## Reflectivity#

The amount of energy received back to the Rx antenna depends on the reflectivity of the object ($$\gamma$$), the radar cross section (RCS) of the object ($$\sigma$$), and the distance to the object ($$R$$). A reflection occurs when there is a difference in relative permittivity between two media that the signal is propagating through. $$\gamma$$ is then given as

(3)#$\gamma=\left(\frac{\sqrt{\varepsilon_1}-\sqrt{\varepsilon_2}}{\sqrt{\varepsilon_1}+\sqrt{\varepsilon_2}}\right)^2$

where $$\varepsilon_1$$ and $$\varepsilon_2$$ is the relative permittivity, at 60 GHz, on either side of the boundary. Keep in mind that the relative permittivity is generally frequency dependent and may also vary depending on the exact material composition and manufacturing process. Table 1 lists approximate values for the real part of the relative permittivity for some common materials.

Table 1 Approximate relative permittivity of common materials#

Material

Re($$\varepsilon$$) at 60 GHz

$$\gamma$$ with air boundary

Air

1

0

ABS

2.5-4.0

0.05 - 0.11

Polyethylene (PE)

2.3

0.042

Polypropylene (PP)

2.2

0.038

Polycarbonate

2.75

0.06

Mobile phone glass

6.9

0.2

Plaster

2.7

0.059

Concrete

4

0.11

Wood

2.4

0.046

Textile

2

0.029

Metal

1

Human skin

8

0.22

Water

11.1

0.28

Table 1 shows that some materials are semi-transparent to 60 GHz signals and it is hence possible to detect reflecting objects behind a surface of these materials, each boundary with a change in permittivity gives a reflection. This is a useful property in applications where the sensor measures through the product housing or when detecting objects behind other objects such as walls and clothing. For optimal design of the product housing, refer to the radome chapter in the Hardware and physical integration guideline.

For most objects it is not possible to analytically calculate $$\sigma$$, instead it needs to be measured or modeled.