Lect. 20: Dielectric Resonators & Excitation of Resonators • Made of ...

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