Accuracy of ADC dynamic parameters measurement. Jiri Brossmann, Petr Cesak, Jaroslav Roztocil

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1 ccurcy o dymc prmtrs msurmt Jr Brossm Ptr Csk Jroslv Roztocl Czch Tchcl Uvrsty Prgu Fculty o Elctrcl Egrg Tchck CZ-667 Prgu 6 Czch Rpublc Pho: Fx: E-ml: jr.brossm@gml.com cskp@l.cvut.cz roztocl@l.cvut.cz bstrct-bsd o modl o tst sgl grtor ccurcy stmtor ws dsgd d mplmtd. Th proposd stmtor uss computr smultos to obt xpctd bs o dymc prmtrs o log-to-dgtl covrtr. Th usg o th mthod or stmto o dymc prmtrs msurmt ccurcy or th bst s-wv t d th rucy dom lyss usg th DFT wll b prstd ths ppr. I. Itroducto Th mprctos o tst sgl grtor d sgl pth rom th grtor to puts o th tstd r m sourcs o rrors th tstg d msurmt o s dymc prmtrs. Othr prts o th tstg ch r th udr tst d rlvt lytcl rmwork tht procsss ld dt to obt dymc prmtrs o th tstd. Th two lttr prts r ot rlvt or bs vluto th s drd to b blck box wth prmtrs udr vstgto d t s rltvly smpl to chg th sttgs o lytcl rmwork comprd to th possblts o chgg prmtrs o th tst sgl grtor.. Tst sgl grtor modl II. Proposd pproch To rlct ll usul sourcs o dstorto s-wv grtor modl o th s-wv sgl grtor ws crtd. Th modl drvto bgs wth th ormul dscrbg s wv wth ost m vlu V th tm dom: x t V s t ow dr two m kds o dstorto to ths dl sus sgl: th prstc mpltud modulto d ddtv os: m s mod mod 3 os whr s umbr o ls mod s mpltud d mod s rucy o sgl whch cuss prstc mpltud modulto os s mpltud o os dstorto d orm s th l grtd by os grtor wth orml dstrbuto d stdrd dvto o. Th grc ucto combg both sourcs o dstorto d th dstortd m vlu V c b dd s: orm

2 Q Q s 4 whr Q s th dstortd m vlu s th th os l s th mpltud o os s th mpltud o prstc modulto d s th rucy o prstc mpltud modulto. Usg th ucto 4 th s-wv grtor wth udsrbl modctos o ll thr prmtrs ost mpltud d phs c b modld by th ollowg ormul: s x vz 5 Th proposd modl llows smulto o th cts o os prstc mpltud modulto vrtos o th ost lvl d rucy o dl s-wv. B. Ucrtty lyss lyss o proposd modl trms o stdrd ucrtts ws prormd. Gol o lyss ws to dtrm how rsults o tst mthods would b ctd by ch sourc o dstorto prst sgl grtor modl. For ucrtty lyss sgl grtor modl c b xpdd to ollowg orm: vz x s s s s 6 lyss th c b sprtd two prts: o or prstc mpltud modulto d o or ddtv os luc. I ollowg lyss us o dl dgtzr d cohrt lg s ssumd. For lyss o prstc mpltud modulto lt us suppos tht ll ddtv os sourcs r ul to zro: x s s s s s s For tst mthod usg DFT thr r ollowg spctrl compots prst mpltud rucy spctrum: o spctrl compot or ost dstorto: s 8

3 spctrl compots corrspodg to phs modulto o crrr: s s 9 spctrl compots grtd by prstc mpltud d phs modulto o crrr: s s s 0 Ths compots wll b rlctd SID s crs o dstorto powr s ollows: compot wll crs dstorto proportolly to. Phs modulto o crrr wll troduc spctrl compots dtrmd grlly by Bssl ucto. Howvr prmtr φ s lss th 0. phs modulto c b smpld to s d rucy spctrum wll cot two spctrl compots o rucs φ d - φ wth mgtud φ /. By pplyg prvous ssumpto prstc modulto o mpltud d phs o crrr wll smply to s s For << c compots b gord d prvous ormul c b rducd to 3 Spctrum th wll cot compots o rucs wth mgtud /. Formul or SID clculto th c b updtd to ollowg orm: SID 0log S Β Β Β 4 φ < 0 d << B B φ d B r powrs o corrspodg spctrl compots. For mthod usg bst s-wv t ll ssumptos d pproxmtos usd or DFT mthod c b usd. Prstc mpltud modulto th pprs subtrcto o dgtzd d t s-wv rsdu s ollows:

4 s 5 RMS o rsdu th wll b dscrbd by ormul: ut rms s 6 whr ut s RMS vlu o utzto os. Stdrd ucrtty typ B o SID c b vlutd rom uto 4. For mthod usg DFT complc wth mthodology usd or stdrd ucrtts vluto stdrd ucrtty typ B s dscrbd by ormul 0 Β Β Β B u 7 whr φ r stdrd dvtos o B B φ B. Thr vlus r dtrmd by lyss o B B φ B vlus or drt cogurtos o msurmt vrous umbrs o ls rsoluto o dgtzr tc.. For mthod usg bst s-wv rst rwrt ormul 6 to ollowg orm: kvt rms 8 Th stdrd ucrtty typ B o EOB s dd by ormul: rms B u 9 whr φ r stdrd dvtos o dtrmto o prmtrs φ. Ucrtty cusd by ddtv os prst th modl ws lt to sttstcl lyss d should b vlutd s stdrd ucrtty typ whch s obtd s stdrd dvto o multpl msurmts. C. Smultos Th bov mtod modl ws usd xtsv st o smultos whch covrd rsobl sp

5 o put prmtrs o modl to obt dtld ormto bout bst s-wv t d rucy dom lyss tst mthods bhvor. Fgur shows rprsttv rsult o smultos whr s-wv dstorto sourcs luc th tst sgl. O th vrtcl xs s rltv vlu o SID horzotl xs rprsts combtos o s-wv dstorto sourcs corrspodg wth dscrbd modl o th s-wv grtor. Icrsg cumultv luc o drt sourcs o dstortos s clrly vsbl. 000 Průměr z DFT SID orm dc_os_mul _os_mul phs_os_mul dc_modulto_mul _modulto_mul phs_modulto_mul Fgur. Rltv vlu o SID obtd by lyss rucy dom or slctd rsolutos bts d drt dstorto sourcs lvls umbr o ls trm Blckm & Hrrs tm wdow mpltud 98% o th ull scl Smultos wth prstc mpltud modulto wr lso usd to vry rsults o ucrtty lyss. Rsults o 6-bt dgtzr bhvor smultos o wr comprd to rsults gv by ormuls prstd ucrtty lyss s tbl. Comprso show tht stmtos md by uto 4 r rlvt or stutos whr vlus o modl s prmtrs r ot gttg clos to trts gv ucrtty lyss. For wdr rg o prmtrs vlus drcs rsults strt to b sgct. Tbl. Comprso o smultd rsults d stmtos gv by ucrtty lyss. Rsoluto 6-bt. prstc mpltud modulto lvls φ 0.00 φ φ φ 0.5 SID clcultd SID stmto SID drc C. Th proposd stmtor Bcus rsults gv by ormuls obtd by modl lyss wr ot ccurt wd ough rg o put codtos dcso to crt sotwr bs stmtor ws tk. Estmtor tks smultd dt d by thr lyss prdcts how rsults o tst mthod would b ctd by sgl grtor prmtrs whl dgtzd by dl dgtzr. It llows to dcd whthr msurmt wth prtculr sgl sourc s or s ot vld. Th stmtor rurs to prorm comprhsv st o smultos whch covrs codtos whch grtor should b usd grto o ths dt s utomtd usr sts prmtrs o smultos oly. Ths dt r lodd by stmtor d wh prmtrs o sgl sourc corrspodg to prmtrs o dscrbd modl r trd stmtor srchs dt to d how rsults wr ctd by

6 smlr cogurto smulto. Bcus thr r svrl wys how to gt to dsrd rsults ll o ths pths r ollowd d rom vrg o smultd rsults bs stmto s clcultd. log wth bs stmto ts stdrd dvto s clcultd. Tbl shows rsults o stmto o bs or prtculr cogurto o sgl grtor modl d Tbl 3 prsts svrl rlztos o msurmt or th sm cogurto o dstorto sourcs or 6-bt. Vlus Δ SID DFT d Δ SID SWF rprst drcs btw dl SID d xpctd rsults o rucy dom lyss d bst s-wv t rspctvly or gv cogurto o modl s dstorto sourcs grtr drc or DFT tst s cusd by tst sgl mpltud d tm wdow luc. lso th stdrd dvto o bs stmto s clcultd d dsplyd. Tbl. Estmtor output Δ SID DFT [db] Δ SID SWF [db] Stdrd Stdrd Bs stmto Bs stmto dvto o bs dvto o bs Tbl 3. Smulto rsults. Rlzto Δ SID DFT [db] Δ SID SWF [db] III. Coclusos Th modl rspctg th mprctos o th s-wv tst sgl grtor ws prstd. It ws usd to lys bhvor o tst mthods or vluto o dymc prmtrs. Bsd o smultd dt stmtor o ccurcy o dymc prmtrs ws dsgd d ts prdctos wr vrd. Rrcs [] IEEE: Stdrd or dgtzg wvorm rcordrs IEEE Stdrd 057. [] IEEE: Stdrd or log to Dgtl Covrtrs IEEE Stdrd 4. [3] Burr-Brow: Dymc Tsts For /D Covrtr Prormc pplcto ot B [4] Roztocl J. Msco F. Pokorý M.: Prctcl spcts o /D Plug- Bords Dymc Tstg IMEKO 997. [5] Mxm: Dg d Tstg Dymc Prmtrs Hgh-Spd s pplcto ot [6] Hädl P.: Evluto o Stdrdzd S Wv Ft lgorthm IEEE ordc Sgl Procssg Symposum ORSIG 000. [7] Dorbrg J. L H-Sug Hodgs D.. : Full-Spd Tstg o /D Covrtrs IEEE Jourl o Sold-stt Crcuts Vol. SC-9 o. 6 Dcmbr 984. [8] Itrtol Orgzto or Stdrdzto: Gud to th Exprsso o Ucrtty Msurmt 993. [9] glt Spctrum lyss mpltud d Frucy Modulto pplcto ot 50-.