A rectangular hollow metal waveguide has dimensions a = 2.29 cm and b = 1.02 cm. Microwave power at 10 GHz is transmitted through the waveguide in the TE _{10} mode.
(a) Calculate the cut-off wavelength and the guide wavelength for this mode.
(b) What are the other (TE or TM) modes that can propagate through the waveguide?
(c) If a = b = 2.29 cm, what are the modes which can propagate through the waveguide?
a = 2.29, b = 1.02 cm, c = 10 GHz
(a) λ = 20 = 4.58 cm
(b) for TE _{10}, f_{c_{1}}=\frac{V_{0}}{2 a}=6.55 GHz
for TE _{01}, f_{c_{2}}=\frac{V_{0}}{2 b}=14.7 GHz,
f c_{2}>f \text { so only } TE _{10} mode can propagate through the given rectangular waveguide.
(c) a = b = 2.29 cm
f = 10 GHz
for TE _{10}, f_{c_{10}}=\frac{V_{0}}{2 a}=\frac{3 \times 10^{10}}{2 \times 2.29}=6.55 GHz
for TE _{01} f_{c_{01}}=\frac{V_{0}}{2 b}=\frac{3 \times 10^{8}}{2 \times 2.29}=6.55 GHz
for TE _{11} \text { or } TM _{11}
f_{C_{11}}=\frac{V_{0}}{2 a} \sqrt{1^{2}+1^{2}}=\frac{V_{0}}{\sqrt{2 a}}=9.226 GHz
for TE _{20} \text { and } TE _{02}
f_{C_{20}}=f_{C_{02}}=\frac{V_{0}}{a}=\frac{3 \times 10^{10}}{2.29}=13.1 GHz
So, only TE _{10}, TE _{01}, TE _{11} \text { and } TM _{11} are the possible mode that propagates through the rectangle wave guide.