Hardware and physical integration guideline A1 PCR sensors
Page 14 of 30
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3.6 Electromagnetic propagation
The following concepts are important for understanding how the radar can be properly integrated into
product encapsulations.
3.6.1 Transmission and reflection
When an electromagnetic (EM) wave hits the interface between two dielectrics, reflection and
refraction take place at the boundaries. Inside the dielectric, the propagation speed and wavelength
changes depending on the material permittivity. If the wavelength in free space is Ξ»
0
, the wavelength
within the material is π
ο΄
/
β
π
ο₯
, where π
ο₯
is the relative dielectric constant of the material.
In the case of linearly polarized propagation at normal incidence, the Fresnel equations then relate the
ratio between the incident and transmitted fields [5]:
(3)
where Z
1
and Z
2
are the corresponding wave impedances. We can also calculate the transmission
factor from π‘=1 + π. In most cases we have non-magnetic materials so that
π=
ο₯
π
ο₯
/π
ο₯
=1/
β
π
ο₯
.
An important special case is normal incidence between air and dielectric. The reflection coefficient
then simplifies to
π=
1 β
β
π
ο₯
1 +
β
π
ο₯
It is immediately obvious that the higher the dielectric constant, the stronger the reflected signal.
Conductors have a high dielectric constant (π
ο₯
ββ) and will therefore give a strong reflection. Most
polymers have a dielectric constant in the range of 2 β 4 and will therefore give a weaker reflection.
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