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Dielectric Coaxial Resonator

A high-Q, temperature stable, compact circuit element.

Dielectric Coaxial Resonator

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.

Inductivity vs frequency

Inductance of coaxial resonators versus operating frequency. [Siemens Matsushita]

Measure Data of the 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.

Schematics of Measurement Adapter [Siemens]
Realised Circuit

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:

Measure S21 DCR

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 :

Formula Q

... 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.

DCR Dimensionen

Geometry of Dielectric Coaxial Resonator

... and the table below shows what we measured at our device ...

 LENGTH [mm]
 WIDTH [w]

Relative Permittivity of the 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

Formula Epsilon

... 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

Formula Z

... in our case Z0 = 5.9748 Ω

Calculating the data of the equivalent network


Equivalent Network, [Siemens Matsushita Components]

Formula L Formula C Formula R

... in our case :

 Resistor [Ω]
 Inductor [nH]
 Capacitor [pF]

Calculate the data of the Dielectric Resonator

Length λ/4 (end shorted)

f0 [MHz]
Bandwidth [MHz]  
Dimension l [mm]  
Dimension w [mm]  
Dimension d [mm]  
Relative Permittivity Εr  
R [Ω]  
L [nH]  
C [pF]  
Z [Ω]  

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t1 = 6586 d

t2 = 212 ms

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