FMCW Radar 108 - Antennas

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While it is beyond the scope of this writeup to cover the details of antenna designs. A few key points will be covered here.

Different types of antennas

Antenna patches

Fundamental Resonant Frequency

The resonant frequency of a patch antenna depends on its physical dimensions, the dielectric material, and the mode of operation. For a rectangular microstrip patch antenna, the fundamental resonant frequency (dominant mode, \(TM_{10}\) mode) is approximately given by:

\[f_r = \frac{c}{2L \sqrt{\varepsilon_r^{\text{eff}}}}\]

where:

  • c is the speed of light in vacuum (3 :nbsphinx-math:`times 10`^8 m/s),

  • L is the length of the patch,

  • \(\varepsilon_r^{\text{eff}}\) is the effective permittivity of the dielectric substrate, given by:

\[\varepsilon_r^{\text{eff}} = \frac{\varepsilon_r + 1}{2} + \frac{\varepsilon_r - 1}{2} \left( 1 + 12 \frac{h}{W} \right)^{-1/2}\]

where:

  • \(\varepsilon_r\) is the relative permittivity of the substrate,

  • h is the substrate thickness,

  • W is the width of the patch.

Higher-Order Modes

It should be noted that while the main mode offers the highest radiation efficiency (i.e. ratio of Pout/Pin, not to be confused with impedance matching - as a 50 Ohm impedance has perfect matching but zero radiations).

Other modes such as \(TM_{01}\) and \(TM_{11}\) have different resonance conditions. While they have lower efficiency, they may provide in systems with strong space constraints lower footprint.

$ f_{mn} = \frac{c}{2} \sqrt{\left(\frac{m}{L}\right)^2 + \left(\frac{n}{W}\right)^2} \cdot `:nbsphinx-math:frac{1}{sqrt{varepsilon_r^{text{eff}}}}`$

where m, n are the mode indices.

Key Factors Affecting Resonance

  1. Patch Size: A larger patch lowers the resonant frequency.

  2. Dielectric Constant: A higher \(\varepsilon_r\) lowers the resonant frequency.

  3. Substrate Thickness: Increasing h affects effective permittivity and bandwidth.

  4. Edge Effects: Fringing fields increase the effective electrical length, reducing resonance slightly.

For futher reading: https://www.cust.edu.pk/static/uploads/2021/02/PhD-Thesis-Zubair-Ahmed.pdf

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