A Tuning Computation Technique for a Multiple-Antenna-Port and Multiple-User-Port Antenna Tuner

<div>Quality factor <svg height="11.8174pt" id="M267" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 15.0779 11.8174" width="15.0779pt" 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="M699 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z" id="g113-82"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="722" vert-adv-y="722"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,9.321,3.132)"><path d="M567 167L534 181C505 122 482 94 454 70C428 46 385 42 330 42C288 42 248 44 235 55C216 70 213 91 220 130L295 528C310 609 314 611 401 618L409 650H140L131 618C222 611 224 609 209 528L133 126C118 47 108 41 25 33L18 0H497C514 33 554 126 567 167Z" id="g50-77"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="579" vert-adv-y="579"></glyph.data></g></svg> of the diagonal entries of the impedance matrix <svg height="11.9218pt" id="M268" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -8.7403 13.7992 11.9218" width="13.7992pt" 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="M574 193C552 131 535 101 511 78C482 51 412 45 334 45C271 45 243 47 210 51C335 250 459 440 584 635L576 650H170C138 650 127 652 112 675H86C84 623 78 553 75 476L108 475C119 522 135 552 147 570C163 594 182 605 284 605H410C286 412 157 211 29 17L40 0H571C581 35 599 136 607 185L574 193Z" id="g13-88"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="619" vert-adv-y="619"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.047,3.132)"><path d="M567 167L534 181C505 122 482 94 454 70C428 46 385 42 330 42C288 42 248 44 235 55C216 70 213 91 220 130L295 528C310 609 314 611 401 618L409 650H140L131 618C222 611 224 609 209 528L133 126C118 47 108 41 25 33L18 0H497C514 33 554 126 567 167Z" id="g50-77"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="579" vert-adv-y="579"></glyph.data></g></svg> and quality factor <svg height="11.927pt" id="M269" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 16.1375 11.927" width="16.1375pt" 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="M699 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z" id="g113-82"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="722" vert-adv-y="722"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,9.321,3.132)"><path d="M690 629C653 643 577 667 483 667C225 667 24 528 24 292C24 92 174 -17 367 -17C448 -17 534 1 570 10C592 34 642 131 658 174C648 180 639 186 629 192C562 89 499 21 382 21C223 21 130 138 130 298C130 467 255 627 462 627C582 627 643 589 650 462L686 466C689 517 688 580 690 629Z" id="g50-68"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="714" vert-adv-y="714"></glyph.data></g></svg> of all entries of the admittance matrix <svg height="12.0314pt" id="M270" style="vertical-align:-3.2911pt" version="1.1" viewbox="-0.0498162 -8.7403 15.3285 12.0314" width="15.3285pt" 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="M646 650H414V615C488 606 489 592 473 552C449 491 398 397 369 340C330 414 289 488 254 558C237 594 236 606 301 615V650H16V615C71 607 88 597 125 531C185 425 222 358 249 304C258 284 262 274 262 249V138C262 47 253 41 168 34V0H493V34C403 41 396 47 396 138V266C396 297 399 308 414 335C462 429 489 472 526 531S583 608 646 615V650Z" id="g13-87"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="655" vert-adv-y="655"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.515,3.132)"><path d="M690 629C653 643 577 667 483 667C225 667 24 528 24 292C24 92 174 -17 367 -17C448 -17 534 1 570 10C592 34 642 131 658 174C648 180 639 186 629 192C562 89 499 21 382 21C223 21 130 138 130 298C130 467 255 627 462 627C582 627 643 589 650 462L686 466C689 517 688 580 690 629Z" id="g50-68"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="714" vert-adv-y="714"></glyph.data></g></svg>, for the antenna tuner of Section <a href="https://static.hindawi.com/articles/ijap/volume-2016/4758486/figures/#sec5">5</a>.</div>

International Journal of Antennas and Propagation

fig7

Figure 7

Figure 7: A Tuning Computation Technique for a Multiple-Antenna-Port and Multiple-User-Port Antenna Tuner 