A rectangular waveguide is filled with a (non-magnetic) perfect dielectric. The metal is a PEC. X & = 2.25, µ, = 1 a = 4 cm , and b 1 cm. a) Consider a single pure mode, whereby the component of the magnetic field in the z-direction is H,(r)= H, cos(B,x)cos(B,y)ejz Construct an expression for the magnetic field phasor. H(r) where B, = 3n rad/cm and B, = 1.25T rad/cm. You may quote formulae for the eigenvalues of the rectangular Helmholtz Equation without derivation. b) Which mode is this? Suppose a coupler at z = 0 excites the waveguide at a frequency, f= 12 GHz. Con tho modo ribod in (o) (h) pronngoto Evzploin ample

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A rectangular waveguide is filled with a (non-magnetic) perfect dielectric. The metal is a PEC.
X
Z.
& = 2.25, µ, = 1
a = 4 cm , and b 1 cm.
a) Consider a single pure mode, whereby the component of the magnetic field in the z-direction is
H,(F) = H, cos(B,x)cos(B,y)ez
Construct an expression for the magnetic field phasor. H(r)
where B, = 3n rad/cm and B, = 1.25T rad/cm.
You may quote formulae for the eigenvalues of the rectangular Helmholtz Equation without derivation.
b) Which mode is this? (
c) Suppose a coupler at z = 0 excites the waveguide at a frequency, f=12 GHz.
Can the mode described in (a), (b) propagate. Explain.
ample
Transcribed Image Text:A rectangular waveguide is filled with a (non-magnetic) perfect dielectric. The metal is a PEC. X Z. & = 2.25, µ, = 1 a = 4 cm , and b 1 cm. a) Consider a single pure mode, whereby the component of the magnetic field in the z-direction is H,(F) = H, cos(B,x)cos(B,y)ez Construct an expression for the magnetic field phasor. H(r) where B, = 3n rad/cm and B, = 1.25T rad/cm. You may quote formulae for the eigenvalues of the rectangular Helmholtz Equation without derivation. b) Which mode is this? ( c) Suppose a coupler at z = 0 excites the waveguide at a frequency, f=12 GHz. Can the mode described in (a), (b) propagate. Explain. ample
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