Lect. 20: Dielectric Resonators & Excitation of Resonators â¢ Made of ...

More documents

Recommendations

Info

Approximated solution (10% error): In the dielectric region, |z| < L/2, the propagation constant is real: 2 2 2 2 ⎛ p01 ⎞ β = ε r k0 − kc = ε rk0 − ⎜ ⎟ ⎝ a ⎠ In the air region, |z| > L/2, the propagation constant will be imaginary, so we write: 2 2 2 ⎛ p01 ⎞ 2 α = jβ = kc − k0 = ⎜ ⎟ − k0 ⎝ a ⎠ Implementing the boundary condition leads to Q-factor: tan β L / 2 = α / β Q d = 1 tanδ Numerically solving this equation can result in the finding of resonant frequencies of the TE 01δ mode. ELEC344, Kevin Chen, HKUST 5 Excitation of Resonators Common coupling techniques: 1. Gap coupling 2. Aperture coupling Gap coupling aperture coupling feed coupling Microstrip feedline coupling Waveguide antenna coupling ELEC344, Kevin Chen, HKUST 6 Critical Coupling - a resonator matched to a feedline at the resonance frequency: to obtain maximum power transfer between a resonator and a feedline Consider this: a series resonant circuit coupled to a feedline Z in ≈ R + j2L∆ω ≈ R(1 + The unloaded Q is At resonance, we have ω0 Q = L R Z = Z * = in R 0 ∆ω j2Q ) ω 0 Then 0L Q = ω Z0 ω L Q e = 0 = Q Z ELEC344, Kevin Chen, HKUST 7 0 the external Q Coupling Coefficient: g Q ⎧Z0 / R for series resonator g = = ⎨ Qe ⎩R / Z0 for parallel resonator Three different coupling situation: (1) g < 1, undercoupled; (2) g = 1, critically coupled; (3) g > 1, overcoupled A Gap-Coupled Microstrip Resonator λ/2 A λ/2 open-circuited microstrip resonator is coupled to a microstrip feedline. ELEC344, Kevin Chen, HKUST 8
Equivalent circuit of the gap-coupled microstrip resonator The normalized input impedance seen by the feedline is Z [(1/ ωC) + Z0 cot βl] tan βl + bc z = = − j = − j Z Z b tan βl 0 0 Where b c =Z 0 ωC is the normalized susceptance of the coupling capacitor, C. c When does the resonance occur? z = 0 In practice, b c
Page 1: Lect. 20: Dielectric Resonators & E

Lect. 20: Dielectric Resonators & Excitation of Resonators â¢ Made of ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?

Lect. 20: Dielectric Resonators & Excitation of Resonators â¢ Made of ...