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

<div><svg height="12.5794pt" id="M479" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 32.3571 12.5794" width="32.3571pt" 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="M584 650H137L131 622C214 614 217 612 200 521L125 127C109 41 101 35 23 28L17 0H288L294 28C201 35 193 42 209 128L242 309H348C440 309 442 300 443 226H471L510 422H482C452 354 449 348 357 348H251L295 575C302 609 304 615 338 615H426C502 615 517 604 526 581C534 560 536 524 537 492L565 494C574 554 583 631 584 650Z" id="g113-71"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="607" vert-adv-y="607"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,7.895,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.393,0)"><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,-0.0091,20.44,3.132)"><path d="M757 650H506L497 618C579 615 596 608 596 570S591 477 571 380L560 327C516 117 435 41 309 41C199 41 108 114 144 303L187 529C202 609 208 612 291 618L296 650H30L24 618C109 612 113 606 99 529L58 299C33 161 62 83 113 41C161 0 222 -17 283 -17C348 -17 417 3 470 48C546 111 584 203 603 311L615 380C631 474 647 531 658 567C667 599 672 616 750 618L757 650Z" id="g50-86"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="769" vert-adv-y="769"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,27.67,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg> at the tuning frequency, versus a relative capacitance variation of a single adjustable impedance device contributing to <svg height="12.0314pt" id="M480" style="vertical-align:-3.2911pt" version="1.1" viewbox="-0.0498162 -8.7403 16.1505 12.0314" width="16.1505pt" 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="M625 186C574 85 512 32 429 32C293 32 194 153 194 337C194 485 274 621 419 621C496 621 573 586 606 468L643 475C636 537 629 583 620 638C593 644 519 665 438 665C199 665 42 523 42 317C42 158 152 -15 418 -15C486 -15 578 5 604 11C621 46 647 122 660 171L625 186Z" id="g13-65"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="676" vert-adv-y="676"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.788,3.132)"><path d="M757 650H506L497 618C579 615 596 608 596 570S591 477 571 380L560 327C516 117 435 41 309 41C199 41 108 114 144 303L187 529C202 609 208 612 291 618L296 650H30L24 618C109 612 113 606 99 529L58 299C33 161 62 83 113 41C161 0 222 -17 283 -17C348 -17 417 3 470 48C546 111 584 203 603 311L615 380C631 474 647 531 658 567C667 599 672 616 750 618L757 650Z" id="g50-86"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="769" vert-adv-y="769"></glyph.data></g></svg>: curve A if its initial value is <svg height="11.927pt" id="M481" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 22.0642 11.927" width="22.0642pt" 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="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="668" vert-adv-y="668"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.619,3.132)"><path d="M757 650H506L497 618C579 615 596 608 596 570S591 477 571 380L560 327C516 117 435 41 309 41C199 41 108 114 144 303L187 529C202 609 208 612 291 618L296 650H30L24 618C109 612 113 606 99 529L58 299C33 161 62 83 113 41C161 0 222 -17 283 -17C348 -17 417 3 470 48C546 111 584 203 603 311L615 380C631 474 647 531 658 567C667 599 672 616 750 618L757 650Z" id="g50-86"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="769" vert-adv-y="769"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,15.081,3.132)"><path d="M722 297H451L442 267C561 257 561 253 547 182L531 98C521 44 465 24 390 24C228 24 130 134 130 296C130 482 252 628 465 628C592 628 657 579 656 458L692 461C695 540 699 605 702 631C664 642 590 667 492 667C203 667 24 502 24 285C24 93 170 -17 368 -17C464 -17 543 11 617 28C613 43 612 68 620 106L635 182C649 255 652 258 716 268L722 297Z" id="g50-72"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="734" vert-adv-y="734"></glyph.data></g></svg>; curve B if its initial value is <svg height="11.927pt" id="M482" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 23.2607 11.927" width="23.2607pt" 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="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="668" vert-adv-y="668"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.619,3.132)"><path d="M757 650H506L497 618C579 615 596 608 596 570S591 477 571 380L560 327C516 117 435 41 309 41C199 41 108 114 144 303L187 529C202 609 208 612 291 618L296 650H30L24 618C109 612 113 606 99 529L58 299C33 161 62 83 113 41C161 0 222 -17 283 -17C348 -17 417 3 470 48C546 111 584 203 603 311L615 380C631 474 647 531 658 567C667 599 672 616 750 618L757 650Z" id="g50-86"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="769" vert-adv-y="769"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.826,3.132)"><path d="M870 650H622L613 619C694 615 708 606 708 559C708 531 702 477 686 396L636 136H633L281 650H127L120 619C180 616 198 611 212 592C227 572 232 558 220 503L166 254C148 169 139 131 126 89C112 43 85 35 33 32L24 0H280L286 32C208 37 189 44 189 93C189 124 198 179 212 250L267 526H271L622 -8H655L732 396C747 477 762 532 770 556C785 600 798 616 862 619L870 650Z" id="g50-79"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="888" vert-adv-y="888"></glyph.data></g></svg>; curve C if its initial value is <svg height="11.927pt" id="M483" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 21.096 11.927" width="21.096pt" 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="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="668" vert-adv-y="668"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.619,3.132)"><path d="M757 650H506L497 618C579 615 596 608 596 570S591 477 571 380L560 327C516 117 435 41 309 41C199 41 108 114 144 303L187 529C202 609 208 612 291 618L296 650H30L24 618C109 612 113 606 99 529L58 299C33 161 62 83 113 41C161 0 222 -17 283 -17C348 -17 417 3 470 48C546 111 584 203 603 311L615 380C631 474 647 531 658 567C667 599 672 616 750 618L757 650Z" id="g50-86"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="769" vert-adv-y="769"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.826,3.132)"><path d="M606 650H137L129 618C217 609 221 609 203 518L129 129C115 46 106 40 26 32L18 0H300L307 32C210 40 203 45 218 129L249 305H358C454 305 455 296 457 219H491L531 425H497C465 353 463 350 366 350H259L300 569C306 605 310 611 346 611H444C522 611 535 598 541 578C550 557 553 519 552 485L588 489L606 650Z" id="g50-71"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="630" vert-adv-y="630"></glyph.data></g></svg>.</div>

International Journal of Antennas and Propagation

fig19

Figure 19

Figure 19: A Tuning Computation Technique for a Multiple-Antenna-Port and Multiple-User-Port Antenna Tuner 