A. Brat$ 2. University 1. Motorola SPS -Logic and h a l o Technolo ies Group, Tempe, AZ 85284, of Arizona ECE Dept. Tuscon, AZ 8 5 7 2 1 , 3 .~i n g t o n~i c r~e l e c t r o n i c s Limited, Northwich, Cheshire, UK. AbstractA Field Programmable Analog Array (FPAA) is presented based on switched capacitor technology. The architecture offers an unconstrained topology similar to its digital counterpart, containing an array of identical undedicated analog cells. This makes it possible to program both the functionality of each cell and the interconnect between cells. As a result a large number of diverse architectures may be implemented.The analog array can be programmed to perform many of the routine tasks associated with control systems design. It's linear and non-linear signal processing abilities can provide a wide range of waveform generation functions. The device can also be programmed for precise phase and magnitude characteristics. Some examples related to control systems are discussed.

A Field Programmable Analog Array (FPAA), built in CMOS technology, contains uncommitted operational amplifiers, switches, and capacitors. A FPAA containing banks of programmable switched capacitors (SC) can be used to build filters for analog signals as well as a large number of diverse analog applications. The parameters of a given application, such as a filter, are functions of the capacitor values. Manufacturing and quantization errors may result in capacitor values in the FPAA other than those required by the application. For an FPAA to be a viable substitute for dedicated devices we must examine the error performance of the implementation. Such performance analysis can be built into the software to provide circuit designers with additional information. A methodology is described for determining a bound for the filter error as a function of capacitor errors and capacitor sizes. An example of detailed analysis for a low pass filter is included. Measurements of a low-pass filter implemented using Motorola's prototype FPAA compared favorably with the model predictions.

and Compctci-3ngineeIing University of Arizom 'Tacson, AZ 85721 A h t r a c t the following linear mapping IntrDd .icti?n Analyze? circuit; are dzscribe? as a szt of nonlinear ordinary differentid equations created using modified nodal analysis (MNA). A new method based on Newton -Kan-torovich's approach is used for linearization of the equations and a very fast spectral algorithm based on Chebyshev polynomials is used to solve these linearized eqv3.c.i xu. Numerous properties of Chebyshev series are applied to develop an efficient algorithm and speed-~p the ;ixx-la,ion process. Solving Diferential EquationsUsing Chebyshev Series L,-rmr aifLier-tial squations zre solved using a specid spectral algorithm developed for utilizing the Chebyshev series and their properties. In this section some details of this numerical algorithm are piesectzd. Consider the following scalar differential equationwhere functims i'(2), S[2) and k (2) are kn3wr-for a specific time intervai where y : yf?) :L S e xnkrlawq and c(t), g ( t ) and h(t) are known hnctionr 3t i 0 : t h y i r t e r d [-1,1]. The solution of the rlifferxit:a' Oqkatiop ' s c5tmned in the form 1V y!t) = Y?To\.j + C a J T J ( t ) (5) 1=1 ?. where T'(f\ den-ste. the Chebyshev polynomial of j f h order, cy1 (j = 0 , i, . . I 'j are constant coefficients, and N is an integer aetcrm,r,r.g the order or expansion. Using the special proppertks c: C+-JrdLc-i pc.jnomials equation (4) can be rewrittea i-% 3 iii&:x =-->I where the unknown parameters are the CbeLyc3s 7 =-/paxion coefficients. The process is descrited in LeLiis :c '1. (,he Fnal relation is (C -<;R'y-=z yog + h (6)where (2, G m i~i B a.e g:d?n ( X + 1) x ( N + 1) square matrices, g and h 5rt bi%,G-i :1? -t 1) dimensional vectors.The ( N + 1) dirnen;imal /ectar y * contains the coefficients of the Chebyshe7 zqznsioi: of tl-e derivative % of the unknown function y(t). TNZ? is y' = [ao*, a~* ,After solving for the entries of the vector y* based on reand P = P(t) is the unknown function On the same interVal. TO simplify mathematica1 operations the independent lation (6), vector y = [aO,a1, . . . , (yNIT of the expansion coefficients of the unknown function can be obtained using variable has been scaled to the interval [-1,1] using the following identity: y = By* + 2yoe (8) 89 0-7803-0593-0192 $3.00 1992 IEEFA

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