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

Lect. 20: Dielectric Resonators &
Excitation of Resonators
Dielectric Resonator --- raise your high-Q
What is it? A piece of high-dielectric constant material, usually in the
shape of a disc, that functions as a miniature microwave resonator.
• Made of low-loss high dielectric constant materials.
• High dielectric constants ensures that most of the field is
confined within the dielectric.
• Advantages: small size, low price, excellent integrability with
microwave integrated circuits.
• Conductor loss is absent, but dielectric loss increases with
dielectric constant.
• Qs of up to several thousand can be achieved.
How does it work? The dielectric
element functions as a resonator
because of the internal reflection of
electromagnetic waves at the high
dielectric constant material/air
boundary. This results in
confinement of energy within, and in
the vicinity of, the dielectric
material, which, therefore, forms a
resonant structure.
ELEC344, Kevin Chen, HKUST 1
ELEC344, Kevin Chen, HKUST 2
Why use it? High-Q tuning network enhances the stability of
oscillators. The Q of a resonant network using lumped elements or
microstrip lines and stubs is typically limited to a few hundred.
Usually coupled to an oscillator circuit by positioning in close
proximity to a microstrip line.
Waveguide cavity resonators can
have Qs of 10,000 or more, they are
not well-suited for integration in
miniature microwave integrated
circuitry. Metal cavities also have
significant frequency shift caused by
dimensional expansion due to
temperature variation.
Dielectric resonators can replace traditional, high-Q waveguide cavity
resonators in most applications, especially in microwave integrated
circuit (MIC) and monolithic microwave integrated circuit (MMIC)
structures. The resonator is small, lightweight, high-Q, temperaturestable,
low-cost and easy-to-use. A typical Q exceeds 10,000 at 4
Cylindrical Dielectric Resonator:
Dominant Mode: TE 01δ
Where δ = 2L/λg (

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