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
Coordinates		x				x = S
		y				y = S
		z				z = Sz
Frequency		f				f = /S
Complex relative		'		'		' = '
permittivity		"		"		" = "
Conductivity						= /S
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 = /f = 100 MHz/13.56 MHz = 7.38.

		Full-Size Model		Scaled Model
Sphere diameter		d = 52 cm		d = d/S = 52/7.38 = 7.05 cm
Frequency		f = 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