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.gitignore

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### Hugo ###
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# Generated files by hugo
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/public/
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public
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/resources/_gen/
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/assets/jsconfig.json
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hugo_stats.json

public/posts/mmas/index.html

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<a href="/posts/" class="flex items-center text-gray-500 hover:text-primary-600 dark:hover:text-primary-400">
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<p class="text-base font-medium" title="Posts">
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<p class="text-base font-medium" title="">
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Blog
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</p>
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</a>
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<li class="mt-1">
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<a href="/posts/" class="flex items-center text-gray-500 hover:text-primary-600 dark:hover:text-primary-400">
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<p class="text-bg font-bg" title="Posts">
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<p class="text-bg font-bg" title="">
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Blog
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</p>
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</a>
@@ -555,46 +555,94 @@ <h4 class="relative group"><em>this post is a work in progress</em>
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</h4>
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<p>In the fall semester of academic year 2024-2025 I decided took upon a project in order to
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design a microwave absorber based on metamaterials. In this post I document the
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progress as per the development of the cell and the modeling in order to lay everything
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publicly available and understand better as I try explaining the process
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to this figurative rubber &#x1f986; that <em>is</em> my editor. Finally I have opened a
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GitHub repository for the report that will eventually be submitted to my university and
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based upon I&rsquo;ll be <em>eventually</em> credited; it can be found <a href="https://github.com/markdlp/ParametricStudy_MicrowaveAbsorberBasedOnMetamaterials" target="_blank">here</a>.</p>
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<p>So to start by designing a basic layout in CST I&rsquo;ll implement a three-layer structure:</p>
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design a microwave absorber based on metamaterials. In this post I will document the
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progress as I learn and develop the cell and the modeling in order to lay everything
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publicly available and also to short of understand better as I try and explain the process
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to this figurative rubber ducky that <em>is</em> my editor, not the one it <em>has</em> because vs code
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pets is not very feature rich at the moment. Finally I have opened a GitHub repository
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for the report that I&rsquo;ll eventually submit to my university and for based upon I&rsquo;ll be
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credited, it can be found <a href="https://github.com/markdlp/ParametricStudy_MicrowaveAbsorberBasedOnMetamaterials" target="_blank">here</a>.</p>
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<p>So at first I start by designing a basic layout in CST..</p>
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<p>for this I&rsquo;ll implement a three-layer structure:</p>
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<ul>
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<li>A dielectric Substrate w/ a metal Resonance Layer*</li>
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<li>A dielectric Substrate w/ a metal Resonance Layer</li>
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<li>An Air Layer</li>
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<li>A Metal Copper Back-Plate</li>
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</ul>
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<p>*The metal resonance layer is technically an extra layer on top of the substrate and as a
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matter of fact it&rsquo;s the only layer above Z=0 for reasons that&rsquo;ll become obvious later on.</p>
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<p>At first placing the substrate without the resonance layer, then I&rsquo;ll place the two other
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layers, turn on the orthographic side view to remove shadows and voila:
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<p>At first I&rsquo;ll place the substrate without the resonance layer:
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<figure>
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<img
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class="my-0 rounded-md"
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loading="lazy"
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srcset="
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/img/substrate_hu18442868287700864391.bmp 330w,
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/img/substrate_hu11217334527716438528.bmp 660w,
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/img/substrate_hu5407345050010800719.bmp 1024w,
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/img/substrate_hu10713040185621226230.bmp 2x"
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src="/img/substrate_hu11217334527716438528.bmp"
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alt="Substrate"
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/>
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</figure>
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Later I&rsquo;ll place the metal resonance layer as well but there are a number of possible candidates
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I think of trying to simulate whereas the vertical layout is pretty much fixed.</p>
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<p>Without <em>further&rsquo; ado</em> I&rsquo;ll place the two other layers below Z=0, turn on the orthographic side
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view to remove shadows and voila:
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<figure>
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<img class="my-0 rounded-md" loading="lazy" src="./verticaLayout.bmp" alt="verticaLayout" />
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<img
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class="my-0 rounded-md"
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loading="lazy"
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srcset="
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/img/verticaLayout_hu17444719045100834034.bmp 330w,
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/img/verticaLayout_hu6000837079044255391.bmp 660w,
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/img/verticaLayout_hu2957778947878561907.bmp 1024w,
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/img/verticaLayout_hu979292433013569203.bmp 2x"
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src="/img/verticaLayout_hu6000837079044255391.bmp"
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alt="verticaLayout"
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/>
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</figure>
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I think it really gives a sense of scale as the air layer truly dwarfs the others.</p>
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I think it really gives a sense of scale as the air layer truly shadows the other two.</p>
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<p>Now its time to add the ring that is of the same material and thickness as the backplate and lies
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on top of the dielectric substrate.
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<figure>
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<img class="my-0 rounded-md" loading="lazy" src="./ring.bmp" alt="ring" />
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<img
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class="my-0 rounded-md"
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loading="lazy"
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srcset="
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/img/ring_hu216817671663296563.bmp 330w,
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/img/ring_hu11656417394376380414.bmp 660w,
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/img/ring_hu12569261092461304868.bmp 1024w,
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/img/ring_hu7271321325565709438.bmp 2x"
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src="/img/ring_hu11656417394376380414.bmp"
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alt="ring"
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/>
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</figure>
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</p>
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<p>For the arrows I make the assumption that both the arrow body and point are
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<p>Then I will move the substrate, air and backplate layers all below Z=0 just ti make is easier
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with designing the arrows. For this I make the assumption that both the arrow body and point are
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\(\alpha = 0.5mm\) of width.
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<figure>
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<img class="my-0 rounded-md" loading="lazy" src="./parallel.png" alt="nonparallel" />
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<img
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class="my-0 rounded-md"
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loading="lazy"
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srcset="
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/img/parallel_hu8971957134052069245.png 330w,
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/img/parallel_hu15227971895423968964.png 660w,
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/img/parallel_hu11531056128589387579.png 1024w,
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/img/parallel_hu3002488718345335167.png 2x"
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src="/img/parallel_hu15227971895423968964.png"
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alt="nonparallel"
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/>
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</figure>
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In order to accurately place all the curve points that define the arrow some basic calculations
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shall be made. The two points of the arrow base lay exactly on the arc of the ring (w/ r=2.7mm)
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and are equidistant from curve y=x so the in order to find their cartesian coordinates the following
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shall be made. The two points of the arrow base lie exactly on the arc of the ring and are
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equidistant from curve y=x so the in order to find their cartesian coordinates the following
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system shall be solved.</p>
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<div class="highlight"><pre tabindex="0" class="chroma"><code class="language-matlab" data-lang="matlab"><span class="line"><span class="cl"><span class="n">syms</span> <span class="n">x1</span> <span class="n">x2</span>
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</span></span><span class="line"><span class="cl">
@@ -606,82 +654,82 @@ <h4 class="relative group"><em>this post is a work in progress</em>
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</span></span></code></pre></div><p>$$
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\displaystyle \begin{array}{l} \left(\begin{array}{cc} \sigma_3 -\frac{2916,\sigma_1 }{1433} &amp; -\sigma_1 \newline \sigma_4 -\frac{2916,\sigma_2 }{1433} &amp; -\sigma_2 \newline \frac{2916,\sigma_1 }{1433}-\sigma_3 &amp; \sigma_1 \newline \frac{2916,\sigma_2 }{1433}-\sigma_4 &amp; \sigma_2 \end{array}\right)\newline\newline \textrm{where}\newline \sigma_1 =\sqrt{\frac{729}{200}-\frac{7,\sqrt{59}}{80}}\newline \sigma_2 =\sqrt{\frac{7,\sqrt{59}}{80}+\frac{729}{200}}\newline \sigma_3 =\frac{400,{{\left(\frac{729}{200}-\frac{7,\sqrt{59}}{80}\right)}}^{3/2} }{1433}\newline \sigma_4 =\frac{400,{{\left(\frac{7,\sqrt{59}}{80}+\frac{729}{200}\right)}}^{3/2} }{1433}\end{array}
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$$</p>
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<p>Which results in two points per quadrant, picking out the two points of the 1st quadrant and
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<p>Which results in two points/quadrant so picking out the two points of the 1st quadrant and
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inserting them to CST the arrow body is parallel again
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<figure>
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<img class="my-0 rounded-md" loading="lazy" src="./corretArrowBase.png" alt="corrected" />
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<img
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class="my-0 rounded-md"
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loading="lazy"
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srcset="
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/img/corretArrowBase_hu7479383311875984674.png 330w,
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/img/corretArrowBase_hu15877110722483822483.png 660w,
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/img/corretArrowBase_hu14724749847662966044.png 1024w,
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/img/corretArrowBase_hu738687063664218640.png 2x"
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src="/img/corretArrowBase_hu15877110722483822483.png"
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alt="corrected"
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/>
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</figure>
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</p>
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<p>Then the arrow is mirrored against the X, the Y and the XY planes in order to reach all four
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sides of the cell, then the face is covered with copper and a height of d=0.035mm is also
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attributed, which is why it was important to move all other layers below Z=0.</p>
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<table>
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<thead>
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<tr>
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<th></th>
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<th></th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td style="text-align: center">
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attributed, which is why it was important to move all other layers below Z=0.
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<figure>
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<img class="my-0 rounded-md" loading="lazy" src="./mirroredArrows.png" alt="mirrored" />
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<img
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class="my-0 rounded-md"
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loading="lazy"
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srcset="
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/img/mirroredArrows_hu10758359463766756690.png 330w,
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/img/mirroredArrows_hu1909564240433509484.png 660w,
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/img/mirroredArrows_hu1714510141530817139.png 1024w,
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/img/mirroredArrows_hu14530626319326304251.png 2x"
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src="/img/mirroredArrows_hu1909564240433509484.png"
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alt="mirrored"
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/>
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</figure>
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</td>
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<td style="text-align: center">
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<figure>
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<img class="my-0 rounded-md" loading="lazy" src="./RingAndArrows.png" alt="rna" />
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</figure>
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</td>
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</tr>
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</tbody>
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</table>
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<p>Now I&rsquo;ll try and perform a simulation using the frequency solver in CST from 2.7 to 12.7 GHz,
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adding a port with space (\(Z_{max}\)) in front of the cell and setting the orientation to
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negative so that is faces the absorber and the coordinates as full-plane the boundaries
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will be periodic along the XY plate and I will add an absorbing condition (\(Z_{min}\)).</p>
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<p>The mesh of after of the structure after the simulation is as:
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<figure>
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<img class="my-0 rounded-md" loading="lazy" src="./mesh.png" alt="mesh" />
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<img
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class="my-0 rounded-md"
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loading="lazy"
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srcset="
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/img/RingAndArrows_hu15001361394227660321.png 330w,
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/img/RingAndArrows_hu14697718748176495339.png 660w,
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/img/RingAndArrows_hu6892010459903894309.png 1024w,
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/img/RingAndArrows_hu1686997742458895736.png 2x"
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src="/img/RingAndArrows_hu14697718748176495339.png"
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alt="rna"
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/>
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</figure>
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</p>
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<p>For the Electrical Field Simulation &gt; and for the frequency [2.7, 7.7, 12.7] GHz and for \(Z_{max}(1)\) is as:</p>
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<table>
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<thead>
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<tr>
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<th></th>
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<th></th>
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<th></th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td style="text-align: center">
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<figure>
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<img class="my-0 rounded-md" loading="lazy" src="./UnitCell/UnitCell_E_Zmax1_027e2MHz.gif" alt="UnitCell_E_Zmax1_2.7GHz" />
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</figure>
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</td>
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<td style="text-align: center">
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<p>Now I&rsquo;ll try and perform a simulation using the frequency solver in CST just to get an idea
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how the component behaves, the boundaries will be periodic along the XY plate and I will add
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absorbing conditions along the Z axis.</p>
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<p>For reference the mesh with only the ring element on the surface ends up such as:
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<figure>
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<img class="my-0 rounded-md" loading="lazy" src="./UnitCell/UnitCell_E_Zmax1_077e2MHz.gif" alt="UnitCell_E_Zmax1_7.7GHz" />
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<img
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class="my-0 rounded-md"
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loading="lazy"
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srcset="
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/img/mesh_hu17537972005702603468.png 330w,
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/img/mesh_hu10698237440036260462.png 660w,
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/img/mesh_hu16945353822138668859.png 1024w,
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/img/mesh_hu1303269888237817625.png 2x"
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src="/img/mesh_hu10698237440036260462.png"
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alt="onlyRing"
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/>
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</figure>
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</td>
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<td style="text-align: center">
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</p>
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<p>Adding the arrows and running the simulation mesh output looks something like:
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<figure>
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<img class="my-0 rounded-md" loading="lazy" src="./UnitCell/UnitCell_E_Zmax1_127e2MHz.gif" alt="UnitCell_E_Zmax1_12.7GHz" />
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<img class="my-0 rounded-md" loading="lazy" src="/static/images/MMA_UnitCell_E_27e2MHz_Zmax1.gif" alt="panda" />
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</figure>
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</td>
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</tr>
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</tbody>
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</table>
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</p>
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</div>
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themes/blowfish/.gitignore

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# Hugo and Blowfish
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public/
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public
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resources/
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exampleSite/resources/
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