# Antennas Questions and Answers – Frequency Independent Antenna – Design of LPDA

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This set of Antennas Multiple Choice Questions & Answers (MCQs) focuses on “Frequency Independent Antenna – Design of LPDA”.

1. What is the ratio of maximum frequency to minimum frequency if the scaling factor is 0.5 for 5 elements LPDA?
a) 16
b) 2
c) 4
d) 8

Explanation: The relation between frequency ratio and the scaling factor is given by
$$\frac{f_{max}}{f_{min}} = \frac{1}{τ^{N-1}}$$
$$\frac{f_{max}}{f_{min}} =\frac{1}{τ^{N-1}} =\frac{1}{(0.5)^{5-1}}=2^4=16.$$

2. The value of periodicity factor in LPDA is _____
a) < 1
b) >1
c) ≥1
d) =0

Explanation: The periodicity factor also known as the scaling factor is the ratio of the adjacent lengths of the dipole $$\frac{L_N}{L_{N+1}} = τ \,and\, L_N < L_{N+1}$$ where L is the length of the dipole.

3. The longest and shortest dipole lengths are taken in the form of the wavelength of the operating frequencies in LPDA.
a) True
b) False

Explanation: The longest length of the dipole is taken as the λu/2 where λu is the wavelength corresponding to upper frequency and shortest dipole length is taken as λl/2. In LPDA, the adjacent dipole spacing ratios and their length ratios are equal.

4. The relation between the spacing factor σ and the scaling factor τ is given by ____
a) $$σ=tan^{-1}(\frac{1-τ}{4σ})$$
b) $$σ=tan^{-1}(\frac{1-τ}{2σ})$$
c) $$σ=tan^{-1}⁡(\frac{4σ}{1-τ})$$
d) $$σ=tan^{-1}⁡(\frac{2σ}{1-τ})$$

Explanation: In LPDA, the ratio of successive spacing of elements is equal to the ratio of adjacent dipole lengths. The spacing factor is $$σ=\frac{d_n}{2L_n} \,and\, d_n =$$ spacing betwwen adjacent elements ‘n’ and ‘n+1’ and Ln is the length of nth dipole. The relation between the spacing factor σ and the scaling factor τ is $$σ=tan^{-1}(\frac{1-τ}{4σ}).$$