Antennas. Yi Huang

where ε_r = ε/ε₀ is called the relative permittivity (also called dielectric constant, but it is normally a function of frequency, not really a constant, thus relative permittivity is preferred in this book). The relative permittivities of some common materials are listed in Table 1.2. Note that they are functions of frequency and temperature. Normally, the higher the frequency, the smaller the permittivity in the radio frequency band. It should also be pointed out that almost all conductors have a relative permittivity of one.

Table 1.2 Relative permittivity of some common materials at 100 MHz

Material	Relative permittivity	Material	Relative permittivity
ABS (plastic)	2.4–3.8	Polypropylene	2.2
Air	1	Polyvinylchloride (PVC)	3
Alumina	9.8	Porcelain	5.1–5.9
Aluminum silicate	5.3–5.5	PTFE‐teflon	2.1
Balsa wood	1.37 @ 1 MHz	PTFE‐ceramic	10.2
1.22 @ 3 GHz	PTFE‐glass	2.1–2.55
Concrete	~8	RT/Duroid 5870	2.33
Copper	1	RT/Duroid 6006	6.15 @ 3 GHz
Diamond	5.5–10	Rubber	3.0–4.0
Epoxy (FR4)	4.4	Sapphire	9.4
Epoxy glass PCB	5.2	Sea water	80
Ethyl alcohol (absolute)	24.5 @ 1 MHz	Silicon	11.7–12.9
	6.5 @ 3 GHz	Soil	~10
FR‐4(G‐10)		Soil (dry sandy)	2.59 @ 1 MHz
– low resin	4.9	Water (32 °F)	88.0
– high resin	4.2	(68 °F)	80.4
GaAs	13.0	(212 °F)	55.3
Glass Gold	~41	Wood	~2
Ice (pure distilled water)	4.15 @ 1 MHz
	3.2 @ 3 GHz

      The electric flux density is also called the electric displacement, hence, the symbol D. It is also a vector. In an isotropic material (properties independent of direction) D and E are in the same direction and ε is a scalar quantity. In an anisotropic material, D and E may be in different directions if ε is a tensor.

      If the permittivity is a complex number, it means that the material has some loss. The complex permittivity can be written as

(1.20)

      The ratio of the imaginary part to the real part is called the loss tangent, that is

      (1.21)

      It has no unit and is also a function of frequency and temperature.

The electric field E is related to the current density J (in A/m²), another important parameter, by Ohm’s law. The relationship between them at a point can be expressed as

      (1.22)

where σ is the conductivity, which is the reciprocal of resistivity. It is a measure of a material’s ability to conduct an electrical current and is expressed in Siemens per meter (S/m). Table 1.3 lists conductivities of some common materials linked to antenna engineering. The conductivity is also a function of temperature and frequency.

Table 1.3 Conductivities of some common materials at room temperature

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Material	Conductivity (S/m)	Material	Conductivity (S/m)
Silver	6.3 × 107	Graphite	≈105
Copper	5.8 × 107	Carbon	≈104
Gold	4.1 × 107	Silicon	≈103
Aluminum	3.5 × 107	Ferrite	≈102
Tungsten	1.8 × 107