ADAPT: Design assistance for iterative analog synthesis

Transcription

1 ADAPT: Desgn assstance for teratve analog synthess Cheh Ln, Tno Hejmen, Jan ter Maten, Marq Kole Phlps Research Laboratores, Endhoven, The Netherlands; Emal: Abstract Ths paper presents an analog crcut desgn assstance tool called Adapt. The tool can perform automatc crcut szng over a wde range of heterogeneous desgn parameters. We present Adapt s archtecture and the desgn flow, dscuss mportant user-nterface aspects of the tool, dsclose detals on the optmzaton algorthms ncorporated n the tool, and demonstrate the practcal strength of the tool. The ndustral-strength capabltes of the tool are showcased usng an RF low-nose amplfer that s used n Bluetooth applcatons. 1 Introducton Although the current trend n ntegrated crcut desgn s to mplement as much as possble of the functonalty of an ntegrated system n the dgtal doman, analog crcuts are stll ndspensable to nterface to the real world. A clear example s the development n RF applcatons for moble and wreless communcatons. Apart from ths, the desgn of any crcut at the transstor level s bascally analog crcut desgn and that ncludes the desgn of dgtal standard cells used n dgtal crcutry. Desgnng analog and RF buldng blocks s a tmeconsumng and complcated task. Startng from a number of specfcatons, a desgner has to use hs experence and creatvty to select or develop a topology that mght be able to meet those specfcatons. From the chosen crcut topology he has to determne how and under whch condtons the specfcatons can be met. Ths s normally accomplshed by selectng the rght values for all components avalable n the crcut. In the desgn of ntegrated crcuts the desgner has relatvely much freedom n the selecton of possble values through the related geometrcal dmensons of the components, for nstance the wdth and length of MOS transstors and poly resstors, the emtter area of bpolars, etc. Therefore ths s also called the szng of the desgn. Next to component values also the values of bas currents and voltages (ncludng the supples) should be consdered desgn parameters. Manual szng of the desgn s a tedous task, but gves a lot of nsght nto crcut behavor, whch mght be useful at a later stage of the desgn process. As the human desgner knows whch specfcatons are the most mportant or the most dffcult to meet, he can keep possble desgn solutons n mnd for every specfcaton. The mplcatons of ths desgn process are clear. Frstly, analog desgn requres a lot of experence of the desgner. Secondly, automatng ths task s both knowledge and computaton ntensve. Stll, the man reason one would lke to automate ths task s tme reducton of analog buldng block development. Also, wth the scarcty of experenced analog desgners one would lke such a desgner to focus on the creatve part of analog crcut desgn and leave the tedous and less creatve part of t to a computer. In the past 15 or so years qute a number of developments nto the area of analog synthess have appeared. Where ntal efforts focused on the automaton of the complete analog desgn process, the more recent results offer help at partcular ponts n the process: crcut szng, desgn centerng, desgn space exploraton. Other mportant aspects of analog synthess are automated topology selecton and layout generaton. Although a lot of progress has been made n the past decades, tools n the latter areas are not yet mature enough, probably due to more dffcult challenges, compared to crcut optmzaton tools. In ths paper we employ analog synthess to cover only crcut optmzaton. Wthn our group a tool called Adapt has been developed whch focuses on crcut szng. In Secton 2 we present Adapt n the context of prevous analog synthess developments. We wll dscuss ts nteracton wth the user, whch s a vtal pont of each tool; how does the user enter hs desgn problem, how does he nteract wth t, and how s t embedded n the complete desgn flow. In Secton 3 we reveal whch optmzaton algorthms Adapt uses for ts operaton. A new algorthm, developed for Adapt, s dscussed n detal. Secton 4 demonstrates the true power of Adapt; a demandng contemporary crcut has been optmzed and, consequently, has led to a consderable mprovement compared to manual desgn. Fnally, n Secton 5 we wrap up wth a few conclusons and drectons for future research. 2 Adapt: Analog Synthess Whereas dgtal desgn s hghly automated and reles heavly on synthess tools, the bulk of analog desgn s done by hand and requres a sgnfcant amount of desgn effort even though analog parts commonly occupy only a relatvely small part of the slcon area n the fnal desgn. The man reason for ths desgn effort s that analog desgn s knowledge-ntensve due to the strongly non-lnear nature of the performance measures and the hgh senstvty of these measures to varatons n the desgn parameters, resultng n desgn problems wth complex trade-offs. In order to decrease the desgn tme for analog desgn and to be able to handle n-

2 creasngly complex crcuts and desgn processes, sgnfcant effort has been spent durng the past decades on the automaton of analog desgn [4]. In the past, a number of approaches have been proposed to deal wth the problem of automatcally szng the crcut, sometmes n combnaton wth automated topology selecton. These approaches can be roughly categorzed nto knowledge-based methods, usng desgn knowledge and heurstcs, and optmzaton-based methods, applyng numercal programmng technques. The frst generaton of knowledge-based tools for analog crcut synthess were presented n the second half of the 1980s; programs such as BLADES [3], IDAC [1], and OASYS [5]. However, all these programs suffered from the problem that the heurstc knowledge of an analog desgner s dffcult to acqure explctly. Not only was t a very tme-consumng process to encode desgn knowledge for a gven set of specfcatons, but ths desgn knowledge also had a lmted lfetme. The hgh rate of progress n process technologes made knowledge acqured yesteryear less an obvously good choce for current technologes. Therefore, the applcaton of knowledge-based analog synthess approaches has been lmted. Startng from the late 1980s a second generaton of methods emerged that apply optmzaton technques to determne the values of the desgn parameters n order to optmze the crcut performance for a gven set of specfcaton constrants. These methods are more flexble than the knowledge-based approaches and can be extended more easly to new crcut types. Two subcategores can be dstngushed: the equaton-based and the smulaton-based approaches. The equaton-based methods use analytc desgn equatons to descrbe the crcut performance. The advantages of the equatonbased approach are the short evaluaton tme and the flexblty. The man drawback s that analytcal models have to be used to derve the desgn equatons and, despte recent progress n symbolc crcut analyss, not all desgn characterstcs can be easly captured n analytc equatons wth suffcent accuracy. These problems can be avoded by applyng a smulaton-based approach where a crcut analyss tool s executed n the nner loop of the optmzaton to determne the crcut performance. Although ths used to be computatonally too expensve, wth the exponental ncrease of computaton power ths approach has become ncreasngly favorable. Especally for small and medumszed crcuts the relatvely hgh evaluaton cost of numercal smulaton s not an obstacle. Tools such as DELIGHT.SPICE, FRIDGE, ASTRX/OBLX, MAEL- STROM, and ANACONDA (see [4] for an overvew) are examples of smulaton-based tools. Thus, although automated crcut szng s not by far as commonly used as, for example crcut smulaton, t has ganed ncreasng nterest n the analog desgn process durng the last decades. However, a key dffculty s that the analog desgn problem, wth all the nvolved desgn knowledge and heurstcs, has to be formulated as an optmzaton problem such that the fnal optmzed results are acceptable to the desgner. Ths often presents a hgh threshold for usng a crcut-szng tool. 2.1 Adapt Flow In Fg. 1 the Adapt desgn cycle s shown as a contnuous loop. It s assumed that the desgner has selected an approprate crcut topology,.e. t mght be able to fulfll all specfcatons once properly szed ( unoptmzed netlst ). At the top left sde of the fgure, the desgner enters the desgn cycle by defnng the crcut performance targets ( crcut characterstc, operator, target ). Also, each of these crcut specfcatons have to be put n one or more prorty groups, whch s explaned shortly. target operator crcut characterstc prorty groups construct cost functon derve crcut characterstcs specfcatons lst evaluate cost functon crcut smulaton(s) Fg. 1: The Adapt desgn cycle. perform algorthmc optmzaton actons adapt netlst(s) smulatons lst optmze varables compute nstance parameter values unoptmzed netlst Once these nputs have been handled, Adapt starts to construct the cost functon for ths partcular optmzaton problem. Based on sampled values around the gven ntal soluton, the optmzaton routne wll determne the most lkely drecton of a better soluton and provde a new set of values for the optmze varables. Optmze varables are the basc parameters the optmzaton routne operates on. It s better to use optmze varables rather than the desgn parameters drectly as ths wll allow a desgner to specfy a number of desgn parameters that are correlated, for nstance for transstor matchng purposes. Ths approach clearly reduces the number of ndependent optmze parameters whch has a postve effect on overall run-tme. From the optmze varables, the desgn parameters (nstance parameter values) are calculated. These can now be nserted n the orgnal netlst at the approprate postons. Next, the desgner needs to enter a so-called smulatons lst: a lst of smulatons to be carred out for the crcut to be able to obtan the smulaton data necessary to calculate the desgn characterstcs. Ths mght be a number of transent smulatons for a dgtal cell, but may also be a number of complcated RF smulatons for an RF mxer crcut or a VCO. Usng ths smulatons lst, a set of netlsts s produced

3 and the smulaton job s fed to the smulator. Usng the user-defned specfcatons lst, Adapt wll derve from the smulaton output all requred nformaton to compute the crcut characterstcs and quantfy them n terms of the gven specfcatons. The comparson of the desgn characterstcs wth the desgn specfcatons s done through a new evaluaton of the cost functon. The qualty of the desgn characterstcs s quantfed by the cost functon value and ths, n turn, gudes the optmzaton algorthm n choosng the next adaptaton of the optmze varables. Now we have completed a sngle teraton of the Adapt desgn cycle. Typcally the optmzaton algorthm terates ths process untl a predefned number of evaluatons has been performed, (non-)convergence has been detected or the user has stopped the program. Adapt can be hghly nteractve. It gves feedback n a graphcal form and easly allows for exploraton of any crcut topology, enablng the desgner to buld up desgn knowledge when workng wth the tool. Adapt uses an external numercal crcut smulator and a dervatve-free nonlnear constraned optmzaton algorthm. Even though the underlyng methods n Adapt are optmzaton methods, the program hdes the mathematcal complexty mpled by these methods from the user. Ths s acheved by automatcally formulatng the optmzaton problem n a smlar way as s done n a manual desgn process. It provdes a user nterface that uses crcut characterstcs and desgn specfcatons to communcate wth the user. Ths nterface s hghly nteractve and has been desgned to be as close as possble to the desgn envronment the desgner s comfortable wth. It leaves the maxmum amount of freedom to control the desgn process as desred. One aspect of optmzaton that often proves a great barrer to entry of potentally nterested desgners s the formulaton of a mathematcal optmzaton problem. Ths nvolves settng up a cost functon, whch s specfc for each problem and whch gudes the optmzaton n the desred drecton. Adapt provdes automated generaton of the cost functon based on a smple and ntutve set of operators, famlar to analog desgners. The current approach, evolved from many years of user-feedback, s ntutve and straghtforward, hdng as many optmzaton-specfc detals as possble. To analog desgners some specfcatons are more mportant than others. For nstance, a functonal requrement such as phase margn has hgher prorty than mnmzng the power consumpton. Only once the specfcaton of hgher mportance has been satsfed should the szng process try to meet the specfcaton of the lower prorty tem. Ths process has been mplemented n Adapt through so-called prorty groups. The optmzaton algorthm wll try to meet the specfcatons n the hgher prorty groups frst, and optmzes the lower prorty groups whle constranng the acheved hgher prorty specfcatons not to fall below ther accepted values for the remander of the optmzaton process. In practce the desgner wll put the functonal requrements at hgher prorty groups and global optmzaton for power and area n the lower prorty groups. 2.2 Adapt User Interface Adapt ntends to help an analog desgner tune a crcut wth a gven topology to ft ts specfcatons. An mportant perceved beneft s that t allows the desgner to use hs own experence to gude the tool n the rght drecton and arrve at a desgn that meets the specfcatons. The man contrbuton requred from the desgner s smulaton and desgn knowledge. The program s a desgn assstant that gves the user full control over the desgn, the specfcatons, and the way n whch the specfcatons should be met. To measure the performance of the desgn, a so-called test-bench s requred. Ths test-bench s made up from three parts: a test-rg, the specfcatons lst, and the smulatons lst. The latter two were dscussed wth the Adapt desgn cycle; the frst requres some explanaton. A test-rg conssts of extra crcutry (such as voltage and current supples, loads at outputs, bas sources, etc.) that s added to the selected crcut topology n order to allow smulatons specfed n the smulatons lst to be performed. An nterestng applcaton of Adapt s the mgraton of an exstng desgn to a new process technology. For ths approach the test-bench need not be changed. Indeed, t s the centerpece that allows one to test the specfcatons for the new desgn n the same way that they were derved for the old desgn. It s generally a good dea to construct a test-bench n a process-ndependent manner, keepng reuse n mnd. An mportant consderaton for analog synthess s that the desgn process mmcs as much as possble the desgn style and envronment the user s comfortable wth. That means ntegraton nto the common desgn envronment (such as Cadence Desgn Framework II), support of a smulator qualfed for the job (an ndustral-strength smulator such as Avant! Star- Hspce), and access to all necessary output facltes the user would use durng the smlar manual process. At the moment both the Phlps n-house analog crcut smulator Pstar can be used as well as Cadence s Spectre smulator. Amed at the desgn of small or medumszed buldng blocks such as opamps, comparators, logc gates, VCOs, mxers, Adapt has already been appled successfully at several desgn centers throughout Phlps Semconductors. 3 Optmzaton Algorthms Adapt transforms a desgn problem nto a seres of optmzaton problems. Canddate algorthms for solvng

4 these have to satsfy a number of crtera: ffl The algorthm should be capable of handlng nonlnear constraned optmzaton problems. ffl The number of requred functon evaluatons should be as low as possble, because a full crcut smulaton s performed n each optmzaton step. ffl The algorthm should be truly dervatve-free. Dervatves of the performance functons wth respect to changes n the desgn varables are not provded by the smulator. Fnte-dfference schemes cannot be used, because the functon values are contamnated by numercal nose. Adapt apples two dfferent optmzaton algorthms that satsfy these condtons. The frst combnes the Nelder Mead (NM) method for unconstraned optmzaton wth a quadratc penalty functon to nclude constrants. The second uses an augmented Lagrangan as a mert functon, whch s mnmzed by a grd-based trust-regon approach. The latter algorthm has been developed specfcally for Adapt. The search for the optmal values of the optmzaton varables (OVs) can be formulated as a nonlnear constraned optmzaton problem n n varables wth m constrants, mnmze f (x); x =(x 1 ;x 2 ;:::;x n ); subject to c (x)» 0; =1;:::;m; a»x»b ; =1;:::;n; (1) where x denotes the th OV, wth lower and upper bounds a and b, respectvely. The values of the objectve functon f (x) and the constrant functons c (x) are obtaned from crcut smulaton. Equalty constrants are not ncluded n Eq. (1) because Adapt needs and supports only nequalty constrants. However, the algorthms could be easly adjusted to accommodate to problems ncludng equalty constrants. The performance and stablty of the optmzaton algorthms are affected by the scalng of the OVs and the values of the mert functons. Several transformaton types are of nterest n a crcut szng tool. Lnear transformaton s most sutable for OVs that vary only over a small range. On the other hand, OVs wth large ranges are best scaled by a logarthmc transformaton. However, f the varable or functon s not strctly postve or negatve, a transformaton has to be defned that behaves logarthmcally n the nfnte lmt, but that can also be appled to varables of ndefnte sgn. Ths knd of transformaton s called quas-logarthmc. All three scalng types are used n Adapt. The NM algorthm has been wdely used n practcal applcatons because of ts smplcty and robustness. However, t suffers from several drawbacks, such as moderate performance, lack of a sold theoretcal bass, and danger of degeneracy of the smplex. Because the total process tme s manly determned by the number of evaluatons, the relatvely poor performance of the NM algorthm can be a problem n the optmzaton of larger desgns. Therefore, an alternatve algorthm, named Grdmom, was developed for applcaton n Adapt. Ths algorthm s treated below. For a more detaled dscusson we refer to a forthcomng paper [6]. 3.1 Method of Multplers The Grdmom algorthm apples a sequental mnmzaton of an augmented Lagrangan penalty functon. By ntroducng a slack varable s 0, each nequalty constrant n Eq. (1) can be rewrtten as an equalty: c (x) +s =0. The augmented Lagrangan penalty functon can then be wrtten as, Φ ;s (x; ; μ; s) = (2) f (x) + mx Φ 2Ψ [c (x) +s ]+μ [c (x)+s ] ; =1 where the parameters and μ are Lagrange multplers and penalty factors, respectvely. Mnmzaton over the slack varables s yelds a smplfed penalty functon, Φ (x; ; μ) = (3) ( mx» f (x) + μ max c (x) 2 ) ; 0 2 : 2μ 4μ =1 In contrast wth the quadratc penalty functon, an exact soluton of the augmented Lagrangan can be found for fnte values of μ, provded that these values are suffcently large and that the values of are smultaneously optmzed. If these condtons are met, optmzng the penalty functon of Eq. (3) results n a combned set of varable values x Λ and multplers Λ that correspond to a soluton of Eq. (1), ndependent of the chosen values of μ. The algorthm uses the method of multplers (MOM) to solve the problem of Eq. (1), wth the augmented Lagrangan of Eq. (3) as a mert functon [6]. After a counter k s ntalzed (k = 1), the varables x and the penalty factors μ are set to ther ntal values x (0) and μ (0), respectvely, and the multplers are set to (0) = 0. The values of and μ are fxed and the mert functon, Φ (k) (x) =Φ (x; = (k 1) ; μ = μ (k 1) ); (4) s mnmzed, resultng n the argument x (k) for whch the functon s mnmal, x (k) = arg mn Φ (k) x (x): (5) The values of the multplers are updated usng x (k), (k) = (k 1) 2 max[ μ (k 1) c (x (k) ); (k 1) ]: (6)

5 The updated multpler values defne a new mert functon. The value of k s ncremented and Φ (k) (x) s agan mnmzed, gvng a new soluton x (k). Then, ether the multpler s updated, accordng to Eq. (6), or the correspondng penalty factor μ s ncreased. Whch of the two parameters s adjusted depends on the volaton of the correspondng constrant c (x). Thesequence of mnmzng the mert functon of Eq. (3) and updatng the parameters and μ s repeated untl the termnaton crtera have been satsfed. A combned set of varable values x Λ and multplers Λ s regarded as a soluton of Eq. (1), f the frstorder Karush Kuhn Tucker (KKT) condtons are fulflled. The algorthm s also ended f the maxmum allowed number of subproblems has been exceeded wthout fndng a soluton. It s then left to the user to accept the ntermedate results or to modfy the nput specfcatons and restart the optmzaton. 3.2 Trust-Regon Mnmzaton The orgnal nonlnear constraned problem s converted nto a sequence of bound-constraned subproblems, as dscussed above. Each subproblem nvolves the mnmzaton of a mert functon Φ (k) (x). To ths purpose, an algorthm s appled that s smlar to the one reported n [2]. Ths algorthm uses a grd and apples a trust-regon approach that approxmates Φ (k) (x) by a quadratc model functon, q(x) =a+g T (x x ref )+ 1 2 (x xref ) T G (x x ref ); (7) whch s mnmzed wthn a trust-regon B wth radus centered at the reference pont x ref, B = f x 2 R n jkx x ref k1» g: (8) In ths regon, q(x) s assumed to be a good estmate of the true mert functon. Because the nfnte norm kxk1 max jx j s used, the trust-regon has a square or (hyper-)cubc shape. Evaluaton of the mert functon s restrcted to ponts on a grd. Intally the grd s relatvely coarse, but t s refned durng the optmzaton process. The applcaton of successvely refned grds prevents the clusterng of evaluaton ponts n an early stage. The algorthm for mnmzng Φ (k) (x) dstngushes three phases: a startng phase, adescent phase, anda refnement-check phase. After the startng phase, the descent and refnement-check phases are alternately executed untl the termnaton crtera have been fulflled. The detals of the startng and descent phases prmarly determne the progress of the algorthm. On the other hand, the propertes of the refnement-check phase are manly responsble for ts robustness and convergence behavor. Durng the startng phase, the mert functon s evaluated at as many ponts as are necessary to enable the constructon of an approxmatng functon. The Grdmom algorthm ncludes two dfferent startng phase methods: one applyng the Hooke Jeeves (HJ) algorthm, the other usng the Unform Desgn (UD) approach. The second method s based on number theory and generates a unform sample pont dstrbuton n the feasble doman [6]. The trust-regon approach s appled n the descent phase, where the model functon q(x) s constructed by least-squares fttng to a set of ponts at whch the mert functon has prevously been evaluated. The selecton crteron for the ponts n ths set s the dstance from the reference pont. The descent phase s entered as soon as possble, because progress s assumed to be faster than durng the startng phase. Intally, the descent phase apples a lnear approxmatng functon. When more evaluatons have been performed and the number of avalable fttng ponts ncreases, the lnear model s replaced by a quadratc model wth a dagonal Hessan G. When suffcent evaluaton ponts are avalable, the algorthm swtches to a quadratc functon wth a full Hessan. An accurate estmate of the gradent g s more crucal than an accurate approxmaton of the Hessan G n Eq. (7). Therefore, the accuracy of the gradent s mproved locally by performng a second least-squares ft, wth a fxed Hessan obtaned from the frst ft, usng a small number of evaluaton ponts close to x ref. The approxmatng functon s mnmzed wthn the trust-regon and the mert functon s evaluated at the feasble grd pont nearest to the mnmum of the approxmatng functon. The trust-regon radus and the reference pont are updated and a new approxmatng functon s constructed. Ths process s repeated untl ether a grd pont s proposed at whch the mert functon has already been evaluated or untl a maxmum number of successve teratons have not resulted n an mproved estmate of the optmum. The update of the trust-regon radus sbasedonthe change n the value of the true mert functon compared to the reducton predcted by the approxmatng functon. The crteron for updatng the reference pont x ref s determned by a smlar rato. The refnement-check phase determnes whether the grd should be refned. To ths purpose a lnear approxmatng functon s ftted to a set of nearby evaluaton ponts and mnmzed. If necessary for the constructon of a non-sngular lnear functon, the mert functon s evaluated at a number of addtonal ponts. The algorthm returns to the descent phase f the grd pont closest to the mnmum of the lnear model s a better estmate of the optmum than the current approxmaton. Otherwse, f new evaluaton ponts have been attaned durng the refnement-check phase, a quadratc model functon s constructed and mnmzed wthn the trustregon B of Eq. (8), just as n the descent phase. If these efforts do not result n a better estmate of the optmum, the grd spacng s reduced.

6 The current estmate of the optmum s accepted as the soluton of the subproblem when a statonary pont of the mert functon has been obtaned. Crtera wth respect to both the varable values and the functon values of the augmented Lagrangan are appled to test for a statonary pont. The algorthm s also termnated after a maxmum number of functon evaluatons or when the grd has been refned a maxmum number of tmes. Although each mnmzaton of the current augmented Lagrangan s an optmzaton problem on ts own, t s possble to reuse the values of the objectve and constrant functons obtaned when solvng prevous subproblems. The values of f (x) and c (x) computed for prevous evaluaton ponts are stored (an evaluaton pont s defned as a set of OV values). Ths nformaton s used to compute the value of the current augmented Lagrangan for the stored evaluaton ponts, gven the current values of the Lagrange multplers and the penalty factors μ. Thus, a startng set of data for the constructon of approxmatng functons s avalable after the frst subproblem has been solved. Ths reuse of smulaton data can sgnfcantly ncrease the performance of the MOM approach. 4 A Desgn Example In ths secton we demonstrate the strength of Adapt by dscussng some of the results we have obtaned recently on contemporary crcuts. The demonstraton vehcle s an RF low-nose amplfer that s used n Bluetooth applcatons. Due to ntellectual property constrants, we are unable to dsclose detals on the crcut topology. 4.1 RF Low-Nose Amplfer Every analog crcut desgner knows that typcally many specfcaton trade-offs are possble, some of whch are exceptonally attractve. Ths case shows that Adapt can successfully fnd one of these specal cases for an RF low-nose amplfer crcut. Whle we ncrease 40% of the LNA power consumpton (ncludng a mrror suppresson flter), we can gan more than 3dB n nose fgure value, obtan 2dBv ncrease n gan, and reduce thrd order harmonc dstorton by more than 3dBv. Ths s a sgnfcant mprovement of the manual desgn. Ths desgn has 14 optmze varables, 34 desgn parameters, and 4 specfcatons for gan, power, lnearty and nose. Although the number of optmze varables s qute modest, ths partcular desgn requred the use of advanced RF analyss methods that are much more computatonally expensve than conventonal analyses. Therefore, t mght be consdered a challenge to formulate the optmzaton problem n such a way as to fnd a good soluton n a reasonable amount of tme. From the experments, we observed that Adapt (usng Grdmom) s very robust and the overall run-tme does not ncrease dramatcally as the problem sze ncreases (number of specs, number of optmze varables, number of smulatons). The optmzaton run-tme was somewhat more than one hour for 111 smulaton cycles (see Fg. 1) on a standard HP9000/800 UNIX server. 5 Conclusons and Drectons We have shown that Adapt s a true analog desgn assstance that can help a desgner fnd better crcut solutons n less tme. Adapt s very well ntegrated n the overall desgn flow usng the Cadence DF II envronment. It exhbts a frendly graphcal user nterface that shelds the desgner from non-relevant algorthmc aspects. Consequently, settng up the tool for a specfc desgn problem s qute straghtforward. The new Grdmom algorthm n Adapt has been dscussed. Moreover, the ndustral-strength power of Adapt has been demonstrated by the mproved result of an RF low-nose amplfer for Bluetooth applcatons. There are stll ponts for mprovements that we are consderng. Some of those are: effcent determnaton of soluton robustness and better handlng of heterogeneous test-benches. Last but not least, takng nto account layout effects durng optmzaton s of major mportance, especally for RF crcuts. References [1] Degrauwe, M.G.R., Goffart, B.L.A.G., Mexenberger, C., Perre, M.L.A., Ltsos, J.B., Rjmenants, J., Nys, O.J.A.P., Djkstra, E., Joss, B., Meyvaert, M.K.C.M., Schwarz, T.R., Pardoen, M.D., Toward an analog system desgn envronment, IEEE J. SSC, Vol. 24 (1989), pp [2] Elster, C., and Neumaer, A., A Grd Algorthm for Bound Constraned Optmzaton of Nosy Functons, IMA J. Numer. Anal., Vol. 15 (1995), pp [3] El-Turky, F., and Perry, E.E., BLADES: an artfcal ntellgence approach to analog crcut desgn, IEEE Trans. CAD, Vol. 8 (1989), pp [4] Gelen, G.G.E., and Rutenbar, R.A., Computer-Aded Desgn of Analog and Mxed-Sgnal Integrated Crcuts, Proc. IEEE, vol. 88 (2000), pp [5] Harjan, R., OASYS: a framework for analog crcut synthess, IEEE Trans. CAD, Vol. 8 (1989), pp [6] Hejmen, T.G.A., Kevenaar, T.A.M., Pranger, H.-J., Adapt: an Optmzaton-Based Analog Desgn Assstance Tool, submtted for publcaton. [7] Kole, M., Hejmen, T., Kevenaar, T., Pranger, H.-J., Sevat, M., Adapt, an nteractve tool for analog synthess, Proc. SAME Conf., Sopha Antpols, France, 2001.