Switched-capacitor neural networks for linear programming

obse ed in an o dina y asymme ic e lec i i y DFB lase wi hou L/4 phaseshi was due o a mode pa i ion be ween he DFB mode and Fab y-Pe o modes caused by insu icien AR coa ing a one end o he lase . So a TE-TM mode pa i ion as shown in Fig. 3 has no been obse ed. In he 44 shi ed DFB lase he h eshold gain di e ence AaL among TE modes o among TM modes is a ound 0.7 when op imally de~igned,~ i.e., KL is 1.25, while he mode selec ion be ween TE and TM mode p o ided by he di e - ence in he coupling coe icien and he mode con inemen ac o is e y small. Theo e ical calcula ion assuming a ec- angula shaped co uga ion using a model by S ei e e aL4 showed ha he e was no di e ence in he coupling coe icien be ween TE and TM modes o he ac i e laye hickness d, o 0.15pm. Fo a hinne d, o 0.1 pm he e was a sligh di e - ence. Howe e , e en in his case, he AKL o op imum KL o 1.25 was only 0.06, which co esponded o he h eshold gain di e ence AaL be ween TE and TM mode o only 0.07. The di e ence in mode loss owing o he mode con inemen ac o could no be as la ge because o he small abso p ion coe i- cien o he cladding laye s. The mode selec ion be ween TE and TM mode in a 1/4 shi ed DFB lase is much smalle han ha in an o dina y asymme ic e lec i i y DFB lase in which TE-TM mode selec ion is p o ided by he ace e lec i i y. Fig. 4 shows he ime a e aged spec a o a 1/4 shi ed DFB lase unde modula ion measu ed using a pola ise . We can iden i y a small ampli ude TM emission. This small ampli ude TM emission is e idence o TM mode lasing wi h a e y small p obabili y, o he o de o IO-’’, unde modula ion due o he gain o e shoo . n TM h I I I wa eleng h, p m 1 30 131 132 Fig. 4 Time a e aged spec a unde modula ion TM spec um was measu ed using a Clan-Thompson pola ise We ha e de eloped a e y-low- h eshold-cu en high- e iciency i/4 shi ed DFB lase ha ing bandwid h o 11 GHz. Howe e , ansmission expe imen e ealed ha he e exis ed a mode pa i ion be ween TE and TM mode. This mode pa i- ion is due o a small h eshold gain di e ence be ween TE and TM mode. To make ull use o he a ac i e ea u e o he 1/4 shi ed DFB lase , Le., he la ge h eshold gain di e - ence be ween modes, we mus inco po a e a s ong mode selec ion mechanism be ween TE and TM mode. This is espe- cially impo an o a lase o be used in se e al Gbi /s sys ems unde a di ec modula ion scheme. The au ho s wish o hank M. Ma suda o his ab ica ion o he 144 shi ed co uga ions, and S. Isozumi, T. Kusunoki, T. Tanahashi, H. Sudo and M. Sugano o hei co-ope a ion in his wo k. They also wish o hank T. Misugi, M. Kobay- ashi, and T. Saku ai o hei encou agemen . H. ISHIKAWA K. KAMITE K. KIHARA H. SODA H. IMAI Fuji su Labo a o ies L d. 10-1 Mo inosa o- Wakumiya, A sugi, Japan 496 26 h Feb ua y 1988 Re e ences ISHIKAWA, H., SODA, H., WAKAO, K., KIHARA, K., KAMITE, K., KOTAKI, Y., MATSUDA, M., SUDO, H., YAMAKOSHI, s., ISOZUMI, s., and IMAI, H.: ‘Dis ibu ed eedback lase emi ing a 1.3 pm o gigabi commu- nica ion sys ems’, J. Ligh wa e Technol., 1987, LT-5, pp. 848-855 KAMITE, K., sum, H., YANO, M., ISHIKAWA, H., and IMAI, H.: ‘Ul a- high speed InGaAsP/InP DFB lase s emi ing a 1.3pm wa e- leng h, IEEE J. Quan um Elec on., 1987, QE-23, pp. 10561058 SODA, H., KOTAKI, Y., sum, H., ISHIKAWA, H., YAMAKOSHI, s., and IMAI, H.: ‘S abili y in single longi udinal mode ope a ion in GaInAsP/InP phase-adjus ed DFB lase s’, IEEE J. Quan um Elec- on., 1987, QE-23, pp. 804-814 STREIFER, w., SCIFRES, D. R., and BRUNHAM, R. D.: ‘TM-mode coup- ling coe icien s in guided-wa e dis ibu ed eedback lase s’, IEEE J. Quan um Elec on., 1976, QE-12, pp. 7478 SWITCH ED-CAPACITOR NEURAL NETWORKS FOR LINEAR PROGRAMMING Indexing e ms: Neu al ne wo ks, Swi ched-capaci o ne - wo ks, Linea p og amming sol e s, Ci cui heo y and design A ci cui o online sol ing o linea p og amming p oblems is p esen ed. The ci cui uses swi ched-capaci o echniques and is hus sui able o monoli hic implemen a ion. The con- nec ion o he p oposed ci cui o analogue neu al ne wo ks is also ou lined. In oduc ion: I has been shown ha bo h linea and nonlin- ea p og amming p oblems can be sol ed by using analogue ci cui s wi h a neu al-like s uc u e.’,’ These ci cui s exhibi s ong po en ial o hose applica ions whe e online op i- misa ion is equi ed as is he case in obo ics, sa elli e guid- ance, e c. B eadboa d p o o ypes ha e been buil using o - he-shel ci cui componen s. ‘G~ Since he equi ed componen -coun is e y high e en o simple examples, i makes sense o explo e he possible ealisa ion o hese ci cui s using ully in eg a ed echniques. Nonlinea p og amming sol e s a e pa icula examples o he b oade amily o analogue neu al ne wo ks, which is o inc easing in e es because i seems o pa e he way o ana- logue a i icial in elligence ci cui ^.'.^ Howe e , he ield o analogue neu al ne wo ks is jus eme ging and e y li le has been done on he p ac ical implemen a ion o he di e en classes o such ne wo ks. In a e y ecen le e , Tsi idis and Anas assiou’ p oposed a echnique o he VLSI implemen a- ion o a ype o analogue neu al ne wo k using a swi ched- capaci o neu al cell. The p oposed echnique is adequa e o sol ing op imisa ion p oblems ha can be o mula ed in an explici o m,’ bu no eadily applicable o linea and nonlin- ea p og amming p oblems. A di e en s a egy is equi ed o his ype o analogue neu al ne wo k, since he equa ions desc ibing ma hema ical p og amming p oblems a e implici in na u e and do no admi o being cas in an explici o m.’ In his le e we p opose a me hod o he ealisa ion o linea p og amming sol e s using swi ched-capaci o ech- niques. The p oposed ci cui s a e membe s o he gene al amily o analogue neu al ne wo ks, being mo e adequa e o monoli hic implemen a ion han p e ious linea p og amming sol e p oposals. P oblem o mula ion and p oposed ci cui s uc u e: The gene al linea p og amming p oblem can be s a ed as ollows.6 Minimise a scala cos unc ion @(x) = 1 aixi i= 1 subjec o a se o p cons ain s, n LXx) = 1 bji xi 2 0 i= 1 l<j<p (2) whe e x is he ec o o a iables o he p oblem, p and n a e in ege numbe s and a and bj, o each j, a e ec o s o coe i- cien s. ELECTRONICS LETTERS 14 h Ap il 1988 Vol. 24 NO. 8 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on Ma ch 31,2020 a 14:34:02 UTC om IEEE Xplo e. Res ic ions apply. By using he concep o he penal y unc ion' and applying a g adien s a egy we ob ain he ollowing nume ical algo- i hm o sol e he abo e gene al linea p og amming p oblem, whe e a is an a bi a y posi i e cons an , q is an in ege numbe o he i e a ion coun and unc ions w( ) and pj a e de ined as ollows, 1 0 o he wise i j 2 0 o e e y j w(n = { (4) whe e No e ha he in oduc ion o he unc ion w( ) means a modi ica ion o he adi ional way o combining and @ o de ine penal y unc ions.' This modi ica ion is impo an o imp o e he con e gence o he algo i hm. Using eqns. 4 and 5 and eqns. 1 and 2 in eqn. 3 we ob ain he ollowing ela ionship o each componen o x: is an a bi a y posi i e cons an . whe e sgn (.) is he well-known sign unc ion. IV I ll II 'qdd phose Fig. 1 Block diag am o p oposed linea p og amming sol e Fig. 1 shows he concep ual block diag am o he imple- men a ion o he gene al linea p og amming p oblem using swi ched-capaci o echniques. No e ha one in eg a o is equi ed pe p og am a iable. The p cons ain unc ions a e ob ained ia a se o summe s whose inpu s a e he in eg a o ou pu s. The nonlinea unc ions w( ) gi en in eqn. 4, and = +(I - sgn (L)) a e espec i ely ob ained om he ou pu s o he summe s ia he block a he bo om o he Figu e on he igh , hence o h called he cons ain block. Fig. 2 shows a de ail o he i h in eg a o block. A wo- phase clock signal is used o con ol he analogue swi ches. The inpu swi ches a e di ec ly con olled by one o he phases ( he e en clock phase) and he swi ches connec ed o he op-amp nega i e inpu lead a e con olled by he ou pu s o he cons ain block. These ou pu s a e de ined du ing he odd clock phase. By elemen a y analysis in ol ing cha ge conse - a ion p inciples i is clea ha he ci cui in Fig. 2 imple- men s eqn. 6. The summe block appea ing in Fig. 1 can be implemen ed by using echniques epo ed elsewhe e.' Fig. 2 De ail o in eg a o block P ac ical esul s: The p oposed ci cui has been compu e simula ed using DIANA' and a de ailed mac omodel o he op-amps.' The simula ed p og amming p oblems a e lis ed in Table I, whe e bo h he heo e ical solu ion and he one com- pu ed by DIANA a e shown o e e y example. Also included in Table 1 is he numbe o clock pe iods equi ed o he ci cui o each i s inal s a e. In all he cases, he ini ial s a e was he o igin o he p og am a iable space. As can be seen i is possible o ob ain a e y app oxima e solu ion in ela i ely ew clock pe iods. Conclusions: A ci cui s uc u e is p oposed o implemen ing linea p og amming p oblems using swi ched-capaci o ech- niques. This s uc u e is based on a educed se o basic cells ha a e in e connec ed ollowing a dense egula pa e n. The esul ing ci cui s exhibi a e y high modula i y and in his sense can be conside ed as membe s o he gene al amily o analogue neu al ne wo ks. The me hod is alid o any linea p og amming p oblem and is also sui able o monoli hic implemen a ion, a signi ican ad an age as compa ed o p e- ious analogue neu al linea p og amming sol e s.'*2 Acknowledgmen s: This esea ch has been suppo ed by Spanish CICYT unde con ac no. ME87-0004. A. RODRIGUEZ-VAZQUEZ 9 h Feb ua y 1988 A. RUEDA J. L. HUERTAS R. DOMINGUEZ-CASTRO Depa amen o de Elec icidad y Elec bnica Facul ad de Fisica Uni e sidad de Seuilla Anda. Reina Me cedes sjn, 41012-Se illa, Spain Table 1 THEORETICAL AND SIMULATION RESULTS FOR TWO PROBLEMS Scala unc ion Simula ed Numbe o cons ain s solu ion DIANA pe iods and Theo e ical solu ion using clock @ = , + 2 2 = 5 + u, 2 = 5 - u2 @ = 3 , + (1/2) , - (1/2) 3 l = 35/12 - (5/12) 1 + ~2 1 = -5 ~1 = -4.99 0.03 40 2 = 3512 - (5/2)~1 - VZ u2 -5 02 = -5.03 0.08 , = 6 + 1 + 2 + 3 01 = -6 VI = -5.88 0.3 2 = 6 - V, - 02 - ~3 2 = 0 2 = -0.04 0.11 40 3 = 6 + 1 + 2 - 2 3 4 = 6 - 01 - 02 + 203 s = 6 + VI - 2~2 + 03 6 = 6 - 01 + 2~2 - 03 j = 0 3 = -0.01 0.15 ELECTRONICS LETTERS 14 h Ap il 1988 Vol. 24 No. 8 497 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on Ma ch 31,2020 a 14:34:02 UTC om IEEE Xplo e. Res ic ions apply. Re e ences 1 TANK, D. w., and HOPFIELD, J. J.: ‘Simple “neu al” op imiza ion ne wo ks: an A/D con e e , signal decision ci cui , and a linea p og amming ci cui ’, IEEE T ans., 1986, CAS33, pp. 53>541 KENNEDY, M. P., and CHUA, L. 0.: ‘Uni ying he Tank and Hop ield linea p og amming ci cui and he canonical nonlinea p og am- ming ci cui o Chua and Lin’, IEEE T ans., 1987, CAS-34, pp. 21G214 3 WILSON, G. : ‘Quad a ic p og amming analogs’, IEEE T ans., 1986, 4 TSIVIDIS, Y.: ‘MOS analog IC design-new ideas, ends and obs a- cles’. P oceedings o he 1986 Eu opean Con . on Solid-s a e Ci - cui s, 1986, pp. 113-115 5 TSIVIDIS, Y., and ANASTASIOU, D.: ‘Swi ched-capaci o neu al ne - wo ks’, Elec on. Le ., 1987, 23, pp. 958-959 6 VANDERPLAATS, G. .: ‘Nume ical op imiza ion echniques o enginee ing design: wi h applica ions’ (McG aw-Hill, New Yo k, 1984) 7 GREGORIAN, R., and TEMFS, G. c.: ‘Analog MOS in eg a ed ci cui s o signal p ocessing’ (Wiley-In e science, 1986) 8 ARNOUT, G., REYNAERT, PH., CLAESEN, L., and DIJMLUGOL, D.: ‘DIANA V7E use ’s guide’. ESAT Labo a o y, Ka holieke Uni- e si ei Leu en, 1983 PBREZ-VERDI~, B., HUERTAS, J. L., and RODRIGUEZ-V~ZQUEZ, A.: ‘A new nonlinea ime-domain op-amp mac omodel using h eshold unc ions and digi ally-con olled ne wo k elemen s’, IEEE J. Solid-s a e Ci cui s, 22, o be published 2 CAS-33, pp. 907-91 1 9 second s uc u e (58N). We ha e measu ed o he hi d s uc- u e (SON) shee concen a ions as high as 8 x 10” cm-’ wi h mobili ies o 3500cmZ/Vs. The p ocessing o hese MESFETs was simila o ha epo ed p e iously.6 The MESFETs had a ga e leng h o 0.7 pm wi h a 4.0pm sou ce/d ain spacing. The 1/V cha ac e - is ics o 58N-s uc u e MESFET ha ing a 100pm ga e wid h a e shown in Fig. 1. A d ain sa u a ion cu en o 870mA/mm and comple e pinch o a a ga e ol age o -3.5V is achie ed. Fo he 48N s uc u e MESFET, a d ain cu en o 680mA/mm wi h a pinch o ol age o - 3.0V was measu ed. Fo de ices on he SON-s uc u e wi h a shee concen a ion o 8.0 x 1012cm-z, we measu ed cu en s as high as l.OA/ mm bu hey could no be pinched-o . Fig. 2 shows he a ia- ion o he ansconduc ance wi h ga e ol age o he 58N-s uc u e MESFET. The la ge bandgap AlInAs con ines he ca ie s in he channel, esul ing in he b oad peak in he ansconduc ance agains ga e ol age and imp o ed linea i y o high-powe FETs. Ex insic ansconduc ances as high as 325 mS/mm we e achie ed. Fo he 48N-s uc u e MESFETs, we achie ed ansconduc ances be ween 250 and 3 10 mS/mm. A ga e/d ain b eakdown ol age o 3.2V was measu ed a a leakage cu en o 0.5 pA/pm o ga e wid h o he 58N s uc- u e. Highe b eakdown ol ages can be ob ained wi h hicke undoped AlInAs laye s, bu a a sac i ice o ansconduc ance. g=o - HI G H - C U R R E NT P U LS E - DOPED Ga I n As MESFET Indexing e ms: Semiconduc o de ices and ma e ials, Field- e ec ansis o s, Gallium compounds We epo he DC and mic owa e pe o mance o pulse- doped GaInAs powe MESFETs. Fo a 0.7pm ga e-leng h de ice, a maximum d ain-cu en densi y o 870mA/mm and a peak ansconduc ance o 325 mS/mm we e measu ed. A maximum s able gain o ll.7dB a 26GHg and an ex apo- la ed , o 33 GHz we e ob ained. These alues a e he highes epo ed o MESFETs ha ing ga es as long as 0.7 pm. Powe ampli ie s based on GaAs/AlGaAs HEMTs su e om low d ain-sa u a ion cu en . Recen ly, mul ichannel and pseudomo phic HEMTs ha e been de eloped o inc ease cu en densi ies,‘-4 bu he low he mal conduc i i y o he GaAs subs a e limi s he maximum achie able powe o hese de ices. Imp o ed pe o mance can be ob ained by using AlInAs/GaInAs he e os uc u e FETs, which combine high mobili y wi h high shee -ca ie concen a ion. In addi ion, he InP subs a e o e s highe he mal conduc i i y han GaAs. The mic owa e pe o mance o AlInAs/GaInAs HEMTs is beginning o su pass ha o GaAs/AIGaAs HEMTs.*’ We ecen ly epo ed n -pulse-doped GaInAs MESFETs o 0.7pm ga e leng h wi h excellen maximum s able gains o 14dB a 26.5 GHz, and a maximum equency o oscilla ion o g ea e han 100GHz.6 In his le e , we epo he ab ica ion and pe o mance o n+-GaInAs-channel MESFETs wi h bo h high cu en densi ies and high gains. The pulse-doped GaInAs MESFET s uc u e was g own by MBE on a semi-insula ing InP subs a e. The de ice s uc u e consis ed o a 2500A AlInAs bu e laye , lOOA o undoped GaInAs, a 200A n+-GaInAs laye , 500A o undoped AIInAs, and a l00A n+-GaInAs cap. All he laye s we e la ice ma ched o InP. The undoped AlInAs laye educes he ga e leakage cu en and inc eases he ba ie heigh . We ha e g own h ee s uc u es wi h a ying elec on concen a ion. Fo he i s s uc u e (48N), a Hall mobili y o 4100cm2/Vs wi h an elec on concen a ion o 4.8 x 10’2cm~Z was mea- su ed a 300K. A Hall mobili y o 4100cm2/Vs wi h an elec- on concen a ion o 5.8 x 10’2cm-2 was measu ed o he * FATHIMULLA, A,, ABRAHAM, J., and LOUGHRAN, T.: ‘High pe o mance InGaAs/InAlAs HEMTs and MESFETs’. Submi ed o publica ion (IEEE Elec on. De ice Le s.) 498 / s I- 2 5 g = -3 o g =-3 5 ::e,;, 10 0 05 10 15 20 25 sou ce d ain ol age, V Fig. 1 IIV cha ac e is ics o a pulse-doped GalnAs MESFET The mic owa e pe o mance o hese MESFETs o di e - en sou ce/d ain ol ages and ga e ol ages was measu ed o e he equency ange 0.5-26.5 GHz using an au oma ed Cascade wa e p obe and an HP 8510 ne wo k analyse . Fig. 3 is a plo o he maximum s able gain (MSG) agains e- quency compu ed om he measu ed S-pa ame e s. An MSG o ll.7dB a 26.0GHz and an ex apola ed mx o o e 100GHz was ob ained. The cu en gain was also compu ed om he measu ed S-pa ame e s. Ex apola ing a 6 dB/oc a e oll-o , a cu en -gain cu o equency C ,) o 33GHz was ob ained. The mic owa e-gain measu emen s we e pe o med bo h be o e and a e isola ing he ga es om he edge o he mesa.* A e ga e isola ion, we measu ed an inc ease in he MSG, which we a ibu ed o a dec ease in he ga e-leakage cu en . 350 lOOV , I I I I I -3 5 -3 0 -2 5 -2 0 -1 5 -1 0 -0 5 0 ga e ol age, V 111312/ Fig. 2 T ansconduc ance agains ga e ol age o pulse-doped GalnAs MESFET ELECTRONICS LETTERS 14 h Ap il 1988 Vol. 24 No. 8 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on Ma ch 31,2020 a 14:34:02 UTC om IEEE Xplo e. Res ic ions apply.