Microwave Characterization of Metal-Decorated Carbon Nanopowders Using a Single Transmission Line

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">Case</td><td class="align_center">Topology</td><td class="align_center"><span style="width: 9.01029ptpx;"><svg height="9.14241pt" id="M89" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -5.96091 9.01029 9.14241" width="9.01029pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.005,3.132)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z"></path></g></svg></span></td><td class="align_center"><svg height="9.32509pt" id="M90" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -6.14359 10.7719 9.32509" width="10.7719pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z"></path></g></svg> (S/m)</td><td class="align_center"><span style="width: 10.9024ptpx;"><svg height="9.39034pt" id="M91" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 10.9024 9.39034" width="10.9024pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M538 96L524 119C492 88 454 63 446 63C439 63 434 70 440 101C463 223 491 341 518 448H508L433 422L401 276C355 192 240 56 188 56C163 56 154 89 163 133C184 233 207 338 235 443L230 448L152 424L58 17C40 -60 23 -143 23 -185C23 -241 42 -261 63 -261C92 -261 117 -241 125 -227L124 -221C109 -209 89 -165 89 -103C89 -55 96 -13 105 26H107C121 -3 134 -12 151 -12C172 -12 194 -5 221 16C279 61 330 124 384 194H386C381 159 377 141 368 105C343 3 363 -12 383 -12C416 -12 486 35 538 96Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.89,3.132)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">1</td><td class="align_center">Microstrip</td><td class="align_center"><b>3.0</b><i> 2.971</i></td><td class="align_center"><b>0.5</b><i> 0.4934</i></td><td class="align_center"><b>1.5</b><i> 1.501</i></td></tr><tr><td class="align_left">2</td><td class="align_center">Microstrip</td><td class="align_center"><b>6.0</b><i> 6.07</i></td><td class="align_center"><b>1.0</b><i> 0.92</i></td><td class="align_center"><b>3.0</b><i> 3.14</i></td></tr><tr><td class="align_left">3</td><td class="align_center">CPW</td><td class="align_center"><b>3.0</b><i> 2.97</i></td><td class="align_center"><b>0.5</b><i> 0.44</i></td><td class="align_center"><b>1.5</b><i> 1.497</i></td></tr><tr><td class="align_left">4</td><td class="align_center">CPW</td><td class="align_center"><b>6.0</b><i> 6.18</i></td><td class="align_center"><b>1.5</b><i> 1.26</i></td><td class="align_center"><b>3.0</b><i> 3.1</i></td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Nominal (bold) and retrieved (italics) values of <span class="nowrap"><svg height="9.14241pt" id="M85" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -5.96091 9.01029 9.14241" width="9.01029pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.005,3.132)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z"></path></g></svg>,</span> <span class="nowrap"><svg height="9.39034pt" id="M86" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 10.9024 9.39034" width="10.9024pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M538 96L524 119C492 88 454 63 446 63C439 63 434 70 440 101C463 223 491 341 518 448H508L433 422L401 276C355 192 240 56 188 56C163 56 154 89 163 133C184 233 207 338 235 443L230 448L152 424L58 17C40 -60 23 -143 23 -185C23 -241 42 -261 63 -261C92 -261 117 -241 125 -227L124 -221C109 -209 89 -165 89 -103C89 -55 96 -13 105 26H107C121 -3 134 -12 151 -12C172 -12 194 -5 221 16C279 61 330 124 384 194H386C381 159 377 141 368 105C343 3 363 -12 383 -12C416 -12 486 35 538 96Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.89,3.132)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z"></path></g></svg>,</span> and <span class="nowrap"><svg height="9.32509pt" id="M87" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -6.14359 10.7719 9.32509" width="10.7719pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z"></path></g></svg>,</span> using <span class="nowrap"><svg height="8.8423pt" id="M88" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 6.25863 8.8423" width="6.25863pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z"></path></g></svg>-</span>parameters of microstrip and CPW topologies of Figures <a href="../fig3/">3</a> and <a href="../fig4/">4</a> simulated with COMSOL Multiphysics and equations (<a href="https://static.hindawi.com/articles/jnm/volume-2019/3280461/figures/#EEq1" target="_blank">3</a>), (<a href="https://static.hindawi.com/articles/jnm/volume-2019/3280461/figures/#EEq2" target="_blank">4</a>), (<a href="https://static.hindawi.com/articles/jnm/volume-2019/3280461/figures/#EEq3" target="_blank">5</a>), (<a href="https://static.hindawi.com/articles/jnm/volume-2019/3280461/figures/#EEq5" target="_blank">7</a>), (<a href="https://static.hindawi.com/articles/jnm/volume-2019/3280461/figures/#EEq6" target="_blank">8</a>), (<a href="https://static.hindawi.com/articles/jnm/volume-2019/3280461/figures/#EEq7" target="_blank">9</a>), and (<a href="https://static.hindawi.com/articles/jnm/volume-2019/3280461/figures/#EEq8" target="_blank">10</a>).</div>

Journal of Nanomaterials

tab1

Table 1

Table 1: Microwave Characterization of Metal-Decorated Carbon Nanopowders Using a Single Transmission Line 