Table 7.15. Scaling Relationships For Typical Values Of Scaling Parameters

CONDITIONS

  1. Both the full-size and scaled models are in air.
  2. Both models are nonmagnetic (* = * = o).
  3. Both models are irradiated by similar sources with correspondingly equal intensities. That is, at corresponding points (x, y, z) and (, , ), E (x, y, z) = (, , ) and H(x, y, z) = (, , ).
  4. The models have equal mass densities (m = m).

RELATIONSHIPS

Quantity in the
Full-Size Model
Quantity in the
Scaled Model

Relationships
Coordinatesxx = S
yy = S
zz = Sz
Frequencyff = /S
Complex relative ' ' ' = '
permittivity
" " " = "
Conductivity = /S
SARSAR SAR = /S


EXAMPLE

Measured SAR distribution in a 0.52-m-diameter spherical model of muscle-equivalent tissue at 13.56 MHz is desired. A generator operating at a frequency of 100 MHz is available. Design a scaled model for appropriate measurements.

The scale factor is determined by the two frequencies:
S = /f = 100 MHz/13.56 MHz = 7.38.

Full-Size ModelScaled Model
Sphere diameterd = 52 cmd = d/S = 52/7.38 = 7.05 cm
Frequencyf = 13.56 MHz = Sf = 7.38 x 13.56 = 100 MHz
Permittivity' = 149 =' = 149
Conductivity = 0.62 S/m = S = 7.38 x 0.62 = 4.58 S/m
SAR(Calculated)
SAR =/S = 4/7.38 =
0.54 W/kg
(Measured) = 4 W/kg