Mathcad Professional 14.0Olasheeni 1Peter Stuckey25CE8092E-0D2B-4E9B-B1D9-DFF873B8E36FC5515DF1-5222-48B7-A4A4-553AC2CA234A00000000-0000-0000-0000-00000000000000000000-0000-0000-0000-000000000000
fundamental constants
dielectric properties of PTFE spacer
inner and outer diameters of RG402/U (note 0.255 mm and 0.84 mm, respectively, for RG405/U)
frequency mulitiplication and conversion
resistivites of conductors (inner silver, outer copper); values are those of pure metals at 293 K
surface resistance of inner and outer conductors
Note: in what follows, frequency has units of MHz (i.e. multiplier M has been chosen)
characteristic impedance when lossless
resistance per unit length
conductor and dielectric attenuation constants; wavenumber in PTFE
total attenuation constant and propagation constant
length of coaxial probe
Fundamental resonant frequency
based on actual length
Unloaded
quality factor
of each mode
The alternate equations below are solely to show the form of the solution.S21 needs to have as many zeros in the denominator as expected peaks in the response.Multiplying f0 by n is a convenient way to show this for demonstration ONLY (it is not based on physics).
power absorption coefficients
The following graphs show reflected power as a function of permittivity of sample. The final graphs show the curve fitting used to obtain resonator parameters.