Symbolic Nodal Analysis of Analog Circuits with Modern Multiport Functional Blocks

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1 58. SNHEZ-LOPEZ, ET L., SMBOL NODL NLSS OF NLOG UTS Syl Nl ly l rut wth Mr Multrt Futl Blk rl SNHEZ-LOPEZ, r UZ-PSTO, OHO-MONTEL, Mul Ál SO-GUL Dt. Eltr, utu Urty Tll, zqut k..5, 9 z-tll, M rl@yh.., ruz@l., r7@htl., rr@l. trt. Th r r tt tr l t rh th hr r ultrt utl lk ll: rtl r lr, rtl r rtl lt lr, rtl r rtl rrr lr, rtl r urrt yr, urrt kwr trut lr urrt r trut lr. Th lty tht th hr y t t tly tru th l tt tr y u th r tt tr l wthut rqur th u tr rl. Thrr, tr l ly l t ut ully-yl ll-l rr rtr l rut t y t t. Th tht t ly th z th tt tr llr th th rt y ly l ly th, r t, ut l, th ur zr lt th rt llt-tr r th ru. ly l r h lr r rr t hw th uul th r t. Kywr Nl tt tr, yl ly, t trll ur, rtl lr.. trut Dur th lt w yr, ru t h r t u th l l r [], uh th Drtl Dr lr (DD [], th Drtl Dr Ortl Flt lr (DDOF [], th Drtl Dr Ortl Mrrr lr (DDOM [], th Drtl Dr urrt yr (DD [5], th urrt Bkwr Trut lr (BT [6] th urrt Dr Trut lr (DT [7], thr [], [8], [9]. t lt, th ltr rut hr rt y url ult r yl r []-[6]. th rr, url ult t y rt ut whh t ly th t rtt rl th trr ut hr, url ult r u t ry th rut hr lt t th. th lttr, yl ly thqu r ry uul t ut yl trr ut, yl r r rt ht th lu h rut t r th rut hr t ll th. Thrr, yl ly tl lt t url ult. y, rult th rh r tr r rqur t rult th yt qut ltr, rur trt- thqu r l rr t ut thr ur r yl ll-l rr rtr th rut []-[6]. O th thr h, ll th rult th rh r tr, th l ly th (MN w t r th lt url ultr lk H, l th lt yl lyzr lk S SNP, whr th lt t u t ll th tt tr [], [], [5]. th tt, trll ur r u t l th hr lt-, urrt- hyr- t h th lu th tt tr y u t []-[5]. Urtutly, ly th hr lt-trll urrt ur (S urrttrll urrt ur (S tly tru th l tt tr (NM y ly l ly (N ly. Fr th thr tw trll ur,.., th urrt-trll lt ur (S th lt-trll lt ur (S, lu rw l wth zr lt ut t th tt tr y h trll ur u []-[5]. Tht tht th yt qut l rut wh hr l wth trll ur lr. But, th uttl lty ry ut r th r wh rur trt- thqu r l rr t ut ully-yl trr ut. Thrr, th trut rut thqu th z th tt tr try.

2 DOENGNEENG, OL., NO., JUNE 59 ( ( F.. ( Syl th DD, ( qult l. rr t ru th lty th lut th, t ly th tt tr ut r l, ut l th z th yt qut ut kt lw l. th r, w lt t r th tw -N tl trll ur h rrt, whh r th t tr rt-qul lt-rl [7]-[]. Hwr, lthuh th hr th tw trll ur tly tru th NM, thy rt rl rwk. Th jr rwk tht h r t tru lt-rl thy ut tk lt t ty yl trr ut r ut [8], [], []. Thrr, lul utr rur wll wt rt yl tr tht wll ru wh th lt r l th yl r ut. O th thr h, llw th t lt-rl, th hr h trll ur thr ullyrtl l- r l S, h lry rrt []-[]. Th r th t wth th rrt [7]-[], tht ut-utut t t h trll ur r tk t ut. rult, th hr y t l wth trll ur rtly tru t NM, lu ut-utut, yl trr ut r ut wthut l ury. Th trut th r l th l th ut lt t r th t t t th wrk rrt []-[]; thry thy u t rtly ll th NM, r th PU-t ry ut u ur th ut th yl trr ut.. DD St Th DD w r [] w t. Th yl rrtt t F. ( t qult l y u S hw F. (. Th lr hl lt l t ut trl lt r t utut trl. r t [], [], th t th DD t ( ( F.. ( Syl th DDOF, ( qult l. ( whr r th ut tt, th utut tt (lly, = th t -l lt., ( u t rult th yt qut l rut t DD y u tr N. O th thr h, whthr ut tt r r l (.., = =, ( l t.(. DDOF St Th DDOF, wh yl hw F. (, h tw rtl ut rt r tw l utut urrt []. Th qult l y u tw S t F. (. Th t hl lt l t ut trl urrt l t utut-trl. r t [], th t th DDOF u (

3 5. SNHEZ-LOPEZ, ET L., SMBOL NODL NLSS OF NLOG UTS ( ( F.. ( Syl th DDOM, ( qult l. whr r th ut tt th t -l trut., ( tly u t rult th NM l rut t DDOF. By r l ut tt (.., = =, ( ru t. (. DDOM St Th DDOM h r ltrt l ul lk whh hrt ll th t urrt thqu []. Blly, th hr th DDOM lr t th DDOF, ly tht hr, tw urrt ur wth th rt r u th utut trl. Nt tht th DDOF DDOM r t r th rtl lt lr. Th yl rrtt t F. ( t qult l y u tw S hw F. (. Sl ly F. ( llw t t qut y (5 whr r th ut tt th t -l trut. Slrly ru t (.., = =, (5 ru t. (6 Thrr, (5 (6 u t ut yl ll-l hrtrt l rut t DDOM y ly tr N ly. ( ( F.. ( Syl th DD, ( qult l. ( ( F. 5. ( Syl th BT, ( qult l. ( - ( ( F. 6. ( Syl th DT, ( qult l. 5. DD t Th DD, wh yl t F. (, -trl twrk t qult l y u trll ur hw F. ( [5]. Th hyr t hl lt urrt l t ut trl ly urrt l t ututtrl. r t [], []-[] lyz h trl F. (, th yt qut wrtt rl tt tr y

4 DOENGNEENG, OL., NO., JUNE 5 (7 whr,, (lly, = r th ut tt, r th t -l lt urrt, rtly. By r l ut tt (.., = = =, (7 ru t. (8 6. BT St Th BT hl urrt l t th ut trl th lt urrt l t t utut trl [6]. Th rut yl th BT hw F. 5( t qult l y u trll ur t F. 5(. r t [], [], [], th t th BT u (9 whr th utut tt (lly, =,, r th t -l t-t urrt lt, rtly; th t l trut. qu, (9 rtly u t rult th NM l rut t BT. 7. DT St Th DT hl urrt th ut-utut trl [7]. Blly, t urrt rtl lr wth ltry r th z-trl. Th rut yl th DT hw F. 6( t qult l t F. 6(., r t [], [], [], th t th DT y ( ( F. 7. ( lt rtr, ( qult rut. ( whr, r th ut tt (lly, = =, th t -l urrt th t -l trut. 8. llutrt El th t, l r r t trt th u th r t rr t ut ullyyl ll-l hrtrt l rut t DD, DDOF, DDOM, DD, BT DT. Lt u wth th l tly hw F. 7( []. t qult rut y u F. ( t F. 7(. r t F. 7( (, tr N l th yt qut y ( whr = = r r. Fr ( th yl trr ut ut. ( l, lt u r th DDOF- ly rtl trtr tk r [] whh hw F. 8(. t qult rut llutrt F. 8(. r t F. 8( y ly (, th NM y

5 5. SNHEZ-LOPEZ, ET L., SMBOL NODL NLSS OF NLOG UTS ( whr = = r r. Fr ( th utut lt ut. ( Lt u w tuy th DDOM- rtl lt lr tk r [] whh llutrt F. 9( l wth t qult l y u trll ur hw F. 9(. r t F. 9(, th NM rult u th t y (6 ( (5 whr = = r r. Thrr, th utut lt ut r (5 y (. (6 DD- lt- qu ltr tk r [5] t F. (. t qult rut llutrt F. (. By ly (8 F. (, th NM ult 5 (7 u = =, Z = / = Z = / =, th yl trr ut r - lw- r r y, (8. (9 ( ( F. 8. ( DDOF- rtl trtr, ( qult rut. ( ( F. 9. ( DDOM- rtl lt lr, ( qult rut. ( ( F.. ( DD- lt- qu ltr, ( qult rut.

6 DOENGNEENG, OL., NO., JUNE 5 th l, w r th BT- lltr tk r [5] whh hw F. (. t qult rut llutrt F. ( wth 5 utut. r t F. ( y ly (9, th NM y 5. ( Thrr, th hrtrt qut r th lltr rut y ( ( Z Z ( whr Z = / h r. Fr (, th t rquy llt r ut, ( Z. ( Fr (, tht th t llt trll y r, whl th rquy llt trll y r. lt l, lt u r th DT- Krw-Hul-Nw (KHN qu tk r [6] t F. (. t qult rut llutrt F. (. By ly ( F. (, th yt qut y 6 5 L ( Syl trr ut r lw-, - hh- r r y L, ( B, (5 H. (6 ( ( F.. ( Sul lltr u BT, ( qult rut. ( 5 ( L 6 H B L ( F.. ( DT- KHN ltr, ( qult rut. 9. Sury lu Syl ly wrul tl whh lrt th ltr r, yl r tht r th hr rut rt tht ltry t rt ul y url ult []-[5]. th t, rl yl lyzr wr r rr t ut yl rr rtr ltr rut [], [], [5]. th lyzr, th MN th w rlly u t rult th yt qut. Hwr, th z th tt tr th ur zr lt r y h trll ur u. Fr t, whthr th MN rult l F. (, th z th tr 9 9 wth 9 zr lt, whh lrr r th (7. Thrr, th uttl lty ry ut r wh rur trt thqu r l rr t ut

7 5. SNHEZ-LOPEZ, ET L., SMBOL NODL NLSS OF NLOG UTS rr rtr []. Fr th r, thr rh t ru th z th yt qut h rrt [] [5] thy r kw rw / th. th rr th, th ur qut qul t th ur t, lrly N. Hwr, r t [5], th th ly uul r l t. th lttr, l t r r, r th l rut t l lr, th ur qut ru y h lr. Tht, th ur qut qul r l th th ur t [], [5]. th th, lthuh th z th yt qut qul r l t r wth th NM y u th r th hr, ly l t u. t ru rwk, r th t w l r, ut-utut l wth th ut lu t th yl r t ut, rr t t hrl l r rlt urt. Furthrr, hul rul t ly th lt th rw lu t tt, ut l hw t ty th r, wh th trt ut [], [5]. Mrr, w t r th S S wr rtly r thy u t tly lu th hr y t t th NM []-[]. qu, t ly llr l tr t, h lry trt thruhut th r, ut l th PU-t ry ut u ur th lut th NM r r [8], [9]. t wrth t tht th ru l, Nrt qult w l t trr th t lt ur t urrt ur. t rt t th rt ru th tt tr rr. Furthrr, thll qult t h l r t th ltrtur [8], [9], [], [7]-[] wth th trt ru th z th yt qut r th utt yl r rut. E thll lt h l u yth th [], [7], [8]. t, thr th lt t th r thll lt u t ru t ly th z th NM th ur zr lt, ut l th rt lltr. Flly, th r t r l th hr t ly lu D tl, rult, yl rr rtr ut y ly tr N ly. th tt, ll th r t th rrt [], [], [], l wth ll th thll qult t rrt [8], [9], [], r lry lt t twr ll: Syl lyzr D l trt rut (S, l t th utu Urty Tll, M. kwlt Th wrk h urt y th rjt UT- D- yp-ut- th u y UT- M. r [] BOLEK, D., SENN,., BOLKO,., KOLK, Z. t lt r l l r: lt, rw, w rl. r, 8, l. 7,., [] SÄKNGE, E., GUGGENBÜHL, W. rtl ul lk: Th MOS rtl r lr. EEE Jurl Sl-Stt rut, 987, l. S-,., [] MHMOUD, S.., SOLMN,. M. Th rtl r rtl lt lr: w lk r l l r MOS thly. EEE Trt rut Syt, l Dtl Sl Pr, 998, l. 5,., [] SOLTN,., SOLMN,. M. MOS rtl r rtl rrr lr. trtl Jurl Eltr ut (EU, 9, l. 6,. 9, [5] HU, W., LU, S.-L., TSO, H.-W., HEN, J.-J. MOS rtl r urrt yr thr lt. EE Pr rut, D Syt, 996, l.,., [6] TEN, U. E., SGBS, M., SEDEF, H. urrt lr lr ltr u w t lk. trtl Jurl Eltr ut (EU,, l. 6,. 6, [7] BOLEK D. DT- ul lk r urrt- l l r. Pr. EEE Eur r rut Thry D. Krków (Pl,, l., [8] SNHEZ-LOPEZ,., FENNDEZ, F.., TLELO- UUTLE, E., TN, S. X.-D. Pthll lt- t l thr lt t yl ly. EEE Trt rut Syt,. r,, l. 58,. 6, [9] SNHEZ-LOPEZ,. Pthll qult ully-rtl t r yl l ly. EEE Trt rut Syt,. r,, l. 6,., [] LN, P. M. Syl Ntwrk ly. tr (Th Nthrl: Elr S Pulhr, 99. [] GELEN, G., SNSEN, W. Syl ly r utt D l trt rut. US: Kluwr Pulhr, 99. [] KOLK, Z., BOLEK, D., BOLKO,. Syl ly lr rut wth r t lt. WSES Trt Eltr, 8, l. 5,. 6, [] LH, J., SNGHL, K. utr Mth r rut ly D. Nrwll (M, US: Kluwr, 99. [] FENNDEZ, F.., ODGUEZ-ZQUEZ,., HUETS, J. L. GELEN, G. Syl ly Thqu: lt t l D utt. Ptwy (NJ, US: EEE Pr, 998.

8 DOENGNEENG, OL., NO., JUNE 55 [5] FKHFKH, M. TLELO-UUTLE, E. FENNDEZ, F.. D l rut Thruh Syl ly. Bth S Pulhr Lt.,. [6] FKHFKH, M. TLELO-UUTLE, E. STO-LOPEZ. l/f M Sl rut Sytt D. Srr. [7] HGH, D. G., DMOE, P. Sytt yth th r lu rut Prt : Ntt yth tl. Pr EEE trtl Syu rut Syt (SS. ur (,, l., [8] HGH, D. G., TN, F. Q., PPSSLOU,. Sytt yth th r lu rut Prt : t- rut yth. Pr EEE trtl Syu rut Syt (SS,, l., [9] HGH, D. G., TN, F. Q., PPSSLOU,. Sytt yth th r lu rut Prt : ll-trtr rut yth. Pr EEE trtl Syu rut Syt (SS,, l., [] HGH, D. G., TN, F. Q., PPSSLOU,. Sytt yth t- rut ul-lk. l trt rut Sl Pr, 5, l., [] SNHEZ-LOPEZ,., FENNDEZ, F.., TLELO- UUTLE, E. Grlz tt tr l OT O. Mrltr Jurl,, l.,. 8, [] SNHEZ-LOPEZ,., NTE-MHOL, B., MOLES- LOPEZ, F. E., SO-GUL M.. Pthll qult M M wth ult-utut. l trt rut Sl Pr,, l. 75,., [] SNHEZ-LOPEZ,. Grlz tt tr l ully-rtl S. Pr. EEE t. Sy. rut Syt., r. [] SNHEZ-LOPEZ,., OHO-MONTEL,., UZ-PSTO,., GONZLEZ-ONTES, B. M. Syl l ly ully-rtl l rut. Pr EEE trtl Lt r Syu rut Syt,, l.,.,. -. [5] HEENS, N., KOTON, J., B, K., LH,., TEN, U. E., SGBS, M. w t MOS rlzt ul lltr u l BT. Pr trtl r lktrk. Br (zh ul,, l.,. -. [6] KESKN,. Ü., BOLEK, D., HNOGLU, E. BOLKO,. urrt- KHN ltr ly urrt r trut lr. trtl Jurl Eltr ut (EU, 6, l. 6,., [7] SOLMN,. M. Nl tt tr thll rlzt BOO, DD, DDOF DDOM. Sr Jurl St rh,, l.,., [8] SD,.., SOLMN,. M. U rrr lt th t yth y tt tr. EEE Trt rut Syt : ulr r, 8, l. 55,. 9, [9] SD,.., SOLMN,. M. w rh r u th thll rrr lt th l rrtt t. t. J. rut Thry l.,, l. 8,., [] TLELO-UUTLE, E., SNHEZ-LOPEZ., MOO-FS, D. Syl ly (MO(((- l rut trtl Jurl rut Thry lt,, l. 8,. 6, [] TLELO-UUTLE, E., SNHEZ-LOPEZ,., MTNEZ- OMEO, E. Syl ly l rut t lt rrr urrt rrr. l trt rut Sl Pr,, l. 65,., ut uthr... rl SNHEZ-LOPEZ r th M.S. Ph.D. r, th ltr r, r th Ntl ttut r trhy, Ot Eltr (NOE, M, 6, rtly. Jury 6, h j utu Urty Tll (UT, M, t rr rrhr. Fr Ju 9 t Str, h w ttrl rrh llw t Mrltr ttut Sll (S-MSE-NM, S. Otr h j UT. H -uthr uthr k htr r th 9 rrh jurl r trtl r ulh th l l ult lr lr rut yt, ht lltr, yl ly, l rut, F-rut utr- rut. Dr. Sáhz-Lóz r th Ntl Syt r rhr (SN-ONyT M. H rulrly r t th rr tt rl trtl r rwr hh ttr jurl. r UZ-PSTO r th B.S. r Eltr r utu Urty Tll (UT, M, 6. S h wrk twr hr M.S. r th url twrk wth h th l trt rut, t Drtt Eltr utt Er t UT, M. Hr rrh trt lu url twrk, l trt rut, t ltr l l r. OHO-MONTEL r th M.S. r utt Er r utu Urty Tll, M,. Hr rrh trt r url twrk, t-ut, t lrth ttr rh. Mul l SO-GUL r h M.S. r r St Grut Shl Mhl Eltrl Er r Ntl Plyth ttut (ESME-PN, M, 987 Ph.D. r r th Ntl ttut r trhy, Ot Eltr (NOE, M 6. Fr 985 t 989, h w wth Mtrlt utu Urty t Prr r 987 t 988 rtl-t rr t St Grut Shl ESME-PN. 99 h j th utu Urty Tll (UT, M whr h t rr t Fulty B S Thly, Drtt Eltr. H rrh trt lu rwl ry, wr ltr tl yt.

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