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

Solution time:

~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