
⇨ $$cos⁡(\frac{kdcosθ+β}{2})=0$$
⇨ $$\frac{(\frac{2π}{λ})(λ/4)cosθ+0}{2}=\frac{π}{2}$$
⇨ cosθ=2

9. The total radiation pattern of a two element array, elements separated by a distance λ/4 and phase difference $$\frac{π}{2},$$ the nulls occur at (for far field) ____________
a) 0, ±π/2
b) π, ±π/2
c) π, ±π/4
d) π/4, ±π/2

Explanation: The normalized array factor is given by $$AF_n=\frac{AF}{2}=cos⁡(\frac{kdcosθ+β}{2})$$
⇨ AFn=0
⇨ $$cos⁡(\frac{kdcosθ+β}{2})=0$$
⇨ $$\frac{(\frac{2π}{λ})(λ/4)cosθ+\frac{π}{2}}{2}=\frac{π}{2}$$
⇨ Cosθ=1
⇨ θ=0
So Nulls occur at 0°.
For far field, the Eθ=0 => cosθ=0, θEθ=0 cosθ=0, θ=±π/2
Therefore nulls occur atθ=±$$\frac{π}{2},$$ 0.

10. The isotropic element array radiation pattern depends on the nulls of the array factor only.
a) True
b) False

Explanation: For isotropic elements it radiated n all directions. The radiation pattern of the array is the pattern of the individual array element is multiplied by the array factor. So its total radiation pattern depends on the nulls of the array factor only.

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