## 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

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

where $$\varepsilon_1$$ and $$\varepsilon_2$$ is the relative permittivity, at 60 GHz, on either side of the boundary. The relative permittivity for common materials can be found in various data bases, but keep in mind that it is frequency dependent. As an example, Table 1 lists approximate values for the real part of the relative permittivity for some common materials.

Table 1 Relative permittivity of common materials#

Material

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

$$\gamma$$ with air boundary

ABS plastic

2.48

0.049

Mobile phone glass

6.9

0.02

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

Air

1

0

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 use case requires that the sensor measures through, e.g., a wall, clothing or plastic housing.

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