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Published jointly in Journal of VLSI Signal Processing, vol.8, pp.27-44, and in AnalogIntegrated Circuits and Signal Processing, pp.27-44, July 1994.

Analog VLSI Signal Processing:Why, Where and How?

Eric A.VittozCSEM, Centre Suisse d'Electronique et de Microtechnique SA

Maladire 71, 2007 Neuchtel, Switzerland

Abstract

Analog VLSI signal processing is most effective when precision is not required, and istherefore an ideal solution for the implementation of perception systems. The possibility tochoose the physical variable that represents each signal allows all the features of the transistorto be exploited opportunistically to implement very dense time- and amplitude-continuousprocessing cells. This paper describes a simple model that captures all the essential features ofthe transistor. This symmetrical model also supports the concept of pseudo-conductance whichfacilitates the implementation of linear networks of transistors. Basic combinations oftransistors in the current mirror, the differential pair and the translinear loop are revisited assupport material for the description of a variety of building blocks. These examples illustratethe rich catalogue of linear and nonlinear operators that are available for local and collectiveanalog processing. The difficult problem of analog storage is addressed briefly, as well asvarious means for implementing the necessary intrachip and interchip communication.

Introduction

It is a commonly accepted view that the role of analog in future VLSI circuits and systemswill be confined to that of an interface, the very thin "analog shell" between the fully analogouter world and the fully digital substance of the growing signal processing "egg"[1]. Themain advantage of all-digital computation is its cheap and potentially unlimited precision anddynamic range, due to the systematic regeneration of the binary states at every processing step.Other advantages are the cheap and easy design and test of the circuits. Digital circuits aredesigned by computer scientists working with advanced synthesis tools to implement specificor programmable algorithms. According to this view, the task of analog designers will beessentially concentrated on developing converters to translate, as early as possible, allinformation into numbers, with an increasing demand on precision, and to bring the results ofthe all-digital computation back to the real world.

This view is certainly correct for the implementation of all systems aiming at the preciserestitution of information, like audio or video storage, communication and reproduction.Together with very fast but plain computation on numbers, these are the tasks at which thewhole electronic industry has been most successful.

However, the very precise computation on sequences of numbers is certainly not what isneeded to build systems intended for the quite different category of tasks corresponding to theperception of a continuously changing environment. As is witnessed by even the most simpleanimals, what is needed for perception is a massively parallel collective processing of a largenumber of signals that are continuous in time and in amplitude. Precision is not required ( whywould 16-bit data be needed to recognize a human face?), and nonlinear processing is the rulerather than the exception.

- 2 - E.Vittoz:

Low-precision analog VLSI circuits therefore seem to be best suited for the implementationof perception machines, specially if cost, size and/or power consumption are of some concern[2]. The following chapters are intended to show how very efficient small-area processingcells can be implemented by exploiting in an opportunistic manner all the features of theavailable components, in particular those of the transistor. This will allow massively parallelarchitectures to be implemented on single chips to carry out the required collective processingon real-time signals. Whether or not these architectures should be inspired from biologicalsystems depends on the particular task to be solved. For example, handwriting is made for thehuman eye and should therefore be handled by taking inspiration from the human visionsystem, whereas the bar code has been invented for machine-reading and can thus be handledwithout reference to the eye.

The global perception of all relevant data is fundamental for advanced control systems.Therefore, analog VLSI also seems to be an ideal medium for the implementation of fuzzycontrollers [3], [4].

Signal representation in analog processing circuits

Signals in an analog circuit are not represented by numbers, but by physical variables,namely voltage V, current I, charge, frequency or time duration. The various modes of signalrepresentation have respective advantages and drawbacks and can therefore be used in differentparts of the same system.

The voltage representation makes it easy to distribute a signal in various parts of a circuit,but implies a large stored energy CV2/2 into the node parasitic capacitance C.

The current representation facilitates the summing of signals, but complicates theirdistribution. Replicas must be created which are never exactly equal to the original signal.

The charge representation requires time sampling but can be nicely processed by means ofcharge coupled devices or switched capacitor techniques.

Pulse frequency or time between pulses is used as the dominant mode of signalrepresentation for communication in biological nervous systems. Signals represented in thispseudo-binary manner (pulses of fixed amplitude and duration) are easy to regenerate and thisrepresentation might therefore be preferred for long distance transfers of information. It isdiscontinuous in time, but the phase information is kept in asynchronous systems.

OPERATOR

XRi YRj

Y jX i , = physical variables

, = references

XiXRi

x i =

x1x i y j YRj

Yjy j =

x k

y1

yp

Fig. 1 : Physical variables and references.

In any case, each signal x is represented by the value of a physical variable X related to thecorresponding reference value XR. Thus, an operator with k input xi and p output yj (Fig.1)may require as many as k+p references XRi,YRj . These references must either be producedinternally, with their origin clearly identified to keep them under control with respect to processand ambiance variations, or provided from outside.

For some particular operations, the number of physical references required by the operatoritself may be reduced to just one or even none at all , as shown in table 1. If the operation istime dependent, at least one time reference TR is needed.

Analog VLSI signal processing: why, where and how? - 3 -

Product of k variables: y = a x1x2x3...xk

Thus: Y = a YR

XR1XR2XR3...XRk X1X2X3...Xk

single reference

input var. X output var. Y Unit of reference reference for k=1

I I [A1-k] current gain Ai

I V [VA-k] transresistance Rm

V I [AV-k] transconductance Gm

V V [V1-k] voltage gain Av

Table 1 : Product of k variables and necessary physical reference.

All circuit architectures should be based on ratios of matched component values [5], toeliminate the dependency on any other absolute value than the required normalizationreferences XR. As a simple example, the gain of a linear current or voltage amplifier (samerepresentation at input and output) can and must be implemented by means of matchedcomponents to achieve complete independence of any absolute value. In a squarer or in a two-input multiplier with same representation at input and output, matched components must beused to limit the dependency on absolute values to that on the single voltage or current requiredby the operation, which must be provided by a clearly identified and well-controlled reference.These basic rules for sound analog design can only be respected if the circuits are analyzedwith respect to their physical behavior and not simply numerically simulated on a computer.

The MOS transistor: a very resourceful device.

Fig.2 shows the schematic cross-section and the symbol of an n-channel MOS transistor.In order to maintain the intrinsic symmetry of the device, the source voltage VS, the gatevoltage VG and the drain voltage VD are all referred to the local p-type substrate (p-well orgeneral substrate). This practice is very convenient for analog circuit design. The symbol andthe definitions for the p-channel device are also shown in the figure. In schematics, theconnection B to substrate is only represented when it is not connected to the negative supplyrail V- (for n-channel) or to the positive rail V+ ( for p-channel).

VD

G

DS

B

G

B

S

n-channel p-channel

n+ n+p

SG

D

DISV

VG

VD

B

SV

VGDI

Fig. 2 : Schematic cross-section of an n-channel MOS transistor and symbols for n-and p-channel transistors. All voltages are referred to the local substrate.Positive current and voltages for the p-channel transistor are reversed tomaintain the validity of the model derived for the n-channel.

- 4 - E.Vittoz:

Only three basic parameters are needed for a first order characterization and modelling ofthe transistor. These are:

VT0 : the gate threshold voltage for channel at equilibrium,n : a slope factor usually smaller than 2 which tends to 1 for very large

values of gate voltage VG,

= WL Cox : the transfer parameter, measured in A/V2, which can be adapted by the

designer by changing the channel width-to-length ratio W/L. Cox is the

gate oxide capacitance per unit area and is the carrier mobility in the channel.

This last parameter may be conveniently replaced by

IS = 2nU2T : specific c