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19. March 2024
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calc_20.php 13008 Bytes 12-02-2018 11:22:06
DIELECTRIC COAXIAL RESONATOR
Fig 1: Dielectric Coaxial Resonators
Coaxial line elements can be used below resonance to simulate high-Q ,
temperature stable, compact inductors. More precisely, shorted coax lines
will exhibit an inductive reactance when used below quarter-wave resonance
and will aproximate the behaviour of an ideal inductance or coil over a
limited frequency range. As the operating frequency approaches the SRF
(Self Resonance Frequency) the approximtion will be less valid. An exact
equivalent circuit is complex and would include parasitic elements resulting
from a transition from the printed circuit board.
Fig 2: Inductance of coaxial resonators versus operating frequency.
[Siemens Matsushita Components]
MEASURE DATA OF DIELECTRIC RESONATOR
Similiar to the approach on Designing Crystal Filters we need an adapter which
can be easily made of a piece of FR-4 and a milling cutter.
Fig 3: Schematics of Measurement Adapter
[Siemens Matsushita Components]
Fig 4: Realised Circuit of Measurement Adapter
Set the Networkanalyser (or Spectrum Analyser with Tracking generator or
whatever you use) to maximum Span. Somewhere a drop will be observed.
Zoom in to measure the Frequency and the 3dB Bandwidth. Our 'unknown Device'
produced something like that on the Picture below:
Fig 5: Frequency Response, measured with R&S FSP
From the measurement above we know : fcenter = 1116.8 MHz,
BW(3dB) = 2.88 MHz
Therefore we calculate the Q as :
... in our case Q = 388
In order to know more about this DCR we need to take measurements.
The Picture below shows what to measure.
... and the table below shows what we measured at our device ...
Fig 6: Geometry of Dielectric Coaxial Resonator
DIMENSION
LENGTH [mm]
LENGTH [l]
7.20
WIDTH [w]
6.10
INNER DIAMETER [d]
2.60
RELATIVE PERMITTIVITY OF MATERIAL : Εr
With the knowledge of the Dimensions we may calculate the relative permittivity of the ceramic Material.
x = 4 for λ/4 (shorted at the end) or x = 2 for λ/2 (end plane not conducting)
c = speed of light, 3 * 108 m/s
f0 = Centerfreq. (measured above)
l = Length
... in our case Εr = 86.997
CHARACTERISTIC IMPEDANCE : Z0
µr : relative magnetic permeability of the material, here : µr = 1
w : width of resonator
d : internal diameter of resonator
g : geometric factor, here : g = 1.07
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