Question

The relation between the λg, λc, λ0 is given by ____

(a) \(\frac{1}{λ_0} =\sqrt{\frac{1}{λ_g^2} +\frac{1}{λ_c^2}} \)

(b) \(\frac{1}{λ_g}=\frac{1}{λ_0^2} -\frac{1}{λ_c^2} \)

(c) \(\frac{1}{λ_0} =\sqrt{\frac{1}{λ_g^2} -\frac{1}{λ_c^2}}\)

(d) \(\frac{1}{λ_g}=\frac{1}{λ_0^2} +\frac{1}{λ_c^2} \)

The question was posed to me in a national level competition.

I want to ask this question from Standing Wave Ratio Method topic in division Modern Antennas & Antenna Measurements of Antennas

Answer 1

The correct answer is (a) \(\frac{1}{λ_0} =\sqrt{\frac{1}{λ_g^2} +\frac{1}{λ_c^2}} \)

To elaborate: The relation between the λg, λc, λ0 is given by \(\frac{1}{λ_g^2} =\frac{1}{λ_0^2} -\frac{1}{λ_c^2} \)

⇨  \(\frac{1}{λ_0} =\sqrt{\frac{1}{λ_g^2} +\frac{1}{λ_c^2}}\)

and \(λ_0=\frac{c}{f}.\)