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ECEN 5341/4341 March 3,2014 Chapter 10

. ECEN 5341/4341 March 3,2014 Chapter 10. RF Models Start with simple plane wave models Progress to figures of revolution Numerical Approaches . Antennas. Near Field Far Field Transition Range from Short Dipole = λ /2 π. Some Basic Definitions.

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ECEN 5341/4341 March 3,2014 Chapter 10

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  1. . ECEN 5341/4341March 3,2014 Chapter 10 RF Models Start with simple plane wave models Progress to figures of revolution Numerical Approaches

  2. Antennas • Near Field • Far Field • Transition Range from • Short Dipole = λ/2π

  3. Some Basic Definitions • 1 Specific Absorption Rate (SAR) in W/kg Where σ is the conductivity in S/m ρ is the density in kg/m3 and E is the electric field V/m • For short pulses • Where c is the specific heat capacity in J/kg oC • ΔT is the change in temperature • Δt is the length of the pulse

  4. Thermal Relaxation Times • 1. For a short pulse in a Sphere • Where a is the radius and is the thermal diffusivity • And where k’ is the thermal conductivity. • Note for a long thin plate we get much faster thermal relaxation times as the surface to volume ratio increases as 1/t where t is the thickness.

  5. Thermal vs. Non-thermal Biological Effects • 1 Temperature is a convenient way to define a distribution functions. The only case when you have a non-thermal system is when you have only one particle or one state. • 2. The common Maxwell Boltzmann distribution is given by 3 Another common distribution function is a Fermi-Dirac 4. Different temperatures for electrons and lattice.

  6. Plane Waves • 1 This works for R/λ>> 1 • 2 Important parameters are f, polarization, angle of incidence,σ, and ε • 3 At normal incidence reflection coefficient • Where η1, η2 are impedances • The transmission coefficient is given by Going from 1 to 2. • The power reflected is given by Г2

  7. Reflection Coefficients

  8. Power Transmission Coefficients

  9. Penetration of EMF vs Frequency

  10. Depth of Penetration for Some Bio Materials

  11. Reflection as a Function of Angle and PolarizationFrom a Tissue Interface

  12. Phase of Reflection

  13. Multiple Layers

  14. SAR In the Plane of the Fat and Muscle

  15. Peak SAR

  16. Distribution of E Field

  17. Spherical Model For Brain of Cat 918Mhz • 1

  18. Spherical Model for Cat Brain at 2450Mhz

  19. Absorption Characteristics Spherical Model

  20. Frequency Dependent Spherical Model for Human Absorption

  21. Numerical Models • 1 Quasi-static < 30 to 40Mhz • 2 Method of Moments, MoM • 3. Finite Element, FEM • 4. Finite Difference Time Domain, FDTD

  22. 3D Impedance Models • 1. Assumes the dimensions are small compared to the wave length so that everything is at the same time. • zxzz • Zy

  23. Applications of Quasi-Static Method

  24. Volume Integral Method of Moments, VMoM • 1 Transforms Integral Equations into a matrix equations using the volume equivalence principle • 2 Break into N simple cells • 3. Satisfy the Boundary Conditions • 4. Get full matrices • 5. Takes lots of memory.

  25. Surface Method of Moments, SMoM

  26. Finite Element Method FEM • 1. This has not been used much for biological estimates of the fields in humans • 2. It grows with the number of elements as N • 3. The choice of the elements and their shape is important. • 4. Use to form a system of linear equations. • 5. Satisfy the boundary conditions.

  27. Finite Difference Time Domain

  28. Finite Difference Time Domain • 1. Establish values of σ and ε for each cell • 2. Include the source. • 3. The boundary conditions are generated from the curl equations. • 4. Establish the E,H, about the unit cell then evaluate the values at alternate half time steps • 5. This calculation grows linearly with N • 6. This can be fast even for N = 106 • 7. This is the most commonly used approach.

  29. Frequency –Dependent FDTD • 1 Used for short pluses and wide band where ε and σ vary with frequency. • 2 Two approaches • A. convert ε and σ to the time domain • B. Add the differential equation for displacement vector D Solve the equations simultaneously

  30. Tissue Properties

  31. Current Densities in the Body from the Magnetic Fields of an Electric Blanket

  32. Current Densities in the Body from the Magnetic Fields of an Electric Blanket

  33. Current Densities in the Body from the Magnetic Fields of an Electric Blanket

  34. Electric Blanket Exposures

  35. Assume 10W/m2

  36. Power Line Exposure at 10kV/m and H= 26.5 A/m

  37. Cubic Cell Mode. • 1

  38. Cubic Cell Model of Human

  39. Average SAR vs Frequency at10W/m2 and 80MHz Vertical Polarization

  40. Average Absorption

  41. Average SAR Whole Body

  42. AVERAGE SAR

  43. SAR Average for Childern

  44. Base Station Exposures

  45. Debye Constants

  46. Ultra Wide Band EMP at 1.1V/m

  47. Fourier Spectra UWB EMP

  48. Induced Currents at V=1.1V/m

  49. Peak Currents UWB Exposure

  50. Cell Phone Exposures

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