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DESCRIPTIONDesign a birdcage coil in Comsol
A Bird-Cage Coil at 127.74 MHz
The bird-cage geometry:8-rungsEach rung split in 2 with (potential) tuning capacitors in between
Each flap represents a simple circuit or port element such as a 50 Ohm feed or a tuning capacitor.
(Standard finite element modeling approach for RF and Microwave components)
The bird-cage geometry as seen in the COMSOL user interface.
A section of surrounding air is added by enclosing the bird-cage geometry in a sphere.
The only material property is air (permittivity=1, conductivity=0, and permeability=1)
The sphere has a Scattering boundary conditions = non- reflecting.A refined model would, in addition, add a Perfectly Matched Layer for more precise absorption.
The copper stripes are modeled as perfect electric conductors.This is the simplest possible model and neglects losses but includes field discontinuity.
Several more advanced models are possible in COMSOL:- transition boundary conditions (simple field jump discontinuity)- slit boundary conditions (double field jump)
Input Port #1, 5000 V and 50 Ohm
Input Port #2, 5000 V and 50 OhmPhase shift: 90 degreesCan also enter phase in radians, without giving units.
Tuning ElementsHere capacitances (impedances/reactances) at 2.2 pF
Modeled as so called Port Elements
Frequency inputThis parameter (and any other) can be swept
Finite element mesh:1.4M Degrees of Freedom (dofs)230k elements
Second-order vector finite elements
~15 minutes on a PC with 4 cores (64 bit OS)~ 24 minutes on a PC with 2 cores (64 bit OS)
Memory used: ~3.5 GB
Cross-section of the mesh
Mesh on copper stripes
Log10 plot of |B|Arrows: B-field, normalized
Z_in_1=50 Ohm pure resistiveZ_in_2=50 Ohm pure resistiveFeed at 12 is listeningS-parameter: S11 (non-db scale)
Z_in_1=50 Ohm pure resistiveZ_in_2=50 Ohm pure resistiveFeed at 12 is listeningS-parameter: S21 (db scale)
Z_in_1=50-jX(2.2pF) OhmZ_in_2=50-jX(2.2pF) OhmFeed at 12 is listeningS-parameter: S11 (db scale)
Z_in_1=50-jX(2.2pF) OhmZ_in_2=50-jX(2.2pF) OhmFeed at 12 is listeningS-parameter: S21 (db scale)
Log10 plot of surface current density
A Bird-Cage Coil at 127.74 MHz Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21