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By selecting a higher permittivity substrate do we reduce the height of the antenna or we reduce the length of the patch antenna? We cannot reduce the length of the antenna as it is dependent on the wavelength.

JRE
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Mrunal Shinde
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    Higher permittivity -> faster signal propagation speed -> shorter wavelength for a given frequency -> smaller antenna. – Klas-Kenny Jun 13 '22 at 07:01
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    wavelength **in the antenna**, which is on a high k substrate, which modifies speed of light and therefore wavelength – Neil_UK Jun 13 '22 at 07:08

1 Answers1

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Here's an easier explanation:

We know the 2-plate capacitor formula:

$$ C=\epsilon_0\ \epsilon_r \ \frac{A}{d} $$

Where \$\epsilon_r\$ is the relative permittivity of the substrate, \$A\$ is the area of the plates and \$d\$ is the distance between them, or the thickness of the substrate.

So, using a high-permittivity material will make \$C\$ greater.

We know the LC network resonance frequency:

$$ f_r=\frac{1}{2\pi \sqrt{LC}} $$

So, greater \$C\$ makes the resonance frequency lower.

To bring the resonance frequency to its original (design) value \$C\$ should be decreased. Reduced plate area (\$A\$) will make the \$C\$ lower (first formula), therefore a smaller patch.

But there are some drawbacks of course:

  • Since the effective electric field between the plates is inversely proportional to the permittivity, using a high permittivity material will reduce the effective electric field. This means less radiation and therefore less gain.

  • Q will increase and this makes the bandwidth lower -- This can be an advantage or disadvantage, though as it depends on the application (and perspective).

Rohat Kılıç
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  • So to reduce plate area(A) do we reduce the width of the patch? Because length should be half the wavelength. – Mrunal Shinde Jun 13 '22 at 08:13
  • @MrunalShinde length (for a rectangular patch, length is the dimension along the transmission line) is still a design parameter because it determines the resonance frequency, so length should remain. Therefore the only option is to reduce the width. For complex shape patches the things may be different. Remember that using high permittivity material makes the antenna smaller but the performance will degrade. – Rohat Kılıç Jun 13 '22 at 08:36
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    I think this answer is good as op must see a physical effect of the media in a new way. Perhaps show the analogy between LC and mu epsilon and how both relate to wavelength? And add the note about performance/bandwidth in answer? I like your approach. – johnnymopo Jun 13 '22 at 17:07
  • I fully understood. Thankyou! – Mrunal Shinde Jun 14 '22 at 03:20
  • @MrunalShinde you can accept my answer if it's satisfactory enough by clicking the tick under the votes record so that the question does not remain open. – Rohat Kılıç Jun 14 '22 at 06:47
  • @johnnymopo thank you. Yes, I should have added the note about decreased performance. – Rohat Kılıç Jun 14 '22 at 06:49