.MCAD 309000000 \  docDocument MmcObject[    М.М. "d2_graph_format graphData% axisFormat)L)Ltrace2D&&&&&&&&& & & & & &&& dim_formatTmasslengthtimecharge temperature luminosity substanceNumericalFormatQdii shpRectV`╔¤ЄmcDocumentObjectState\РР mcPageModelK???┼ ?mcHeaderFooterI@I |P CHeaderFooterJ@J{n}@J@J№йё╥MbP?№йё╥MbP? TextState? TextStyle>@ Times New Roman0,0,255Serial_ParPropDefaultW?Normal >@Arial@W? Heading 1>@ Arial@W? Heading 2 >@ Arial@W? 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└└@└└`└└А└└аЁ√ дааААА                                                                            ЎЎЎЎЎЎЎ                                                                                                                   ЎЎЎЎЎЎ                                                                                                      ЎЎўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўЎЎ                                                                                          ЎўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўЎЎ                                                                                    ЎўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўЎ                                                                                 ЎўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўЎ                                                                               ўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўў                                                                               ЎўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўЎ                                                                                 ЎўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўЎ                                                                                     ўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўЎЎ                                                                                          ЎўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўЎЎ                                                                                                  ЎЎўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўЎ                                                                                                                ЎЎЎЎЎ                                                                                                                                       ЎЎЎЎЎЎЎЎЎЎЎЎЎЎЎ                                                                                                                                                                           ЎЎЎЎЎЎЎЎЎЎЎ                                                                                                                                                                                                      ўеSS\н                                                                                                                                                                                                   dўЎ                                                                                                                                                                                                еdнўннн\                                                                                                                                                                                               Sdннннннн\                                                                                                                                                                                             SнннннннннннSЎ       ЎЎЎ                                                                                                                                                                 н\dd\ўЎ      ўнннннннннннўS    \                                                                                                                                                              \\\\\\\н     Sннннннннннннў   нS\dеdSе                                                                                                                                                      ЎS\\еўў\\   Sdннннннннннd\\\SЎ еSнннннннўе\Ў                                                                                                                                                    SS\dўўўўўнd\dеўннннннннннd\dеd\ўЎSеннннннннн\d          Ўd\dЎ                                                                                                                                 SSdннн\\ўўўўўўўў\dSS\нннннннн\нўўўd\ўнннннннннннS       ЎSSS\                                                                                                                          Ў   еSннннеdўўўўўўўўўўўн\нўнS\нннннн\ўўўўўўнdнннннннннннннS\d\\d\\SSўннўўўнSS                                                                                                             ЎЎ     ўе\\еSнннўўеdўўўўўўўўўўў\енннdнннннн\ўўўўўўўў\ннннннннннннў\\\\d\\\\dеннўўўўўн\S                                                                                                           \dенd\ўЎdSSSннўўўўdнўўўўўўўўўўўddннннddннннн\ўўўў\ннннннннннннеd\dўўе\нўўўўўўў\ў                                                                                                         \нўўе\\SdенннSннўўўўdеўўўўўўўўўddнннннdннннн\ўўў\ннннннннннннd\нўўўўўўd\ўўўўўўўўнSS                                                                                                         \нўўўўўўў\dнннннн\ннўўўеdўўўўўўўddнннннdннннн\ўўўўdннннннннннне\dўўўўўўўўў\\ўўўўўўнн                                                                                                        еўўўўўўўddннннннdнўўўўў\еўўўўўd\ннннннннннннўdўўўн\ннннннннннннdеўўўўўўўўўўн\ўўўўўўўнSў                                                                                                       ўўўўўўўўе\ннннннdнўўўўў\dўўўў\\нннннннннннў\\ў\\ннннннннннннdеўўўўўўўўўўн\ўўўўўўннн                                                                                                       ўўўўўўўўе\нннннўdннўўўўўн\dўўўўнddеннннннннннўўў\\\\\ннSннннннннннн\ўўўўўўўўўўўў\еўўўўўннн                                                                                                       еўўўўўўўddнннннн\ннўўўўўўн\еўўўў\\енннннннннннўўўўўненнннўннннннннннdнўўўўўўўўўdеўўўўннSн                                                                                                       dеўўўўўўў\енннннннSнннўўўўўўў\\\dd\\dннннннннннннўўўўўўўўўўўне\нннннннннdеўўўўўн\ўўўўўннн  ЎЎ                                                                                                 \\ўўўўўеdннннннннdнннўўўўўўўеd\\\\dнннннннннненнўўўўўўўўўўўнееннннннннеdўўўўўўd\ўўўнннееSS\d                                                                                              Sне\dене\dннннннннннннннннннннннннннннннннннdSннўўўўўўўўўўўн\ SSSннннн\dўўўўў\\нннннннеS\dееd\S                                                                                           ўнннннеенннннннннннннўўўўўнннннS\ўннннннннdSннўўўўўўўўўнS ннннне\dнўўўўў\dнннннннннн\d\ўўўdSў                                                                                         еўннннннннннннннннннўўўўўннннSеннннннўdSSўнўўўўўўўннSнннннне\\ўнd\нннннннннннн\нўўўўўў\S                                                                                       \Sенннннне\\\\\ннннннўўўўўўўўнн\ SSdеdSS\ннўўўнdS Sенннннннd\\\\\\dнннўўўўўўнннееўўўўўўўd                                                                                       SннSўннннd\еўўнddнннннўўўўўўўўўннdSSS еннўўўне dннннннннеd\\dенннўўўўўўўўннdўўўўўўўўdS                                                                                      еSнннненннеdўўўўўнdнннўўўўўўўўўўннd SSSSS \ннннннннннннSенўўўўўўўўўўнdўўўўўўўўdнS                                                                                     ўеннннннне\ўўўўўў\\ннўўўўўўўўўўннd  ннннннннннў\Sенўўўўўўўўўўнеdўўўўўўў\ў\                                                                                     енннннннне\ўўўўўўўd\ннўўўўўўўўўўнн\ Sенннннннн\енўўўўўўўўўўўн\ўўўўўўўў\ў\                                                                                     Sўннннннне\ўўўе\нннўўўўўўўўўнў SSнўнннSSSdнўўўўўўўўўўнне\ўе\нў\                                                                                     Sўнннннннd\ўўўd\\ннўўўўўўўўнн SS\\S \нўўўўўўўўўўннне\еўне\dнн\                                                                                     \ўнннннннн\ўўў\SSннўўўўўўннd  нўўўўўўўўўннннннееееннне                                                                                     ннннннннннн\еў\Sнннннннн\ SннўўўўўннннннннннннннS                                                                                     \ннннннннн\\ўўўнd \dннўнеS ннўўўўўнннўннннннннннн                                                                                     Ўннннннннннннd\\S SеўнннўнSенннннннўе\Ў                                                                                    SdўнннннннннўS  S\еее\SSннннннўdSЎ                                                                                     SнннннннннSSSSSSd                                                                                   \SdнўнўнdS                                                                                     S\                                                                                     н                                                                                                                                                                                                                                                                                                                                                            Sн                                                                                       ў Ў                                                                                                                                                                                 н \dm╢о                                                                                           \\о╢ооmо╖m S                                                                                           ╖оmmmmmmmmооо╖╢ ў                                                                                           ╢mmmmmmmmооооо╢╢\                                                                                            SS оmmmmmmmооооооо╖╖╖ \S н                                                                                           Ў         S \mmmmmmmоооооо╢╖╖\d ў         ЎўЎ                                                                                                         ў \mmmmmmооооооо╖╖оS╖S                                                                                                                           mmmm\mоооооо╖╖S\mS                                                                                                                           meS dоооооо╖╖оS                                                                                                                          е S ╖ ооооо╢╖╖оо                                                                                                                           S о\Sоо╢dd mоооо╖╖о\d                                                                                                                            d Sdооо S\Sооооm╖dSо                                                                                                                            Ў оо\╖╖S╖╖╖о ╢оо╢╖е ў                                                                                                                             \╖m╖╖о╖╖╖╖ о╢о╖╖╖S Ў                                                                                                                            S ╖╖╖╖╖╖╖╖╖S о╖SS                                                                                                                              Ў d╖╖оооооо╢mS Sо                                                                                                                                 о╖╢оооо╢╖m                                                                                                                                  dо╢d н                                                                                                                               н                                                                                                                                 Ў е                                                                                                                                 е                                                                                                                                                                                                                                                                     S                                                                                                                                   Sў                                                                                                                                   Ў                                                                                                                                      \                                                                                                                                     Ўн                                                                                                                                                                                                                                                                             SЎ                                                                                                                                      SЎ                                                                                                                                      S                                                                                                                                       S                                                                                                                                       S                                                                                                                                       SЎ                                                                                                                                      SЎ                                                                                                                                      S                                                                                                                                                                                                                                                                               dЎ                                                                                                                                                                                                                                                                                  \                                                                                                                                           Ў                                                                                                                                                ЎdS \е                                                                                                                                                       Ў\ dнЎ                                                                                                                                                                Ў                                                                                                                                                                       S                                                                                                                                                                      Ў н╢оеS                                                                                                                                                                       Sd╢╢оооооо╢╢оеSS                                                                                                                                                                      Ў \╢╢оооооооооо╢╢╢╢нSS                                                                                                                                                                       ЎS\н╢╢оооооооооооооооооооо╢╢╢╢╖                                                                                                                                                                       е ооооооооўооўооўоооооооооооооо                                                                                                                                                                       ў оооооооооооооооооооооооооооо╢                                                                                                                                                                       Ў оооооооооооооооооооооооооооо╢н                                                                                                                                                                        ўS оооооооо╢╢╢╢╢╢╢╢╢╢╢╢оооооооо╢                                                                                                                                                                          Ў ооооооо╢╢оооооооооо╢╢оооооооо                                                                                                                                                                           Ў ооооооо╖╢оооооооооо╢╢оооооооо Ў                                                                                                                                                                           Ў ооооооо╖╖╖оооооооо╢╖╖ооооооо\н                                                                                                                                                                            Ў оооооо╢╖╖╖╖оооооо╖╖╖╖ооооооўS                                                                                                                                                                            Ў ооS\╢╖╖╖╖╖╖╢оооо╢╖╖╖╖╖╖╢еmооЎ                                                                                                                                                                             \╖╖╖╖╖╖╖╖╖╖оооо╖╖╖╖╖╖╖╖╖╖                                                                                                                                                                              но╖╖╖╖╖╖╖╖╖╖╖оооо╖╖╖╖╖╖╖╖╖╖╖                                                                                                                                                                          Ў ╖╖╖╖╖╖╖╖╖╖╖╖╖╖оо╢╖╖╖╖╖╖╖╖╖╖╖╖╢                                                                                                                                                                          ╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖еў                                                                                                                                                                     \╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖                                                                                                                                                                     S╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖m                                                                                                                                                                    ╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖Ў                                                                                                                                                                 о╖╖╖╖╖╖╖╖╖╖╖╖╖оооооооооооооо╢╖╖╖╖╖╖╖╖╖╖╖╖d                                                                                                                                                              Ў\S╖╢о╖╖╖╖╖╖╖╖╖оооооооооооооооооо╢╖╖╖╖╖╖╖╖о╢еЎ                                                                                                                                                             ўо╢m╢╖╖╖╖╖╖╖╖оооооооооооооооооооо╢╖╖╖╖╖╖╖╖m╖\н                                                                                                                                                             ╖m╖оmmmоо╢╢╢ооmmmmmо╢оmmmmmmоо╢╢ооmmmm╖╖╖m╖S                                                                                                                                                            оо╖╖╖╖оо╖╖╖╖╖╖╖╖оmmоо╖╖╖╖оmmоо╖╖╖╖╖╖╖╢оо╖╖╖eоS                                                                                                                                                          о╖e╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖о╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖e\╖\н                                                                                                                                                      ў\SS╖╖S╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖mо╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖m\╖о                                                                                                                                                  ўem\╖╖S╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖mmm╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖e\╖╖ S                                                                                                                                            ооmme\╖╖╖оSe╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖mmm╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖e\о╖╖оSооme                                                                                                                                          mmmmm\о╖╖╖╖eSm╖╖╖╖╖╖╖╖╖╖╖╖╖╖mmm╖╖╖╖╖╖╖╖╖╖╖╖╖╖╢eSо╖╖╖╖Sоmmо\ н                                                                                                                                        ЎоmmmmmS╖╖╖╖╖╖╖mS╢╖╖╖╖╖╖╖╖╖╖╖╖╖mmо╖╖╖╖╖╖╖╖╖╖╖╖╖о\о╖╖╖╖╖╖SmmmmmоS                                                                                                                                       ўmmmmmm\╖╖╖╖╖╖╖╖оe╖╖╖╖╖╖╖╖╖╖╖╖mmо╖╖╖╖╖╖╖╖╖╖╖╖╖eо╖╖╖╖╖╖╖\dmmmmm                                                                                                                                       Sdmmeeee╢╖╖╖╖╖╖╖╖╖о\╖╖╖╖╖╖╖╖╖╖╖╖mm╢╖╖╖╖╖╖╖╖╖╖╖╖eо╖╖╖╖╖╖╖╖╖оeeemme                                                                                                                                      mmeeeee╖╖╖╖╖╖╖╖╖╖╖╖о╖╖╖╖╖╖╖╖╖╖оmmmeem╖╖╖╖╖╖╖╖╖╖╖m╖╖╖╖╖╖╖╖╖╖╖╖eeeemоS                                                                                                                                     mmeee\e╖╖╖╖╖╖╖╖╖╖╖╖e╖╖╖╖╖╖╖╖╖╖eeeeeeeо╖╖╖╖╖╖╖╖╖╖d╖╖╖╖╖╖╖╖╖╖╖╖eeeemm\ў                                                                                                                                     dоeee\Sо╖╖╖╖╖╖╖╖╖╖╖╖╢╖╖оemооmeeeeee╖╖╖eemmоmem╢╖m╢╖╖╖╖╖╖╖╖╖╖╖╖e\eeemdd                                                                                                                                     dоmeeeeо╖╖╖╖╖╖╖╖╖╖╖╖╖╢оeeeeeeeeeeem╖╖╖оdeeeeeee╖о╖╖╖╖╖╖╖╖╖╖╖╖╖mSeeeоe\                                                                                                                                     \оmee\m╖╖╖╖╖╖╖╖╖╖╖╖╖╖╢оeeeeeeeemо╖╖╖╖╖╖╖╢оооо╖╖╢╖╖╖╖╖╖╖╖╖╖╖╖╖╖╢\eeeоmS                                                                                                                                     \оmeSe╢╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖eeeeeeeо╖╖╖╖╖╖╖╖╖╖╖╖╖m╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖о\eeоmS                                                                                                                                     \оme\\╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖eeeeeee╖╖╖╖╖╖╖╖╖╖╖╖╢m╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖о\emmmS                                                                                                                                     dоee\\╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖meeeeee╖╖╖╖╖╖╖╖╖╖╖╖╖mо╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖eeemm\                                                                                                                                     еme\\e╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖meeeeee╖╖╖╖╖╖╖╖╖╖╖╖eо╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖S\eme\                                                                                                                                      eSe\m╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╢eeeeee╖╖╖╖╖╖╖╖╖╖╖╖╖о╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖eeSem                                                                                                                                    \e\\\о╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖meeeeem╖╖╖╖╖╖╖╖╖╖╖╖╢о╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖eSeem\                                                                                                                                  Ў eоe\\e╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╢eeeeeeem╖╖╖╖╖╖╖╖╖╖╖m╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖mSe\eeЎ                                                                                                                                  mme\\о╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖eeeeeeeeо╖╖╖╖╖╖╖╖╖оm╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖оSe\emm                                                                                                                                emme\Sо╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖eeeeeeeeо╖╖╖╖╖╖╖╖╖mm╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖\\\emо                                                                                                                              ЎmmmeeS\╢╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖оeeeeeeeо╖╖╖╖╖╖╖╖╖e╢╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖\\eemmmн                                                                                                                             ў оmeee\\╢╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╢eeeeeeeо╖╖╖╖╖╖╖╖╖m╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖S\eeemm                                                                                                                             mmeeee\ ╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖eeeeeeeо╖╖╖╖╖╖╖╖о╢╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖ eeeemоd                                                                                                                           Ў meeee ╖╖╖╖╖╖╖╖╖╖╖╖╖ЎЎ╖╖╖meeeeeeо╖╖╖╖╖╖╖╖e╖╖╖╖ЎЎ╖╖╖╖╖╖╖╖╖╖╖╖S \eeemSў                                                                                                                            Sm\eeSm╖╖╖╖╖╖╖╖╖╖╖ЎЎЎЎЎЎ╖╖оeeeeeeо╖╖╖╖╖╖╖╖e╖╖╖ ЎЎЎЎ╢╖╖╖╖╖╖╖╖╖о\eeemS                                                                                                                            \e mm\dо╖╖╖╖╖╖╖╖edЎЎЎ╖╖meeeeeо╖╖╖╖╖╖╖╢о╖╖ЎЎеЎЎоeо╖╖╖╖╖╖╖ооmоe m Ў                                                                                                                            d\ eоSe╖╖╖╖╖╖╖╖╖eem\\Ў╖╖оeeeeeо╖╖╖╖╖╖╖о╢╖╖ЎЎ╢eо╖╖╖╖╖╖╖╖оdSmоSm Ў                                                                                                                            нSmmmо em╖╖╖╖╖╖╖╖╖оmeee\Ў╖╖eeeeeо╖╖╖╖╖╖╢e╖ЎЎ\Seeem╖╖╖╖╖╖╖╖╖mоmmmоd                                                                                                                              \ee н\о╖╖╖╖e╖╖╖╖╖╢mmeeeeeeeem╖eeeeeо╖╖╖╖╖╖mm╖eeee\eeeemmо╖╖╖╖╖e╖╖╖оо Smооe                                                                                                                              \╢╖╖╖╖m╖╖╖╖╖mmmeeeeeeeо╖eeeeeо╖╖╖╖╖╖eо╖meeeeeeeemm╖╖╖╖╖оe╖╖╖╢mS \S                                                                                                                                  Ў   ╖╖╖╖╖e╖╖╖╖╖оmmmmmmmm╖╖оeeeeо╖╖╖╖╖╖e╖╖╖mmmmmmmmо╖╖╖╖╖mm╖╖╖╢eS ееў                                                                                                                                    ╖╖╖╖╖SS╢╖╖╖╖оmmmmmmо╖╖╢eeeeо╖╖╖╖╖╖m╖╖╖╢mmmmmmо╖╖╖╖╖S╢╖╖╖╢S\                                                                                                                                         Ў ╖╖╖╖╖╖eeо╖╖╖╖╖╖╖╖╖mоeeeeо╖╖╖╖╖╖ооe╖╖╖╖╖╖╖╖╖оeS╖╖╖╖╢                                                                                                                                          ╖╖╖╖╖╖╢Se╖╖╖╖╖╖\mmeeeо╖╖╖╖╖╖╢оm╖╖╖╖╖╖eSо╖╖╖╖╢                                                                                                                                          н ╖╖╖╖╖╖╖meS\оeeeо╖╖╖╖╖о╖eee╖╖╖╖╖╢ ў                                                                                                                                         е ╖╖╖╖╖╖╖╖╖оSоeeeо╖╖╖╖╖e╢\о╖╖╖╖╖╖╖о н                                                                                                                                         d ╖╖╖╖╖╖╖╖╖╖╢оSeeeо╖╖╖╖mmSm╖╖╖╖╖╖╖╖╖о н                                                                                                                                         d ╖╖╖╖╖╖╖╖╖╖╖╖╖╖mSоeeо╖╖╖оо╖Sd╖╖╖╖╖╖╖╖╖╖╖╖m н                                                                                                                                         е ╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖dSeeо╖╖╖e╖\e╖╖╖╖╖╖╖╖╖╖╖╖╖╖m н                                                                                                                                         ў╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖mS\╖╖╖оem╖╖m╢╖╖╖╖eSm╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖e ў                                                                                                                                        Ўо╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖ооmо╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖S                                                                                                                          Ўe╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖Ў                                                                                                                  о╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖                                                                                                             e╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖                                                                                                          ╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖о                                                                                                      нe╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖eе                                                                                                    о╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╢                                                                                                  d ╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖e н                                                                                                 ўо╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖S                                                                                                  ╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖Ў╖╖╖╖╖╖╖                                                                                                          о╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖ЎЎЎ╖╖╖╖╖╖о                                                                                                              e╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╢╖╖╖╖╖ЎЎЎЎ╖╖╖╖о                                                                                                                 ╢╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖ЎЎЎЎЎ╖╖ЎЎЎ╖╖╖╖                                                                                                                     S╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖ЎЎЎЎЎЎЎ╖ЎЎЎ╖╖╖╖╖н                                                                                                                 ╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖ЎЎЎЎЎЎЎЎЎ╖╢╖╖╖╖╖                                                                                                                   d о╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖ЎЎЎЎЎЎЎЎЎ╖╖╖╖╖╖╖                                                                                                                    о╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖ЎЎЎЎЎЎЎЎЎЎ╖╖╖╖e                                                                                                                   ЎS╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖ЎЎЎЎЎЎЎЎЎЎ╖╖╖m                                                                                                                       S╢╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖╖ЎЎЎЎЎЎЎЎЎ╖╖m S                                                                                                                     ╖╖о╖╖оe╖╖╖\e╢╖╖╖╖╖╖╖╖╖ЎЎЎЎЎЎЎЎЎ╖╖e                                                                                                                     m╖eо╖╖S\о╖Sem╖╖╖╖╖╖ЎЎЎЎЎЎЎЎЎ╖о S                                                                                                                    ЎоSeSm╖╖╖ЎЎЎЎЎоS                                                                                                                          \ eS╢╖╖Ўm\Ў                                                                                                                             ў\╢╖╖╖\                                                                                                                                       ўS eS                                                                                                                                      Ў  d                                                                                                                                          \ \                                                                                                                                         \  \                                                                                                                                                  \  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ParPropMap9. RangeElem<. ParPropData: RangeData=@W                         EmbedMap1< EmbedData2EmbedObj3 EmbedObjPtr4LinkMap/.<.LinkData0    @TitleTimes New Roman   eqRegionB@UАgьдбА.tree@ p@@,┼А@@╬@ @@dA!@@ОpА"@@д!s#@@╩А$@@√@#%@@d$\w.u&@@д$s'@@√А#(@@t'1)@@Й╟А'*@@t)1+@@√А),@@d+s-@@д+p2. CollapseBarC@U╚K╘╚╤-@M    &-&- /@Tmasslengthtimecharge temperature luminosity substance@Qdii @V@\Ё┤?        А@O@Pє   Ї         VariablesTimes New Roman@Pє   Ї         ConstantsTimes New Roman@Pє   Ї        TextArial@Pє   Ї        Greek VariablesSymbol@Pє   Ї        User 1Arial@Pє   Ї        User 2 Courier New@Pє   Ї        User 3Arial@Pє   Ї        User 4Times New Roman@Pє   Ї        User 5Times New Roman@Pє   Ї        User 6Arial@Pє   Ї        User 7Times New Roman@Pє   Ї        SymbolsSymbol@Pє   є        Current Selection FontArial@Pє   є        Undefined Font@Pє   є        HeaderArial@Pє   є        FooterArial@Pє   Ї        Rotated Math FontTimes New Roman0LockD@UK Ўuseful functions and identities1*@U5C(ї%%3%3-@U_______________________________________ Useful Functions and Trigonometric Identities7='U2<'3 ChrPropData81nArial4<58126<7814629((-U8<(9:@W                        :<-;:@W                        8::1<<=23>4/U?<A?8A;@ Times New Roman0,0,255AA@A>9OAB@@┤B=6B?@@дB:wattB@@B@U(ДМЭDШ<BA@@ pBB@@ ┴АBABC@@dBBnWBD@@╩АBBBE@@№@BDBF@@tBE10BG@@ХKАBEBH@@┤BG9BI@@дBDwattBJ@B@U░ДЭ╠Ш=BK@@ pBL@@ ┴АBKBM@@dBLpWBN@@╩АBLBO@@№@BNBP@@tBO10BQ@@ХKАBOBR@@┤BQ12BS@@дBNwattBT@B@UЬi╡░>BU@@ pBV@@ ┴АBUBW@@dBVmJBX@@╩АBVBY@@№@BXBZ@@tBY10B[@@ХKАBYB\@@┤B[3B]@@дBXjouleB^@B@UРЬя╡д░?B_@@ pB`@@ ┴АB_Ba@@dB`\mJBb@@╩АB`Bc@@№@BbBd@@tBc10Be@@ХKАBcBf@@┤Be6Bg@@дBbjouleBh@B@U(ЬЗ╡<░@Bi@@ pBj@@ ┴АBiBk@@dBjnJBl@@╩АBjBm@@№@BlBn@@tBm10Bo@@ХKАBmBp@@┤Bo9Bq@@дBljouleBr@B@U░Ь╡─░ABs@@ pBt@@ ┴АBsBu@@dBtpJBv@@╩АBtBw@@№@BvBx@@tBw10By@@ХKАBwBz@@┤By12B{@@дBvjouleB|@B@U╝G═╚BB}@@ pB~@@ ┴АB}B@@dB~VBА@@╩АB~BБ@@tBА1BВ@@дBАvoltBГ@B@UР╝╬═и╚CBД@@ pBЕ@@М┴АBДBЖ@@dBЕmVBЗ@@Ц─АBЕBИ@@+@BЗ@XBЙ@@дBЗvoltBК@B@U(┤Д═?╚DBЛ@@ pBМ@@ ┴АBЛBН@@dBМ\mVBО@@╩АBМBП@@№@BОBР@@tBП10BС@@ХKАBПBТ@@┤BС6BУ@@дBОvoltBФ@B@U░┤ ═╟╚EBХ@@ pBЦ@@ ┴АBХBЧ@@dBЦnVBШ@@╩АBЦBЩ@@№@BШBЪ@@tBЩ10BЫ@@ХKАBЩBЬ@@┤BЫ9BЭ@@дBШvoltBЮ@B@U ┤x═7╚FBЯ@@ pBа@@ ┴АBЯBб@@dBаpVBв@@╩АBаBг@@№@BвBд@@tBг10Bе@@ХKАBгBж@@┤Bе12Bз@@дBвvoltBи@B@U▄IЁ*шз"Bй@@ pBк@@ ┴АBйBл@@dBкV.rmsBм@@дBкvoltBн@B@UР╨с·╣ши"Bо@@ pBп@@ ┴АBоB░@@dBпV.0_pkB▒@@√АBпB▓@@dB▒V.rmsB│@@Ъ{АB▒B┤@@┤B│2B╡@B@U(╨З°Xшл"B╢@@ pB╖@@ ┴АB╢B╕@@dB╖V.pk_pkB╣@@√АB╖B║@@dB╣V.0_pkB╗@@┤B╣2B╝@B@U░╘3Ётш░,B╜@@ pB╛@@ ┴АB╜B┐@@dB╛mV.0_pkB└@@╩АB╛B┴@@№@B└B┬@@tB┴10B├@@ХKАB┴B─@@┤B├3B┼@@дB└V.0_pkB╞@B@UH╘╧ЁБш┤,B╟@@ pB╚@@ ┴АB╟B╔@@dB╚ mV.pk_pkB╩@@╩АB╚B╦@@№@B╩B╠@@tB╦10B═@@ХKАB╦B╬@@┤B═3B╧@@дB╩V.pk_pkB╨@B@UЇs3╜,B╤@@ pB╥@@ ┴АB╤B╙@@dB╥mV.rmsB╘@@╩АB╥B╒@@№@B╘B╓@@tB╒10B╫@@ХKАB╒B╪@@┤B╫3B┘@@дB╘V.rmsB┌@B@UL(, ╖,B█@@ pB▄@@ ┴АB█B▌@@dB▄A.rmsB▐@@дB▄ampB▀@B@UРх2╗ ╕,Bр@@ pBс@@ ┴АBрBт@@dBсA.0_pkBу@@√АBсBф@@dBуA.rmsBх@@Ъ{АBуBц@@┤Bх2Bч@B@U(Л0Z ╣,Bш@@ pBщ@@ ┴АBшBъ@@dBщA.pk_pkBы@@√АBщBь@@dBыA.0_pkBэ@@┤Bы2Bю@B@U░ ;(ы ║,Bя@@ pBЁ@@ ┴АBяBё@@dBЁ mA.pk_pkBЄ@@╩АBЁBє@@№@BЄBЇ@@tBє10Bї@@ХKАBєBЎ@@┤Bї3Bў@@дBЄA.pk_pkB°@B@UH ┼(| ╗,B∙@@ pB·@@ ┴АB∙B√@@dB·mA.0_pkB№@@╩АB·B¤@@№@B№B■@@tB¤10B @@ХKАB¤C@@┤B 3C@@дB№A.0_pkC@B@U,wH5@╝,C@@ pC@@ ┴АCC@@dCmA.rmsC@@╩АCC@@№@CC@@tC10C @@ХKАCC @@┤C 3C @@дCA.rmsC @B@UL@]XGC @@ pC@@ ┴АC C@@dCAC@@╩АCC@@tC1C@@дCampC@B@UРL╤]кXHC@@ pC@@М┴АCC@@dCmAC@@Ц─АCC@@+@C@XC@@дCampC@B@U(Kg]@X╬C@@ pC@@М┴АCC@@dC\mAC@@Ц─АCC@@+@C@XC @@дCampC!@B@U░D]╔XJC"@@ pC#@@ ┴АC"C$@@dC#nAC%@@╩АC#C&@@№@C%C'@@tC&10C(@@ХKАC&C)@@┤C(9C*@@дC%ampC+@B@U DЕ]9XKC,@@ pC-@@ ┴АC,C.@@dC-pAC/@@╩АC-C0@@№@C/C1@@tC010C2@@ХKАC0C3@@┤C212C4@@дC/ampC5@B@UР\шuжpLC6@@ pC7@@ ┴АC6C8@@dC7fAC9@@╩АC7C:@@№@C9C;@@tC:10C<@@ХKАC:C=@@┤C<15C>@@дC9ampC?@B@U(\Вu@pMC@@@ pCA@@ ┴АC@CB@@dCAaACC@@╩АCACD@@№@CCCE@@tCD10CF@@ХKАCDCG@@┤CF18CH@@дCCampCI@B@Ut^Н!ИNCJ@@ pCK@@ ┴АCJCL@@dCKk\WCM@@╩АCKCN@@№@CMCO@@tCN10CP@@┤CN3CQ@@дCMohmCR@B@UР{╓НоИOCS@@ pCT@@М┴АCSCU@@dCTM\WCV@@Ц─АCTCW@@+@CV@XCX@@дCVohmCY@B@U(tАНCИPCZ@@ pC[@@ ┴АCZC\@@dC[G\WC]@@╩АC[C^@@№@C]C_@@tC^10C`@@┤C^9Ca@@дC]ohmCb@B@U░tН╠ИQCc@@ pCd@@ ┴АCcCe@@dCdm\WCf@@╩АCdCg@@№@CfCh@@tCg10Ci@@ХKАCgCj@@┤Ci3Ck@@дCfohmCl@B@U txНEИRCm@@ pCn@@ ┴АCmCo@@dCnkohmCp@@╩АCnCq@@№@CpCr@@tCq10Cs@@┤Cq3Ct@@дCpohmCu@B@U(МuеCа╬Cv@@ pCw@@ ┴АCvCx@@dCw\m\WCy@@╩АCwCz@@№@CyC{@@tCz10C|@@ХKАCzC}@@┤C|6C~@@дCy\WC*@U@Сnг@ая$╨. -)Need to add inverted W symbol for siemens7)CА<CБ8CCВ<CГ8C@ Times New Roman0,0,255CАCД<CЕ8CCВCДCВ9)CЖ<)CЗ:@W,            1CИ</)CЙ<)CК0    @ NormalTimes New Roman  CЛ@B@U░Фн╪иSCМ@@ pCН@@ ┴АCМCО@@dCНmohmCП@@╩АCНCР@@№@CПCС@@tCР10CТ@@ХKАCРCУ@@┤CТ3CФ@@дCПohmCХ@B@U│I┼└TCЦ@@ pCЧ@@М┴АCЦCШ@@dCЧ\mFCЩ@@Ц─АCЧCЪ@@+@CЩ@XCЫ@@дCЩfaradCЬ@B@UР┤╤┼е└UCЭ@@ pCЮ@@М┴АCЭCЯ@@dCЮnFCа@@Ц─АCЮCб@@+@Cа@XCв@@дCаfaradCг@B@U(┤i┼=└VCд@@ pCе@@М┴АCдCж@@dCеpFCз@@Ц─АCеCи@@+@Cз@XCй@@дCзfaradCк@B@U░м┼├└WCл@@ pCм@@ ┴АCлCн@@dCмfFCо@@╩АCмCп@@№@CоC░@@tCп10C▒@@ХKАCпC▓@@┤C▒15C│@@дCоfaradC┤@B@U мЖ┼5└XC╡@@ pC╢@@ ┴АC╡C╖@@dC╢aFC╕@@╩АC╢C╣@@№@C╕C║@@tC╣10C╗@@ХKАC╣C╝@@┤C╗18C╜@@дC╕faradC╛@B@U╠D▌!╪YC┐@@ pC└@@М┴АC┐C┴@@dC└mHC┬@@Ц─АC└C├@@+@C┬@XC─@@дC┬mHC┼@B@UР─ў▌и╪ZC╞@@ pC╟@@ ┴АC╞C╚@@dC╟\mHC╔@@╩АC╟C╩@@№@C╔C╦@@tC╩10C╠@@ХKАC╩C═@@┤C╠6C╬@@дC╔henryC╧@B@U(─П▌@╪[C╨@@ pC╤@@ ┴АC╨C╥@@dC╤nHC╙@@╩АC╤C╘@@№@C╙C╒@@tC╘10C╓@@ХKАC╘C╫@@┤C╓9C╪@@дC╙henryC┘@B@U░─▌╚╪О,C┌@@ pC█@@ ┴АC┌C▄@@dC█pHC▌@@╩АC█C▐@@№@C▌C▀@@tC▐10Cр@@ХKАC▐Cс@@┤Cр12Cт@@дC▌henryCу@B@U ╠T▌/╪]Cф@@ pCх@@ ┴АCфCц@@dCхFCч@@дCхfaradCш@B@U▄2эшК,Cщ@@ pCъ@@ ┴АCщCы@@dCъsCь@@дCъsecCэ@B@UР▄┴экшМ,Cю@@ pCя@@М┴АCюCЁ@@dCяminCё@@Ц─АCяCЄ@@+@Cё@XCє@@АCёCЇ@B@UЇP,хCї@@ pCЎ@@ ┴АCїCў@@dCЎweekC°@@╩АCЎC∙@@tC°7C·@@дC°dayC√@B@UРЇр║шC№@@ pC¤@@ ┴АC№C■@@dC¤weeksC @@дC¤weekD@B@U(ЇZC▀D@@ pD@@М┴АDD@@dDdayD@@Ц─АDD@@+@D@XD@@АDD@B@U░Ї┘┬┌D@@ pD @@М┴АDD @@dD hrD @@Ц─АD D @@+@D @XD @@АD D@B@U ЇI2▌D@@ pD@@М┴АDD@@dDyrD@@Ц─АDD@@+@D@XD@@АDD@B@Uаыф╩▄,D@@ pD@@ ┴АDD@@dDmonthD@@√АDD@@dDyrD@@┤D12D@B@U9% ^D@@ pD@@ ┴АDD@@dDSD @@╩АDD!@@dD 1D"@@дD secD#@B@UР щ%з _D$@@ pD%@@ ┴АD$D&@@dD%msD'@@╩АD%D(@@№@D'D)@@tD(10D*@@ХKАD(D+@@┤D*3D,@@дD'secD-@B@U( x%@ `D.@@ pD/@@ ┴АD.D0@@dD/mSD1@@╩АD/D2@@№@D1D3@@tD210D4@@ХKАD2D5@@┤D43D6@@дD1secD7@B@U░ %┼ aD8@@ pD9@@ ┴АD8D:@@dD9\msD;@@╩АD9D<@@№@D;D=@@tD<10D>@@ХKАD<D?@@┤D>6D@@@дD;secDA@B@U( v%> bDB@@ pDC@@ ┴АDBDD@@dDC\mSDE@@╩АDCDF@@№@DEDG@@tDF10DH@@ХKАDFDI@@┤DH6DJ@@дDEsecDK@B@U$_=8cDL@@ pDM@@ ┴АDLDN@@dDMnsDO@@╩АDMDP@@№@DODQ@@tDP10DR@@ХKАDPDS@@┤DR9DT@@дDOsecDU@B@UР$▐=ж8dDV@@ pDW@@ ┴АDVDX@@dDWnSDY@@╩АDWDZ@@№@DYD[@@tDZ10D\@@ХKАDZD]@@┤D\9D^@@дDYsecD_@B@U($|=>8eD`@@ pDa@@ ┴АD`Db@@dDapSDc@@╩АDaDd@@№@DcDe@@tDd10Df@@ХKАDdDg@@┤Df12Dh@@дDcsecDi@B@U░$ =┼8fDj@@ pDk@@ ┴АDjDl@@dDkpsDm@@╩АDkDn@@№@DmDo@@tDn10Dp@@ХKАDnDq@@┤Dp12Dr@@дDmsecDs@B@U($В=:8gDt@@ pDu@@ ┴АDtDv@@dDufsDw@@╩АDuDx@@№@DwDy@@tDx10Dz@@ХKАDxD{@@┤Dz15D|@@дDwsecD}@B@UDDU-PhD~@@ pD@@М┴АD~DА@@╩@DDБ@@tDА1DВ@@дDАHzDГ@@Ц─АDDД@@+@DГ@XDЕ@@дDГ _n_u_l_l_DЖ@B@UР<рUмPiDЗ@@ pDИ@@ ┴АDЗDЙ@@dDИkHzDК@@╩АDИDЛ@@№@DКDМ@@tDЛ10DН@@┤DЛ3DО@@дDКHzDП@B@U(DhUIPjDР@@ pDС@@М┴АDРDТ@@dDСMHzDУ@@Ц─АDСDФ@@+@DУ@XDХ@@дDУHzDЦ@B@U░DьU═PkDЧ@@ pDШ@@М┴АDЧDЩ@@dDШGHzDЪ@@Ц─АDШDЫ@@+@DЪ@XDЬ@@дDЪHzDЭ@B@UРT▄mпhlDЮ@@ pDЯ@@ ┴АDЮDа@@dDЯkradDб@@╩АDЯDв@@№@DбDг@@tDв10Dд@@┤Dв3Dе@@дDбradDж@B@U(TzmMhmDз@@ pDи@@ ┴АDзDй@@dDиMradDк@@╩АDиDл@@№@DкDм@@tDл10Dн@@┤Dл6Dо@@дDкradDп@B@U░T■m╤hnD░@@ pD▒@@ ┴АD░D▓@@dD▒GradD│@@╩АD▒D┤@@№@D│D╡@@tD┤10D╢@@┤D┤9D╖@@дD│radD╕@B@U░lц}╓xOD╣@@ pD║@@ ┴АD╣D╗@@dD║dollarD╝@@┤D║1D╜@B@Ulp},xъD╛@@ pD┐@@ ┴АD╛D└@@dD┐yenD┴@@╩АD┐D┬@@tD┴110D├@@дD┴dollarD─@B@UlPЕАrD┼@@ pD╞@@ ┴АD┼D╟@@dD╞fCD╚@@╩АD╞D╔@@№@D╚D╩@@tD╔10D╦@@ХKАD╔D╠@@┤D╦15D═@@дD╚CD╬@B@UРl█ЕзАsD╧@@ pD╨@@ ┴АD╧D╤@@dD╨pCD╥@@╩АD╨D╙@@№@D╥D╘@@tD╙10D╒@@ХKАD╙D╓@@┤D╒12D╫@@дD╥CD╪@B@U0lvЕPАtD┘@@ pD┌@@ ┴АD┘D█@@dD┌TOLD▄@@№АD┌D▌@@tD▄10D▐@@ХKАD▄D▀@@┤D▐4Dр@B@UРД╡ХеР┐Dс@@ pDт@@ ┴АDсDу@@dDтsqDф@@┤Dт1Dх@B@U░{√а╧РPDц@@ pDч@@ ┴АDцDш@@dDчcentDщ@@√АDчDъ@@dDщdollarDы@@┤Dщ100Dь@B@UДVХ5РQDэ@@ pDю@@ ┴АDэDя@@dDюcentsDЁ@@дDюcentDё@B@UМDЭ4ШuDЄ@@ pDє@@ ┴АDЄDЇ@@dDєsquareDї@@┤Dє1DЎ@B@UФwе0аьDў@@ pD°@@ ┴АDўD∙@@dD°euroD·@@╩АD°D√@@tD·1.09D№@@дD·dollarD¤@B@UРд╣╡й░▌,D■@@ pD @@ ┴АD■E@@dD pinE@@┤D 1E@B@U0Ьu╡O░Е,E@@ pE@@ ┴АEE@@dEppmE@@№АEE@@tE10E@@ХKАEE @@┤E6E @B@U░дц╡╛░ЫE @@ pE @@ ┴АE E @@tE $E@@дE dollarE@B@U░╗·══╚╓"E@@ pE@@ ┴АEE@@╬@EE@@dE\░E@@ОpАEE@@дExE@@╩АEE@@dExE@@дEdegE@B@U╗_═H╚╫"E@@ pE@@М┴АEE@@╬@EE@@dEcosE@@ОpАEE@@R╠АEE @@tE60E!@@дE\░E"@@Ц─АEE#@@+@E"@XE$@@АE"E%*@Up╣╬╠y╚╪"╪^U-The function 7 E&< E'8E%E(<E)8E%?E&E(E(9E*<E+:@W                        1E,<E-2 3E.4E/@B@U╚╗╧═╩╚ME0@@ pE1@@┤E0\░/E2<E30    @ NormalTimes New Roman  E4@B@U░╙▄х╛р╚E5@@ pE6@@ ┴АE5E7@@dE6\░E8@@дE6degE9@B@U╙Tх=р╔E:@@ pE;@@М┴АE:E<@@╬@E;E=@@dE<asinE>@@ОpАE<E?@@┤E>1E@@@Ц─АE;EA@@+@E@@XEB@@дE@\░EC*@Up╤╨фyр╩╪`U-The variable 7 ED< EE8ECEF<EG8EC?EDEFEF9EH<EI:@W                        1EJ<EK2 3EL4EM@B@U╚╙╧х╩рJEN@@ pEO@@┤EN\░/EP<EQ0    @ NormalTimes New Roman  ER@B@Uь.¤°п,ES@@ pET@@ ┴АESEU@@dETbitEV@@┤ET1EW@B@U░ы╣¤│°┌"EX@@ pEY@@дEX\╗EZ@B@U4$ %E[@@ pE\@@ ┴АE[E]@@dE\bitsE^@@┤E\1E_@B@UH√Ж d %E`@@ pEa@@ ┴АE`Eb@@dEabpsEc@@√АEaEd@@dEcbitsEe@@дEcsecEf@B@Uа№Є┬%Eg@@ pEh@@ ┴АEgEi@@dEhkbpsEj@@╩АEhEk@@№@EjEl@@tEk10Em@@┤Ek3En@@дEjbpsEo@B@U№`0%Ep@@ pEq@@ ┴АEpEr@@dEqMbpsEs@@╩АEqEt@@№@EsEu@@tEt10Ev@@┤Et6Ew@@дEsbpsEx@B@U░╣│█"Ey@@ pEz@@дEy\▒E{@B@Uш4 ▄"E|@@ pE}@@ ┴АE|E~@@╬@E}E@@dE~\╨EА@@ОpАE~EБ@@дEАxEВ@@╬АE}EГ@@dEВargEД@@ОpАEВEЕ@@дEДxEЖ@B@UH╣в▌"EЗ@@ pEИ@@М┴АEЗEЙ@@Q╠@EИEК@@dEЙ\╨EЛ@@ОpАEЙEМ@@Й╟АEЛEН@@tEМ1EО@@╩АEМEП@@tEО2EР@@Ъ{АEОEС@@ХKАEРEТ@@┤EС1EУ@@Ц─АEИEФ@@+@EУ@XEХ@@дEУ\░EЦ@B@Uш-(j$EЧ@@ pEШ@@ ┴АEЧEЩ@@╬@EШEЪ@@dEЩ*EЫ@@ОpАEЩEЬ@@дEЫxEЭ@@кМАEШEЮ@@dEЭxEЯ@B@UH╡-Ю(k$Eа@@ pEб@@М┴АEаEв@@R╠@EбEг@@Оp@EвEд@@Й╟АEгEе@@tEд1Eж@@╩АEдEз@@tEж2Eи@@Ъ{АEжEй@@ХKАEиEк@@┤Eй1Eл@@дEв*Eм@@Ц─АEбEн@@+@Eм@XEо@@АEмEп*@U╪ї+╪(ё$╨√-(Need to superscript the conjugate symbol7(9(E░<(E▒:@W,            1E▓</(E│<(E┤0    @ NormalTimes New Roman  E╡@B@U4aE,@▀,E╢@@ pE╖@@ ┴АE╢E╕@@dE╖cupE╣@@╩АE╖E║@@tE╣236.6E╗@@дE╣mLE╝@B@U`4ЩEy@р,E╜@@ pE╛@@ ┴АE╜E┐@@dE╛tspE└@@╩АE╛E┴@@tE└5E┬@@дE└mLE├@B@U04аEM@ю,E─@@ pE┼@@ ┴АE─E╞@@dE┼pintE╟@@╩АE┼E╚@@tE╟  473.176473E╔@@дE╟mLE╩@B@ULP]2Xё,E╦@@ pE╠@@ ┴АE╦E═@@dE╠cupsE╬@@дE╠cupE╧@B@U`Lж]АXт,E╨@@ pE╤@@ ┴АE╨E╥@@dE╤tbspE╙@@╩АE╤E╘@@tE╙15E╒@@дE╙mLE╓@B@U└L]сXф,E╫@@ pE╪@@М┴АE╫E┘@@dE╪fl_ozE┌@@Ц─АE╪E█@@+@E┌@XE▄@@дE┌mLE▌@B@U@T┤ed`ь,E▐@@ pE▀@@ ┴АE▐Eр@@dE▀quartEс@@╩АE▀Eт@@tEс  0.946352946Eу@@дEсLEф@B@U╨T eу`Ё,Eх@@ pEц@@ ┴АEхEч@@dEцqtEш@@дEцquartEщ@B@U\?m'hє,Eъ@@ pEы@@М┴АEъEь@@dEыgalEэ@@Ц─АEыEю@@+@Eэ@XEя@@дEэLEЁ@B@UPdСulpц,Eё@@ pEЄ@@М┴АEёEє@@dEЄpintEЇ@@Ц─АEЄEї@@+@EЇ@XEЎ@@дEЇcupEў*@UБИз9Ре,E°@HE∙@HE·@L/http://twt.mpei.ac.ru/ochkov/Units/advice64.htm╚p&░-@^Temperature Calculations from Valery Ochkov, http://twt.mpei.ac.ru/ochkov/Units/advice64.htm. 7\+^E√<+E№8Eўm Comic Sans MS0,0,255E¤<E■8EўE√E @@Оp@F=F?@@Й╟АF>F@@@dF?tFA@@┤F?459.67FB@@дF=RFC@B@U█OЁ*шб,FD@@ pFE@@ ┴АFDFF@@dFEt.1FG@@R╠АFEFH@@tFG10FI@@дFG\░CFJ@B@U░█ьЁ┬шв,FK@@ pFL@@ ┴АFKFM@@dFLt.2FN@@R╠АFLFO@@tFN212FP@@дFN\░FFQ*@UёF8г,╨.%*-@XCalculations: (just as you would normally do) (remember they are calculated using K/R)7V XFR< FS8FQg Comic Sans MS0,0,255FT@@М┴АG=G?@@dG>\DtG@@@Ц─АG>GA@@+@G@@XGB@@┤G@\░\DFGC*@UQЎd`Т,╨▐─-"(use this unit for displaying DC)7 "GD<GE8GCGF<GG8GC?GDGH<GI8GC@ Times New Roman0,0,255GFGJ<GK8GCGHGJGF9"GL<"GM:@W,            1GN<GO23GP4GQ@B@U╨S╫e╥`K$GR@@ pGS@@дGR\░/"GT<"GU0    @ NormalTimes New Roman  GV@B@UcHu5pУ,GW@@ pGX@@ ┴АGWGY@@tGX\░\DCGZ@@дGXKG[@B@U{QН+ИФ,G\@@ pG]@@М┴АG\G^@@dG]\DtG_@@Ц─АG]G`@@+@G_@XGa@@┤G_\░\DCGb*@U СЙд6аF,░if- Entering dBm7 Gc< Gd8Gbm Comic Sans MS0,0,2559 Ge< Gf:@W                        1Gg</ Gh< Gi0    @ NormalTimes New Roman  Gj*@U б│3░G,╨ё┘-#Use normal entry for power in watts7#9#Gk<#Gl:@W                        1Gm</#Gn<#Go0    @ NormalTimes New Roman  Gp@B@U ┤q═>╚H,Gq@@ pGr@@ ┴АGqGs@@dGrmWGt@@╩АGrGu@@№@GtGv@@tGu10Gw@@ХKАGuGx@@┤Gw3Gy@@дGtWGz@B@U ╠dр5╪I,G{@@ pG|@@ ┴АG{G}@@dG|P.1G~@@╩АG|G@@tG~0.1GА@@дG~mWGБ*@U сHє*ЁJ,╨(-,Use this function for entering values in dBm7,9,GВ<,GГ:@W                        1GД</,GЕ<,GЖ0    @ NormalTimes New Roman  GЗ@B@U °╟%i K,GИ@@ pGЙ@@ ┴АGИGК@@╬@GЙGЛ@@dGКdBmGМ@@ОpАGКGН@@дGМPdBmGО@@╩АGЙGП@@╩@GОGР@@tGП1GС@@дGПmWGТ@@№АGОGУ@@tGТ10GФ@@√АGТGХ@@dGФPdBmGЦ@@┤GФ10GЧ@B@U ,e@58L,GШ@@ pGЩ@@ ┴АGШGЪ@@dGЩP.2GЫ@@R╠АGЩGЬ@@tGЫ10GЭ@@дGЫdBmGЮ*@U╕(Я=╕8M,╨ч -(actually stored in watts:)7GЯ<Gа8GЮk Comic Sans MS0,0,255Gб<Gв8GЮ+ Comic Sans MS0,0,255GЯGг<Gд8GЮk Comic Sans MS0,0,255GбGгGЯ9Gе<Gж:@W,            1Gз<Gи2;3Gй4Gк@B@U`,Ы@t8б+Gл@@ pGм@@М┴АGлGн@@dGмP.2Gо@@Ц─АGмGп@@@GоG░@@дGоmW/G▒<G▓0    @ NormalTimes New Roman  G│*@U IЩ\<XN,░yr-Displaying dBm7G┤<G╡8G│m Comic Sans MS0,0,2559G╢<G╖:@W                        1G╕</G╣<G║0    @ NormalTimes New Roman  G╗*@U YGk*hO,╨'х-@QUse this invisible function, dBm(), and unitless dBm for displaying power in dBm.7Q9QG╝@@dH=VdBVH?@@┤H=20H@@B@U \np6h\,HA@@ pHB@@ ┴АHAHC@@dHBV.2HD@@R╠АHBHE@@tHD6.02HF@@дHDdBVHG*@U╕XСm╕h],╨┘ч-(actually stored in volts:)7HH<HI8HGk Comic Sans MS0,0,255HJ<HK8HG+ Comic Sans MS0,0,255HHHL<HM8HGk Comic Sans MS0,0,255HJHLHH9HN<HO:@W,            1HP<HQ2.3HR4HS@B@U`\Оpuhб+HT@@ pHU@@М┴АHTHV@@dHUV.2HW@@Ц─АHUHX@@@HWHY@@дHWV/HZ<H[0    @ NormalTimes New Roman  H\*@U БЦФ<Р^,░vq-Displaying dBV7H]<H^8H\m Comic Sans MS0,0,2559H_<H`:@W                        1Ha</Hb<Hc0    @ NormalTimes New Roman  Hd*@U СHг*а_,╨(щ-@SUse this invisible function, dBV(), and unitless dBV for displaying voltage in dBV.7S9SHe<I?23I@4/1IA<1IB0    @ Normal  IC@B@UDPUAP╤ID@@ pIE@@┴АIDIF@@dIEORIGINIG@@┤IE1IH*@UI╪[X╥П╪┴-Origin for Matrices and Vectors79II<IJ:@W?1IK</IL<IM0    @ Normal  IN@B@UZ<mh╙IO@@ pIP@@ ┴АIOIQ@@dIPjIR@@Ъ{АIPIS@@ХKАIRIT@@┤IS1IU*@UYЕkh╘ЧЕu-Imaginary Constant79IV<IW:@W?1IX</IY<IZ0    @ Normal  I[@B@UkТР$А╒I\@@ pI]@@ ┴АI\I^@@dI]\e.0I_@@╩АI]I`@@╩@I_Ia@@tI`8.8542Ib@@№АI`Ic@@tIb10Id@@ХKАIbIe@@┤Id12If@@√АI_Ig@@dIfFIh@@дIfmIi*@U╕q┤Г╕А╓№х-Permittivity of Free Space79Ij<Ik:@W>H1Il</Im<In0    @ Normal  Io@B@UГ|и&Ш╫Ip@@ pIq@@ ┴АIpIr@@dIq\m.0Is@@╩АIqIt@@╩@IsIu@@╩@ItIv@@tIu4Iw@@дIu\pIx@@№АItIy@@tIx10Iz@@ХKАIxI{@@┤Iz7I|@@√АIsI}@@dI|HI~@@дI|mI*@UЙ┐ЫШ╪Ч┐д-Permeability of Free Space79IА<IБ:@W                        1IВ</IГ<IД0    @ Normal  IЕ@B@Uл┤╪╚┘IЖ@@ pIЗ@@ ┴АIЖIИ@@dIЗkIЙ@@╩АIЗIК@@╩@IЙIЛ@@tIК1.383IМ@@№АIКIН@@tIМ10IО@@ХKАIМIП@@┤IО23IР@@√АIЙIС@@╩@IРIТ@@№@IСIУ@@dIТvoltIФ@@┤IТ2IХ@@дIСsecIЦ@@╩АIРIЧ@@dIЦohmIШ@@дIЦKIЩ*@U╣Н╦╚┌pН{-Boltzman's Constant79IЪ<IЫ:@W?1IЬ</IЭ<IЮ0    @ Normal  IЯ@B@U▄xїЁ█Iа@@ pIб@@ ┴АIаIв@@dIбqIг@@╩АIбIд@@tIг1.602Iе@@╩АIгIж@@№@IеIз@@tIж10Iи@@ХKАIжIй@@┤Iи19Iк@@дIеCIл*@UсЩєЁ▄pЩЕ-Charge on an electron79Iм<Iн:@W?1Iо</Iп<I░0    @ Normal  I▒@B@Uєi-▌I▓@@ pI│@@ ┴АI▓I┤@@dI│v.satI╡@@╩АI│I╢@@№@I╡I╖@@tI╢10I╕@@┤I╢7I╣@@√АI╡I║@@dI╣cmI╗@@дI╣secI╝*@U∙╕ ▐J╕в-Electron velocity saturation79I╜<I╛:@W?1I┐</I└<I┴0    @ Normal  I┬@B@UЖH"0▀I├@@ pI─@@ ┴АI├I┼@@dI─n.iI╞@@╩АI─I╟@@╩@I╞I╚@@tI╟1.45I╔@@№АI╟I╩@@tI╔10I╦@@┤I╔10I╠@@√АI╞I═@@tI╠1I╬@@№АI╠I╧@@dI╬cmI╨@@┤I╬3I╤*@U!∙30р┴∙█-'Intrinsic number of carriers in Silicon7'9'I╥<'I╙:@W?1I╘</'I╒<'I╓0    @ Normal  I╫*@UIm[XуЗ]]- Temperature 7 I╪< I┘8I╫gArial0,0,2559 I┌< I█:@W                        1I▄</ I▌< I▐0    @ Normal  I▀@B@U\ЩpIhфIр@@ pIс@@ ┴АIрIт@@dIс Temp.maxIу@@Й╟АIсIф@@╩@IуIх@@tIф273Iц@@дIфKIч@@╩АIуIш@@tIч105Iщ@@дIчKIъ*@UYkhхЧц-!Maximum Operating Die Temperature7!9!Iы@@ ┴АJ=J?@@dJ>V.TJ@@@√АJ>JA@@╩@J@JB@@dJAkJC@@дJATempJD@@дJ@qJE*@Uщr√°%╨rd-Thermal Voltage79JF<JG:@W                        1JH</JI<JJ0    @ NormalSymbol  JK@D@UK  █ Constants  ConstantsJL*@UЁ╨В| JM@HJN@HJO@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd#batterychargersJP@HJQ@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd#tempindicatorJR@HJS@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd #batteriesJT@H"tocJU@HJV@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd#dspregJW@HJX@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd#aeroregJY@HJZ@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd #resetgenJ[@HJ\@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd#rtcJ]@HJ^@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd#backupbatteryJ_@HJ`@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd#simcardJa@HJb@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd #accessoryJc@HJd@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd #leddriverJe@HJf@LC:\John\template\copyright.\..\..\template\copyrightJg@HJh@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd #vibratorJi@HJj@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd#buzzerJk@HJl@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd#audioJm@HJn@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd#gena2dJo@HJp@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd#refvoltJq@HJr@LC:\John\PMIC_Mcad.mcd.\..\..\PMIC_Mcad.mcd #notimplementJs@HJt@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd#introJu@HJv@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd#deriveJw@HJx@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd#modelsJy@HJz@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd#inputsJ{@HJ|@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd #calculationsJ}@HJ~@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd#outputsJ@HJА@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd #functionsJБ@HJВ@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd #examplesJГ@HJД@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd #simulationJЕ@HJЖ@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd #comparisonJЗ@HJИ@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd #referencesJЙ@HJК@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd #copyright╨╨Т╨Т-@╢_______________________________________ Table of Contents I. Introduction II. Inputs III. Phase Margin, Q, and Damping Factor IV. Transient Response V. Copyright and Trademark Notice7Ш'╢JЛ<'JМ8JL~JН<JО8JLJЛJП< JР8JLuJНJС<JТ8JLJПJУ<JФ8JLuJСJХ<JЦ8JLJУJЧ<#JШ8JLeTimes New Roman0,0,255JХJЩ<JЪ8JLJЧJЫ<JЬ8JLeTimes New Roman0,0,255JЩJЭ<JЮ8JLJЫJЯ<Jа8JLuJЭJЯJЛ9UUa╢Jб<(Jв:@W?Jг<Jд:@W,            JбJе<Jж:@W?JгJз< Jи:@W?JеJй@@дK<\w.uK?@@√АK7K@@@dK?sKA@@дK?\w.uKB@@┤K61KC@@√АK+KD@@tKC1KE@@Й╟АKCKF@@Й╟@KEKG@@№@KFKH@@Оp@KGKI@@√АKHKJ@@dKIsKK@@дKI\w.0KL@@┤KG2KM@@╩АKFKN@@√@KMKO@@tKN1KP@@дKNQKQ@@√АKMKR@@dKQsKS@@дKQ\w.0KT@@┤KE1KU@@√АK*KV@@tKU1KW@@Й╟АKUKX@@Й╟@KWKY@@№@KXKZ@@Оp@KYK[@@√АKZK\@@dK[sK]@@дK[\w.0K^@@┤KY2K_@@╩АKXK`@@╩@K_Ka@@tK`2Kb@@дK`\zKc@@√АK_Kd@@dKcsKe@@дKc\w.0Kf@@┤KW1Kg*@UБ╨зР.╨╨&╨&-@и The closed loop gain can be expressed in terms of Q, damping factor, phase margin, or as a function of non-dominant pole location with respect to unity gain bandwidth.7и9иKh<иKi:@W,            1Kj</иKk<иKl0    @ NormalTimes New Roman  Km@B@U0йФ└F╕ -Kn@@ pKo@@,┼АKnKp@@dKo\w.0Kq@@╩АKoKr@@dKq\w.uKs@@Ъ{АKqKt@@дKsp2_\wuKu@B@U0├иыn╪К.Kv@@ pKw@@ ┴АKvKx@@╬@KwKy@@dKxQKz@@ОpАKxK{@@дKzp2_\wuK|@@√АKwK}@@tK|1K~@@Ъ{АK|K@@дK~p2_\wuKА@B@Uш└]ш#╪Л.KБ@@ pKВ@@ ┴АKБKГ@@╬@KВKД@@dKГ\zKЕ@@ОpАKГKЖ@@дKЕp2_\wuKЗ@@√АKВKИ@@Ъ{@KЗKЙ@@дKИp2_\wuKК@@┤KЗ2KЛ@B@Uа├{щш╪М.KМ@@ pKН@@ ┴АKМKО@@╬@KНKП@@dKОPMKР@@ОpАKОKС@@дKРp2_\wuKТ@@И╟АKНKУ@@tKТ90KФ@@╩АKТKХ@@√@KФKЦ@@tKХ180KЧ@@дKХ\pKШ@@╬АKФKЩ@@dKШatanKЪ@@ОpАKШKЫ@@√АKЪKЬ@@tKЫ1KЭ@@дKЫp2_\wuKЮ*@Uщ╨" °{.╨╨9╨9-A: This phase margin expression assumes, the unity gain bandwidth is entirely determined by the dominant pole. In practice, the non-dominant pole will reduce the real unity gain bandwidth from the expected value. For properly placed non-dominant pole this error is only about 5%, as shown in the following figure:7:9:KЯ<:Kа:@W                        1Kб</:Kв<:Kг0    @ NormalTimes New Roman  Kд@B@U╕ ╧▀╕ Г.Kе@@ pKж@@┴АKеKз@@Я┴@KжKи@@Я┴@KзKй@@Я┴@KиKк@@vKй21.385Kл@@╢Kй2.826Kм@@Я┴АKиKн@@@KмKо@@АKмKп@@√АKзK░@@И╟@KпK▒@@tK░1K▓@@╩АK░K│@@√@K▓K┤@@dK│p2_\wuK╡@@Ъ{АK│K╢@@┤K╡2K╖@@Ъ{АK▓K╕@@И╟АK╖K╣@@Ъ{@K╕K║@@Й╟АK╣K╗@@tK║1K╝@@√АK║K╜@@tK╝4K╛@@№АK╝K┐@@dK╛p2_\wuK└@@┤K╛2K┴@@┤K╕1K┬@@дKп%K├@@Я┴АKжK─@@Я┴@K├K┼@@Я┴@K─K╞@@tK┼4K╟@@┤K┼1K╚@@Я┴АK─K╔@@@K╚K╩@@АK╚K╦@@дK├p2_\wuK╠  )Np2/wu)NBandwidth loss (%)$Bandwidth Loss vs. Non-dominant Pole&&&&&&&&& & & & & &&&K═*@Uс╨Ё .╨╨&╨&-@┴ As a designer we have control over the pole locations, which is swept in the following plots to show the relationship between non-dominant pole location and Q, phase margin and damping factor.7┴9┴K╬<┴K╧:@W                        1K╨</┴K╤<┴K╥0    @ NormalTimes New Roman  K╙@B@U0 eO .K╘@@ pK╒@@ ┴АK╘K╓@@dK╒numK╫@@┤K╒50K╪@B@U░ ь╗З.K┘@@ pK┌@@ ┴АK┘K█@@dK┌iK▄@@┬АK┌K▌@@tK▄1K▐@@дK▄numK▀@B@Uu(%И.Kр@@ pKс@@ ┴АKрKт@@¤@KсKу@@dKт\w0tKф@@дKтiKх@@╩АKсKц@@√@KхKч@@И╟@KцKш@@dKчiKщ@@┤Kч1Kъ@@И╟АKцKы@@dKъnumKь@@┤Kъ1Kэ@@┤Kх20Kю@B@UРє(╛Й.Kя@@ pKЁ@@ ┴АKяKё@@¤@KЁKЄ@@dKёp2_\wuKє@@дKёiKЇ@@╩АKЁKї@@√@KЇKЎ@@dKїiKў@@дKїnumK°@@┤KЇ5K∙@B@U( (┼-K·@@ pK√@@┴АK·K№@@Я┴@K√K¤@@Я┴@K№K■@@Я┴@K¤K @@vK■78.69L@@╢K■5.711L@@Я┴АK¤L@@@LL@@АLL@@╬АK№L@@dLPML@@ОpАLL@@¤АLL@@dLp2_\wuL @@дLiL @@Я┴АK√L @@Я┴@L L @@Я┴@L L @@vL 5L@@╢L 0.1L@@Я┴АL L@@@LL@@АLL@@¤АL L@@dLp2_\wuL@@дLiL  )Np2/wu)NPM (deg)"Phase Margin vs. 2nd Pole Location&&&&&&&&& & & & & &&&L@B@U°(▀ °(╟-L@@ pL@@┴АLL@@Я┴@LL@@Я┴@LL@@Я┴@LL@@vL1.118L@@╢L0.158L@@Я┴АLL@@@LL @@АLL!@@╬АLL"@@dL!\zL#@@ОpАL!L$@@¤АL#L%@@dL$p2_\wuL&@@дL$iL'@@Я┴АLL(@@Я┴@L'L)@@Я┴@L(L*@@vL)5L+@@╢L)0.1L,@@Я┴АL(L-@@@L,L.@@АL,L/@@¤АL'L0@@dL/p2_\wuL1@@дL/iL2  )Np2/wu)Ndamping factorDamping vs. 2nd Pole Location&&&&&&&&& & & & & &&&L3@B@U╪(╧ ╪(├-L4@@ pL5@@┴АL4L6@@Я┴@L5L7@@Я┴@L6L8@@Я┴@L7L9@@vL83.162L:@@╢L80.447L;@@Я┴АL7L<@@@L;L=@@АL;L>@@╬АL6L?@@dL>QL@@@ОpАL>LA@@¤АL@LB@@dLAp2_\wuLC@@дLAiLD@@Я┴АL5LE@@Я┴@LDLF@@Я┴@LELG@@vLF5LH@@╢LF0.1LI@@Я┴АLELJ@@@LILK@@АLILL@@¤АLDLM@@dLLp2_\wuLN@@дLLiLO  )Np2/wu)NQQ vs. 2nd Pole Location&&&&&&&&& & & & & &&&LP@E@U@╚-LQ*@U╨C(╩-╨╨3╨3-:_______________________________________ Transient Response7(':LR<'LS8LQ~LT<LU8LQLRLV<LW8LQLTLVLR9:LX<:LY:@W                        1LZ<L[23L\4/:L]<:L^0    @ Heading 1Arial   L_*@UI╨oX.╨╨&╨&-@ь In this section, the settling time is found. This first requires the transient response be found. For a second order system, three possible equations can result, depending on whether the response is under, over, or critically damped.7ь9ьL`<ьLa:@W                        1Lb</ьLc<ьLd0    @ NormalTimes New Roman  Le*@Uy╨ЛИф-╨╨╨-Critically damped79Lf<Lg:@W                        1Lh</Li<Lj0    @ NormalTimes New Roman  Lk*@UЙ╨пШщ-╨╨&╨&-@Ш For a critcally damped system, the damping factor is one. This response has a transient response and settling error given by the following expression:7Ш9ШLl<ШLm:@W                        1Ln</ШLo<ШLp0    @ NormalTimes New Roman  Lq@B@U0│ы┼[└ч-Lr@@ pLs@@ ┴АLrLt@@╬@LsLu@@dLthLv@@ОpАLtLw@@дLv\w0tLx@@И╟АLsLy@@dLx1Lz@@╩АLxL{@@Оp@LzL|@@Й╟АL{L}@@dL|\w0tL~@@┤L|1L@@╬АLzLА@@dLexpLБ@@ОpАLLВ@@ХKАLБLГ@@дLВ\w0tLД@B@U0╦ъ▌h╪ш-LЕ@@ pLЖ@@ ┴АLЕLЗ@@╬@LЖLИ@@dLЗerr0LЙ@@ОpАLЗLК@@дLЙ\w0tLЛ@@╩АLЖLМ@@ХK@LЛLН@@ОpАLМLО@@Й╟АLНLП@@dLО\w0tLР@@┤LО1LС@@╬АLЛLТ@@dLСexpLУ@@ОpАLСLФ@@ХKАLУLХ@@дLФ\w0tLЦ*@Uщ╨√°╫-╨╨╨- Underdamped 7 9 LЧ< LШ:@W                        1LЩ</ LЪ< LЫ0    @ Heading 2Arial    LЬ*@U∙╨Э-╨╨&╨&-@Ы For damping factors less than one, the system is underdamped. This is the preferred operating condition for almost all systems for minimum settling time.7Ы9ЫLЭ<ЫLЮ:@W                        1LЯ</ЫLа<ЫLб0    @ NormalTimes New Roman  Lв@B@U0!@r8Ю-Lг@@ pLд@@ ┴АLгLе@@╬@LдLж@@dLеp.1Lз@@ОpАLеLи@@дLзp2_\wuLй@@Й╟АLдLк@@╬@LйLл@@dLк\zLм@@ОpАLкLн@@дLмp2_\wuLо@@Ъ{АLйLп@@И╟АLоL░@@№@LпL▒@@╬@L░L▓@@dL▒\zL│@@ОpАL▒L┤@@дL│p2_\wuL╡@@┤L░2L╢@@┤Lп1L╖@B@UА!e@┬8Я-L╕@@ pL╣@@ ┴АL╕L║@@╬@L╣L╗@@dL║p.2L╝@@ОpАL║L╜@@дL╝p2_\wuL╛@@И╟АL╣L┐@@╬@L╛L└@@dL┐\zL┴@@ОpАL┐L┬@@дL┴p2_\wuL├@@Ъ{АL╛L─@@И╟АL├L┼@@№@L─L╞@@╬@L┼L╟@@dL╞\zL╚@@ОpАL╞L╔@@дL╚p2_\wuL╩@@┤L┼2L╦@@┤L─1L╠@B@U0C╬IXа-L═@@ pL╬@@,┼АL═L╧@@dL╬A.clL╨@@√АL╬L╤@@tL╨1L╥@@╩АL╨L╙@@Оp@L╥L╘@@Й╟АL╙L╒@@√@L╘L╓@@dL╒sL╫@@дL╒p.1L╪@@┤L╘1L┘@@ОpАL╥L┌@@Й╟АL┘L█@@√@L┌L▄@@dL█sL▌@@дL█p.2L▐@@┤L┌1L▀@B@U0Бч│LШв-Lр@@ pLс@@,┼АLрLт@@╬@LсLу@@dLтhLф@@ОpАLтLх@@дLфtLц@@Й╟АLсLч@@tLц1Lш@@╩АLцLщ@@╠@LшLъ@@dLщeLы@@ОpАLщLь@@╩АLыLэ@@╩@LьLю@@ХK@LэLя@@дLю\zLЁ@@дLэ\w.0Lё@@дLьtLЄ@@ОpАLшLє@@И╟АLЄLЇ@@╩@LєLї@@√@LЇLЎ@@dLї\zLў@@Ъ{АLїL°@@И╟АLўL∙@@tL°1L·@@№АL°L√@@dL·\zL№@@┤L·2L¤@@╬АLЇL■@@dL¤sinL @@ОpАL¤M@@╩АL M@@╩@MM@@Ъ{@MM@@И╟АMM@@tM1M@@№АMM@@dM\zM@@┤M2M@@дM\w.0M @@дMtM @@╬АLєM @@dM cosM @@ОpАM M @@╩АM M@@╩@M M@@Ъ{@MM@@И╟АMM@@tM1M@@№АMM@@dM\zM@@┤M2M@@дM\w.0M@@дM tM@B@U0╣ыШ╨г-M@@ pM@@,┼АMM@@,┼@MM@@╬@MM@@dMerrM@@ОpАMM@@дMtM@@Э{АMM @@И╟АMM!@@╬@M M"@@dM!hM#@@ОpАM!M$@@дM#tM%@@┤M 1M&@@╩АMM'@@╠@M&M(@@dM'eM)@@ОpАM'M*@@╩АM)M+@@╩@M*M,@@ХK@M+M-@@дM,\zM.@@дM+\w.0M/@@дM*tM0@@ОpАM&M1@@И╟АM0M2@@╩@M1M3@@√@M2M4@@dM3\zM5@@Ъ{АM3M6@@И╟АM5M7@@tM61M8@@№АM6M9@@dM8\zM:@@┤M82M;@@╬АM2M<@@dM;sinM=@@ОpАM;M>@@╩АM=M?@@╩@M>M@@@Ъ{@M?MA@@И╟АM@MB@@tMA1MC@@№АMAMD@@dMC\zME@@┤MC2MF@@дM?\w.0MG@@дM>tMH@@╬АM1MI@@dMHcosMJ@@ОpАMHMK@@╩АMJML@@╩@MKMM@@Ъ{@MLMN@@И╟АMMMO@@tMN1MP@@№АMNMQ@@dMP\zMR@@┤MP2MS@@дML\w.0MT@@дMKtMU@B@U0э}?С▌-MV@@ pMW@@ ┴АMVMX@@╬@MWMY@@dMXerr1MZ@@ОpАMXM[@@ ├АMZM\@@dM[p2_\wuM]@@дM[\w0tM^@@╩АMWM_@@№@M^M`@@dM_eMa@@ОpАM_Mb@@╩АMaMc@@ХK@MbMd@@√АMcMe@@Ъ{@MdMf@@дMep2_\wuMg@@┤Md2Mh@@дMb\w0tMi@@ОpАM^Mj@@И╟АMiMk@@╩@MjMl@@√@MkMm@@tMl1Mn@@Ъ{АMlMo@@И╟АMnMp@@√@MoMq@@tMp4Mr@@дMpp2_\wuMs@@┤Mo1Mt@@╬АMkMu@@dMtsinMv@@ОpАMtMw@@╩АMvMx@@Ъ{@MwMy@@И╟АMxMz@@tMy1M{@@√АMyM|@@dM{p2_\wuM}@@┤M{4M~@@дMw\w0tM@@╬АMjMА@@dMcosMБ@@ОpАMMВ@@╩АMБMГ@@Ъ{@MВMД@@И╟АMГMЕ@@tMД1MЖ@@√АMДMЗ@@dMЖp2_\wuMИ@@┤MЖ4MЙ@@дMВ\w0tMК*@UQ╨c`я-╨╨╨- Overdamped 7 9 MЛ< MМ:@W                        1MН</ MО< MП0    @ NormalTimes New Roman  MР*@Ua╨Зp.╨╨&╨&-@Э An overdamped system is very slow. However it is often used in systems with large process variations, to avoid crossing into extreme underdamped scenarios.7Э9ЭMС<ЭMТ:@W                        1MУ</ЭMФ<ЭMХ0    @ NormalTimes New Roman  MЦ@B@U8И▓│TаЁ-MЧ@@ pMШ@@,┼АMЧMЩ@@╬@MШMЪ@@dMЩhMЫ@@ОpАMЩMЬ@@дMЫtMЭ@@Й╟АMШMЮ@@dMЭ1MЯ@@И╟АMЭMа@@╩@MЯMб@@╦@MаMв@@dMбp.2Mг@@ОpАMбMд@@И╟АMгMе@@dMдp.1Mж@@дMдp.2Mз@@╬АMаMи@@dMзexpMй@@ОpАMзMк@@╩АMйMл@@╩@MкMм@@ХK@MлMн@@дMмp.1Mо@@дMл\w.0Mп@@дMкtM░@@╩АMЯM▒@@╦@M░M▓@@dM▒p.1M│@@ОpАM▒M┤@@И╟АM│M╡@@dM┤p.1M╢@@дM┤p.2M╖@@╬АM░M╕@@dM╖expM╣@@ОpАM╖M║@@╩АM╣M╗@@╩@M║M╝@@ХK@M╗M╜@@дM╝p.2M╛@@дM╗\w.0M┐@@дM║tM└@B@U8╖BуЩ╨ё-M┴@@ pM┬@@ ┴АM┴M├@@╬@M┬M─@@dM├err2M┼@@ОpАM├M╞@@ ├АM┼M╟@@dM╞p2_\wuM╚@@дM╞\w0tM╔@@И╟АM┬M╩@@╩@M╔M╦@@√@M╩M╠@@╬@M╦M═@@dM╠p.2M╬@@ОpАM╠M╧@@дM╬p2_\wuM╨@@Ъ{АM╦M╤@@И╟АM╨M╥@@dM╤p2_\wuM╙@@┤M╤4M╘@@╬АM╩M╒@@dM╘expM╓@@ОpАM╘M╫@@╩АM╓M╪@@ХK@M╫M┘@@╬АM╪M┌@@dM┘p.1M█@@ОpАM┘M▄@@дM█p2_\wuM▌@@дM╫\w0tM▐@@╩АM╔M▀@@√@M▐Mр@@╬@M▀Mс@@dMрp.1Mт@@ОpАMрMу@@дMтp2_\wuMф@@Ъ{АM▀Mх@@И╟АMфMц@@dMхp2_\wuMч@@┤Mх4Mш@@╬АM▐Mщ@@dMшexpMъ@@ОpАMшMы@@╩АMъMь@@ХK@MыMэ@@╬АMьMю@@dMэp.2Mя@@ОpАMэMЁ@@дMяp2_\wuMё@@дMы\w0tMЄ@E@U°@ °Z.Mє*@U ╨  є-╨╨╨-,Overall Error vs. Non-Dominant Pole Location7,9,MЇ<,Mї:@W                        1MЎ</,Mў<,M°0    @ Heading 2Arial    M∙*@U ╨, ( .╨╨╨-@H The three transient responses are merged into the following expression:7H9HM·</:N?<:N@0    @ NormalTimes New Roman  NA@B@U0├ g! о╨ .NB@@ pNC@@ ┴АNBND@@╬@NCNE@@dND \w0t.settleNF@@ОpАNDNG@@ ├АNFNH@@dNGp2_\wuNI@@дNGV.accNJ@@╟ЄАNCNK@@╟Є@NJNL@@╚ї@NKNM@@dNLt.valNN@@┤NL0NO@@╧■АNKNP@@╚ї@NONQ@@dNPt.valNR@@╬АNPNS@@dNRifNT@@ОpАNRNU@@ ├АNTNV@@ ├@NUNW@@╩@NVNX@@Оp@NWNY@@.┼АNXNZ@@╬@NYN[@@dNZerrN\@@ОpАNZN]@@ ├АN\N^@@dN]p2_\wuN_@@¤АN]N`@@dN_\w0tNa@@дN_iNb@@дNYV.accNc@@ОpАNWNd@@(┼АNcNe@@Э{@NdNf@@╬АNeNg@@dNferrNh@@ОpАNfNi@@ ├АNhNj@@dNip2_\wuNk@@¤АNiNl@@dNk\w0tNm@@И╟АNkNn@@dNmiNo@@┤Nm1Np@@дNdV.accNq@@¤АNVNr@@dNq\w0tNs@@дNqiNt@@дNUt.valNu@@╚їАNONv@@dNuiNw@@┬АNuNx@@tNw2Ny@@дNwnumNz@@дNJt.valN{*@U1 ╨D @ *.╨╨╨-@Z Settling time is best found by plotting settling error on a logarithmic axis verses time.7Z9ZN|@@╬@O=O?@@dO>PM.optO@@@ОpАO>OA@@дO@V.accOB@@Ц─АO=OC@@+@OB@XOD@@АOBOE@B@U0№ _ O Б-OF@@ pOG@@ ┴АOFOH@@dOGnumOI@@┤OG7OJ@B@U0 l ; В-OK@@ pOL@@ ┴АOKOM@@dOLiON@@┬АOLOO@@tON1OP@@дONnumOQ@B@U0 У4 T( Г-OR@@ pOS@@ ┴АOROT@@¤@OSOU@@dOTSNROV@@дOTiOW@@Й╟АOSOX@@tOW30OY@@╩АOWOZ@@dOYiO[@@┤OY10O\@B@U0. Рe RX Д-O]@@ pO^@@ ┴АO]O_@@¤@O^O`@@dO_V.accOa@@дO_iOb@@№АO^Oc@@tOb10Od@@√АObOe@@ХK@OdOf@@¤АOeOg@@dOfSNROh@@дOfiOi@@┤Od20Oj*@Ui ╨П x c-╨╨&╨&-@╥ Now for the most useful plot of this report: Optimal phase margin verses SNR requirements. 76 degrees represents critical damping. The optimal phase margin approaches this as the SNR requirements get large.7╥9╥Ok<╥Ol:@W                        1Om</╥On<╥Oo0    @ NormalTimes New Roman  Op@B@UИР wИР R.Oq@@ pOr@@┴АOqOs@@Я┴@OrOt@@Я┴@OsOu@@Я┴@OtOv@@vOu75.964Ow@@╢Ou63.435Ox@@Я┴АOtOy@@@OxOz@@АOxO{@@ ├АOsO|@@╬@O{O}@@dO|PM.optO~@@ОpАO|O@@¤АO~OА@@dOV.accOБ@@дOiOВ@@И╟АO{OГ@@tOВ90OД@@╩АOВOЕ@@√@OДOЖ@@tOЕ180OЗ@@дOЕ\pOИ@@╬АOДOЙ@@dOИatanOК@@ОpАOИOЛ@@√АOКOМ@@tOЛ1OН@@┤OЛ4OО@@Я┴АOrOП@@Я┴@OОOР@@Я┴@OПOС@@vOР100OТ@@╢OР40OУ@@Я┴АOПOФ@@@OУOХ@@АOУOЦ@@¤АOОOЧ@@dOЦSNROШ@@дOЦiOЩ + )NSNR (dB))NPhase Margin (deg)Optimal Phase Margin vs. SNR&&Optimal Phase Margin&Critical Damping&&&&&&& & & & & &&&OЪ*@Up╨ЙАA.╨╨╨-@^ Similarly, the optimal non-dominant pole placement approaches 4*wu for large SNR requirements7CA^OЫ<)P?0    @ NormalTimes New Roman  0h