.
1 RF Models
2. 2. Start with simple plane wave models
3. 3. Progress to figures of revolution
4. 4. Numerical Approaches
1.
1
Antennas
 Near Field
 Far Field
R
R
2D 2

2D 2

 Transition Range from
0.2to0.4
D2

 Short Dipole = λ/2π
2
Some Basic Definitions
 1 Specific Absorption Rate (SAR) in W/kg
E 2
SAR 

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
cT
SAR 
t
 Where c is the specific heat capacity in J/kg oC
 ΔT is the change in temperature
 Δt is the length of the pulse
3
Thermal Relaxation Times
 1. For a short pulse in a Sphere

a2

4k
 Where a is the radius and

k
is the thermal diffusivity

 And

k'
k
c
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.
4
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 FermiDirac
4. Different temperatures for electrons and lattice.
5
Plane Waves
 1 This works for R/λ>> 1 R is the radius of curvature
and λ is the wave length
 2 Important parameters are the frequency, f,
polarization, P, the angle of incidence,θ, σ, and ε
 
 3 At normal incidence reflection coefficient   2 1
Where η1, η2 are impedances



 2  1
 The transmission coefficient is given by
2 2
Going from 1 to 2.
T
 2  1
The power reflected is given by Г2
6
Reflection Coefficients E Field
7
Power Transmission Coefficients
8
Penetration of EMF vs Frequency
Power
9
Depth of Penetration for Some Bio Materials
10
Reflection as a Function of Angle and Polarization
From a Tissue Interface
11
Phase of Reflection
12
Multiple Layers
13
SAR In the Plane of the Fat and Muscle
14
Peak SAR
15
Distribution of E Field
16
Spherical Model For Brain of Cat 918Mhz
1
17
Spherical Model for Cat Brain at 2450Mhz
18
Absorption Characteristics Spherical Model
19
Frequency Dependent Spherical Model for Human
Absorption
20
Numerical Models
 1 Quasi-static < 30 to 40Mhz
 2 Method of Moments, MoM
 3. Finite Element, FEM
 4. Finite Difference Time Domain, FDTD
21
3D Impedance Models
 1. Assumes the dimensions are small compared to the
wave length so that everything is at the same time.
 zx
zz

Zy
22
Applications of Quasi-Static Method
23
See Jim Lin’s Book
 Electromagnetic Fields In Biological Systems. CRC
press.
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
28
Finite Difference Time Domain
29
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.
30
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
31
Tissue Properties
32
Current Densities in the Body from the Magnetic Fields
of a low field Electric Blanket
33
Current Densities in the Body from the Magnetic Fields
of a Standard Electric Blanket
34
Current Densities in the Body from the Magnetic Fields of an
Electric Blanket
35
Electric Blanket Exposures
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
Insert Virtual Family
40
See VF
 1. See for Cell Phone Radiation into the Head.
 IEEE Proc. Vol 83, Jan 1995 “Em Interaction of Handset
Antennas and a Human in Personal Communications”
Michael Jensen and Yahya Rahmat-Sami
41
Average Absorption
42
Average SAR vs Frequency at10W/m2 and
80MHz Vertical Polarization
43
Average SAR Whole Body
44
AVERAGE SAR
45
SAR Average for Children
46
2
10W/m
Whole Body SAR At
Plane Wave vs Frequency
47
Base Station Exposures
48
Cell Phone Exposures
49
Cell Phone Exposures
50
Ultra Wide Band EMP at 1.1V/m
51
Fourier Spectra UWB EMP
52
FTDT with Time Varying Dielectric Constant
Start with
D
xH 
t
and
D   * ( ) E
Using the Debye equations  * ( )   o     s1      s 2    

1  j1
1  j 2 
We get the following differential equation with the time
varying dielectric constant to be solved

2 D
D
E
2 E 
 1 2 2  ( 1   2 )
D   o  o E  ( s1 2   s 2 1 )
   1 2 2 
t
t
t
t 

53
Debye Constants
54
Induced Currents at V=1.1V/m
55
Peak Currents UWB Exposure
56
Bio Heat Equation
57
Heating of Body Tissue
 1. Initial conditions Q=0
 2 . Boundary conditions . Assume heat flow
perpendicular to skin.
58
Heat Flow
 1. Radiation
 2. Usually the surface temperature Ts and TA are close
enough together that this is not significant.
 3. The body temperature is tightly temperature
regulated to near 37o C. Thus parameters vary with
temperature
 4. The metabolic rate A depends on the local
Temperature as
59
Blood Profusion
 1 Below 39o C
 2. For
linear increase
 3. For T> 44o the blood flow is at a maximum. C
 4. Control with vasodilatation and profusion through
the skin.
60
Heat Flow
 1. Heat is carried from the interior to the surface of the
skin. The blood temperature TB varies as
61
Numerical Calculations
 1 Need to couple heat generation from the RF to the
basic heat equation.
 2. The geometry is complicated and the coefficients
vary in time and space.
 3. The usual approach is to use FDTD for calculating
the power distribution and a finite difference approach
for solving the heat diffusion equation.
 4. The temperature difference is calculated at the
center of each cube with the heat gain or loss and
repeated at each time interval.
62
Skin Temperature
 1. One signal for temperature control is the
hypothalamic temperature as an indicator of core body
temperature.
63
Temperature Values as
Considered for Standards
 1. Threshold for nerve damage +4.5oC for 30 minutes
 2. Lens of rabbit eye 3-5oC
 3. Skin 8 to 10oC for damage
 4. 1o to 2oC in the core can lead to physiological
changes
 4. Other data shows threshold problems typically
about 41oC
 5. All this data is exposure time dependent.
64
RF Protection
 1 Guide lines set at SAR = 4W/kg for whole body
exposures with estimated core temperature rise of 1oC.
 2. Local heating may be as much as 20: 1 for plain wave
exposures
 3. There are a lot of variables here, position,
environment, humidity , temperature of the air, etc.
 4. One model shows maximum ΔT = 0,72oC at 4oMHz
in the ankles where the estimated damage is at
 ΔT =8oC
65
1
Plain Wave at 40MHz and
2
900MHz at 1mW/cm
66
Head and Cell Phone
 1. Heating from RF
 2. Cell phone blocking convection cooling
 3. Heating from the power losses in the phone.
 4. Example 250mW at 50% efficiency at 900MHz air at
24oC for 15 minutes.
 Some results Brain ΔT= o,1oC from SAR
 Contact heating with no RF to 1.5oC in the ear.
67
Table from Visible Human Model
1
68
Temperature in the Ear
 1 Note cooling on contact.
69
ANSI/IEEE Guidelines
1
 2. Note these guidelines only consider thermal effects.
70
Thermal Therapeutic Applications
 1 Hyperthermia Therapies at ≈ 43oC
 2. Ablations at ≈ 65oC
 3. Microwave Applicator Power ~ 1/r2 Heating ~ 1/r4
 Need to account for blood flow and prevent heat flow
along the wire for heart ablation. f= 2.45GHz Use chokes
to confine the power
71
Power Required for Lesion in
Cardiac Tissue
 1.
 2. Competition , Laser Surgery,
 3. Single electrode and grounded back.
72
Slot Antenna
1
73
Depth of Heating to 75oC as a Function of
the Time and Power
 1, Objective to get tumor T> 43oC and normal T< 42oC
74
Sleeved Slot Antenna
75
An Array For Heating a Larger Volume
1
76