Question 1 |
A waveguide consists of two infinite parallel plates (perfect conductors) at a
separation of 10^{-4} cm, with air as the dielectric. Assume the speed of light in air to
be 3 \times 10^{8} m/s. The frequency/frequencies of TM waves which can propagate in
this waveguide is/are _______.
6 \times 10^{15}Hz | |
0.5 \times 10^{12}Hz | |
8 \times 10^{14}Hz | |
1 \times 10^{13}Hz |
Question 1 Explanation:
Cut-off frequency.
\begin{aligned} f_c&=\frac{c}{2a}\;\;\;(m=1) &=\frac{3 \times 10^8}{2 \times 10^{-4} \times 10^{-2}}\\ &=1.5 \times 10^{14}Hz \end{aligned}
f \gt f_c will only propagate
A and C will propage.
\begin{aligned} f_c&=\frac{c}{2a}\;\;\;(m=1) &=\frac{3 \times 10^8}{2 \times 10^{-4} \times 10^{-2}}\\ &=1.5 \times 10^{14}Hz \end{aligned}
f \gt f_c will only propagate
A and C will propage.
Question 2 |
A standard air-filled rectangular waveguide with dimensions \text{a=8 cm, b=4 cm}, operates at \text{3.4 GHz}. For the dominant mode of wave propagation, the phase velocity of the signal in v_{p}. The value (rounded off to two decimal places) of v_{p}/c, where c denotes the velocity of light, is _____
2.24 | |
3.82 | |
1.2 | |
4.6 |
Question 2 Explanation:
f_{c 10}=\frac{c}{2 a}=\frac{3 \times 10^{8}}{2\left(8 \times 10^{-2}\right)}=1.875 \mathrm{GHz}
Guide phase velocity, V_{p}=\frac{C}{\sqrt{1-\left(\frac{f_{C 10}}{f}\right)^{2}}}
\frac{V_{p}}{C}=\frac{1}{\sqrt{1-\left(\frac{f_{C 10}}{f}\right)^{2}}}=\frac{1}{\sqrt{1-\left(\frac{1.875}{3.4}\right)^{2}}}=1.198
Guide phase velocity, V_{p}=\frac{C}{\sqrt{1-\left(\frac{f_{C 10}}{f}\right)^{2}}}
\frac{V_{p}}{C}=\frac{1}{\sqrt{1-\left(\frac{f_{C 10}}{f}\right)^{2}}}=\frac{1}{\sqrt{1-\left(\frac{1.875}{3.4}\right)^{2}}}=1.198
Question 3 |
The refractive indices of the core and cladding of an optical fiber are 1.50 and 1.48, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is _____ degree.
18.3 | |
3.45 | |
9.37 | |
5.82 |
Question 3 Explanation:
Given that
Refractive index of core \eta_{1}=1.50
Refractive index of clad \eta_{2}=1.48
Critical propagation angle \left(\theta_{P}\right)
\theta_{P}=\sin ^{-1}\left[ \frac{ \sqrt{\eta_{1}^{2}-\eta_{2}^{2}}}{\eta_{1}} \right]=\sin ^{-1} \left[ \frac{ \sqrt{1.5^{2}-1.48^{2}} }{1.5} \right] =9.37
Refractive index of core \eta_{1}=1.50
Refractive index of clad \eta_{2}=1.48
Critical propagation angle \left(\theta_{P}\right)
\theta_{P}=\sin ^{-1}\left[ \frac{ \sqrt{\eta_{1}^{2}-\eta_{2}^{2}}}{\eta_{1}} \right]=\sin ^{-1} \left[ \frac{ \sqrt{1.5^{2}-1.48^{2}} }{1.5} \right] =9.37
Question 4 |
Consider a rectangular coordinate system (x,y,z) with unit vectors a_{x}\:a_{y} and a_{z}. A plane wave traveling in the region z\geq 0 with electric field vector E=10\cos\left ( 2\times 10^{8}t\:+\:\beta z\right )a_{y} is incident normally on the plane at z=0, where \beta is the phase constant. The region z\geq 0 is in free space and the region z \lt 0 is filled with a lossless medium (permittivity \varepsilon \:=\:\varepsilon _{0}, permeability \mu \:=\:4\mu _{0} , where \varepsilon _{0}\:=\:8.85\times 10^{-12}\:\text{F/m} and \mu _{0}\:=\:4\pi \times 10^{-7}\:\text{H/m}). The value of the reflection coefficient is
\frac{1}{3} | |
\frac{3}{5} | |
\frac{2}{5} | |
\frac{2}{3} |
Question 4 Explanation:
Given \vec{E}=10 \cos \left(2 \pi \times 10^{8} t+\beta z\right) \hat{a}_{y} for z \geq 0 having free space. For z \lt 0 medium has
\epsilon_{r 2}=1 ; \mu_{r 2}=4
\Gamma=\frac{\eta_{2}-\eta_{1}}{\eta_{2}+\eta_{1}}=\frac{120 \pi(2)-120 \pi}{120 \pi(2)+120 \pi}=\frac{1}{3}
\epsilon_{r 2}=1 ; \mu_{r 2}=4
\Gamma=\frac{\eta_{2}-\eta_{1}}{\eta_{2}+\eta_{1}}=\frac{120 \pi(2)-120 \pi}{120 \pi(2)+120 \pi}=\frac{1}{3}
Question 5 |
A rectangular waveguide of width w and height h has cut-off frequencies for TE_{10} \; and \;TE_{11} modes in the ratio 1:2. The aspect ratio w/h, rounded off to two decimal places, is ___________
0.85 | |
1.25 | |
1.73 | |
1.92 |
Question 5 Explanation:
f_{c m n}=\frac{c}{2} \sqrt{\left(\frac{m}{a}\right)^{2}+\left(\frac{n}{b}\right)^{2}}
For TE mode
f_{c10}=\frac{c}{2 w} \quad\ldots(i)
and For TE_{11} mode.
\begin{aligned} f_{c11} &=\frac{c}{2} \sqrt{\frac{1}{w}^{2}+\left(\frac{1}{h}\right)^{2}} &\ldots(i)\\ &=\frac{c}{2 w} \sqrt{1+\left(\frac{w}{h}\right)^{2}} &\ldots(ii)\\ \text{given}\quad\frac{f_{c10}}{f_{11}} &=\frac{1}{2} &\ldots(iii) \end{aligned}
put (i). (in) in (ii)
\Rightarrow \frac{\frac{c}{2 w}}{\frac{c}{2 w} \sqrt{1+\left(\frac{w}{h}\right)^{2}}}=\frac{1}{2} \Rightarrow \sqrt{1+\left(\frac{w}{h}\right)^{2}}=2
On solving above equation, we get,
\frac{w}{h}=\sqrt{3}=1.732
For TE mode
f_{c10}=\frac{c}{2 w} \quad\ldots(i)
and For TE_{11} mode.
\begin{aligned} f_{c11} &=\frac{c}{2} \sqrt{\frac{1}{w}^{2}+\left(\frac{1}{h}\right)^{2}} &\ldots(i)\\ &=\frac{c}{2 w} \sqrt{1+\left(\frac{w}{h}\right)^{2}} &\ldots(ii)\\ \text{given}\quad\frac{f_{c10}}{f_{11}} &=\frac{1}{2} &\ldots(iii) \end{aligned}
put (i). (in) in (ii)
\Rightarrow \frac{\frac{c}{2 w}}{\frac{c}{2 w} \sqrt{1+\left(\frac{w}{h}\right)^{2}}}=\frac{1}{2} \Rightarrow \sqrt{1+\left(\frac{w}{h}\right)^{2}}=2
On solving above equation, we get,
\frac{w}{h}=\sqrt{3}=1.732
There are 5 questions to complete.