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 (mu* = tilde r* = muo).
  3. Both models are irradiated by similar sources with correspondingly equal intensities. That is, at corresponding points (x, y, z) and (tilde x, tilde y, tilde z), E (x, y, z) = equation (tilde x, tilde y, tilde z) and H(x, y, z) = equation(tilde x, tilde y, tilde z).
  4. The models have equal mass densities (rhom = m).

RELATIONSHIPS

Property Quantity in the
Full-Size Model		 Quantity in the
Scaled Model
Relationships
Coordinates x x = Stilde x
y tilde y y = Stilde y
z tilde z z = Sz
Frequency f tilde f f = tilde f/S
Complex relative epsilon' tilde e' epsilon' = '
permittivity
 epsilon" tilde e" epsilon" = tilde e"
Conductivity sigma tilde o sigma = tilde o/S
SAR SAR SAR SAR = 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 = tilde f/f = 100 MHz/13.56 MHz = 7.38.

Property Full-Size Model Scaled Model
Sphere diameter d = 52 cm d = d/S = 52/7.38 = 7.05 cm
Frequency f = 13.56 MHz tilde f = Sf = 7.38 x 13.56 = 100 MHz
Permittivity epsilon' = 149 equation =epsilon' = 149
Conductivity sigma = 0.62 S/m tilde o = Ssigma = 7.38 x 0.62 = 4.58 S/m
SAR (Calculated)
SAR =SAR/S = 4/7.38 =
0.54 W/kg		 (Measured)SAR = 4 W/kg

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