Improved Accuracy Function Generator Circuit for Analog Signal Processing

Cosmin Popa
Faculty of Electronics, Telecommunications and Information Technology University Politehnica of Bucharest, Bucharest, Romania, e-mail: cosmin_popa@
each desired function derived from them, using a n − th order limited polynomial series expansion. Considering a continuous function f ( x ) , its Taylor series expansion around x = 0 , for x << 1 could be expressed as:
f (1) f ( x) = f (0 ) + f (1) = f (0 ) +
x =0
x =0
f ( 2) x+ f (2 )
x =0
1!
2!
x =0
x 2 + ... =
1!
g 1 ( x) +
2!
g 2 ( x ) + ... .
(1)
The error resulted by using this approximation will be proportional with the number of terms neglected in the previous expansion. The implementation in CMOS technology of the elementary function generators g k ( x) is based on a single original block, a CMOS current squarer. In order to improve the circuit frequency response, only strong-inverted MOS devices must be used (the weak inversion operation of the MOS transistor is not a proper choice for high-speed CMOS circuits because of the very small currents available for charging and discharging the device capacitances). An alternative choice is to replace the classical MOS transistors by FGMOS (Floating Gate MOS) active devices, allowing an important reducing of the circuit complexity. The errors introduced by the technological parameters drifts and mismatches will be practically removed because the output current expression is designed to be not dependent on technology. A. The CMOS Implementation of the Current Squarer The core of the circuit is represented by the CMOS current-mode current squarer. Deriving from this circuit, it is possible to implement all the desired continuous functions by using the limited Taylor series expansion. There will be presented six possible realizations of the same function (the current squaring), using exclusively MOS transistors or FGMOS transistors biased in saturation region for improving the frequency response. 1) The first CMOS current squarer: the original implementation of a CMOS current squarer using a FGMOS transistor is presented in Fig. 1.
g k ( x ) = x k , k = 1,..., n functions and the computing of
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EUROCON 2007 The International Conference on “Computer as a Tool”
Warsaw, September 9-12
Improved Accuracy Function Generator Circuit for Analog Signal Processing
Abstract— A new current-mode function generator circuit will be presented, having a much smaller complexity per function with respect to the previous reported similar works. The circuit allows to compute an important number of mathematical functions using their n − th order limited polynomial series expansion. The approximation error could be strongly decreased by increasing the number of terms considered in the previous expansion. The selection of the active function is digitally made, the main part of the function generator being common for all the computed functions. The circuit core, the current squarer circuit, will be analyzed in six possible implementations, using exclusively MOS transistors working in the saturation region for improving the circuit frequency response. In order to reduce the circuit complexity, classical MOS active devices will be replaced by a FGMOS (Floating Gate MOS) transistor. A very important advantage of the proposed function generator circuit is the independence of the computed function on the technological parameters. The circuit is implemented in 0.35 µm CMOS technology, the SPICE simulations confirming the theoretical estimated results. Keywords—function generator, complexity, Taylor expansion computing error,
Fig. 1. CMOS squarer using a FGMOS transistor
The FGMOS transistor is a MOS transistor whose gate is floating, being capacitive coupled to the multiple input gates. The drain current of a FGMOS transistor with ninput gates working in the saturation region is given by the following equation:
I. INTRODUCTION A very important goal in analog designs is the VLSI implementation in CMOS technology of the mathematical functions, having the most important advantage of speeding-up the designed circuits and finding many applications in analog signal processing. For example, the exponential circuits are used in telecommunication, medical equipment or disk drives [1] – [6], while the squaring and Euclidean distance circuits find applications in instrumentation circuits, communication, neural network, display systems or vector quantization [7], [8]. The original circuit presented in the following paragraph represents a digitally programmable currentmode function generator, designed for implementing mathematical functions for VLSI applications. II. THEORETICAL ANALYSIS The original idea for obtaining an important number of basic or complex mathematical functions is the utilization of n elementary generators for implementing