AN IMPROVED ANALYSIS FOR THE HARMONIC DISTORTION OF MOS VOLTAGE-CONTROLLED-RESISTORS

In this paper, a fourth-order polynomial expression is obtained for the nonlinear current-voltage characteristic of a MOS transistor operating in the triode region. Using this expression, closed-form expressions are obtained for the second-, third- and fourth-harmonic distortion of a MOS voltage-controlled- resistors. The analytical expressions obtained in this paper can be used for a quantitative study of the effect of different parameters of the performance of MOS voltage-controlled-resistors.


INTRODUCTION
Voltage-controlled-resistors employing MOS transistors operating in their linear region are essential elements in realizing continuous time filters [1][2][3].These resistors, however, exhibit nonlinearities that give rise to harmonic distortion.A circuit designer must, therefore, be able to accurately predict the harmonic performance of these resistors: An essential prerequisite for reliable prediction of the harmonic distortion is the accurate modelling of the MOS current-voltage characteristics in the linear region.While the model proposed by Merckel et al. [4]   enjoys high accuracy, it is too complicated and cannot yield closed-form expressions for the harmonic distortion.A simplified version of this model was used in a modified version of SPICE to predict the harmonic performance of MOS voltage- controlled resistor circuits [5].No attempt has been reported, however, to use this simplified model to obtain closed-form expressions for the harmonic distortion.
Although, the model proposed by White et al. [6] is simpler, and was successfully used to investigate the effectiveness of a range of linearization strategies of MOS resistors [7], it cannot yield closed-form expressions for the harmonic distortion.
The simplified model proposed by Shoucair et al. [8] was successfully usel to obtain closed-form expressions for the harmonic distortion of body driven MOSFET circuits [8,9].At relatively low gate voltages, however, the accuracy of the model deteriorates [8].
In this paper, it will be shown that the simplified model proposed by Ryan [5] can be used to obtain closed-form expressions for the harmonic performance of MOS voltage-controlled resistors operating in the linear region.These expressions are valid over a wide range of gate-source and drain-source voltages. ABUELMA'ATrI
Using (4) the drain current Ins resulting from a drain-to-source voltage Vos Vp sin tat (5) can be expressed as IDS (g + K sin tat + K 2 cos 2tat + K 3 sin 3tat + K4 cos 4tat) and Using (8-11) the second, third, and fourth harmonic distortions can be expressed as K2 HD2 K-- HD 4 K-I

RESULTS
Using (12)-( 14) the harmonic performance of the fully-differential MOS voltage- controlled resistor circuit shown in Fig. 1 [11] can be calculated.However, because of the fully-differential nature of the circuit, the second-and fourth-harmonic components will cancel and only the third-harmonic distortion will dominate.The results obtained, using the parameters of Tables I and II are shown in Fig. 2. From Fig. 2, it is obvious that for input voltages between 0.2 V and 4 V peak-to-peak, the third-harmonic distortion levels relative to the fundamental varies from -91 dB to -40 dB.These trends are similar to the previously reported results [5,11].

CONCLUSION
In this paper, a simple fourth-order polynomial expression has been presented for the dependence of the drain current of a MOS transistor on the drain-to-source voltage and other physical and dimensional parameters.Using this expression, closed-form expressions are obtained for predicting the harmonic performance of a MOS transistor operating in the triode region.
The closed-form expressions obtained in this paper can be used for quantitative analysis of the effect of different MOS transistor parameters on the harmonic distortion performance of MOS voltage-controlled-resistors and for selecting the values of the transistor parameters that will yield a prespecified distortion performance.
The results obtained in this paper are in fairly good agreement with previously published simulation results obtained using a modified version of SPICE [5].

Table I
shows calculated values for d's and h's for

TABLE Values
of the d's and h's.