A MINIMUM COMPONENT GROUNDED-CAPACITOR CFOA-BASED RC OSCILLATOR

A minimum-component grounded-capacitor single-frequency RC-sinusoidal oscillator circuit using the current feedback operational amplifier (CFOA) is presented. The circuit uses a single CFOA, two resistors, and two grounded capacitors. The circuit enjoys low active and passive sensitivity characteristics.


INTRODUCTION
Recently a number of single CFOA-based RC sinusoidal oscillators have been proposed [1][2][3].Assuming ideal CFOA characteristics, the minimum number of passive components used, so far, is five.However, by exploiting the CFOA-pole it is possible to obtain a sinusoidal oscillator using only four externally-connected passive components [4].In this paper, we explore the possibility of synthesizing an RC oscillator using an ideal CFOA and four externally connected passive components.

CIRCUIT CONFIGURATION
Consider the oscillator structure shown in Fig. 1.Assuming that the CFOA is ideal with Vx Vy, z ix, iy 0 and v0 Vz, routine analysis yields the characteristic equation of this circuit configuration given by $2C1C2 + S(G1C 2 + G2C G1C1) + G1G2 0 (1) Using the Barkhausen principle, by equating the real and inmaginary parts of (1) to zero, the frequency and the condition of oscillation of the circuit of Fig.
From ( 2) and ( 3) one can see that the frequency and the condition of oscillation are fully coupled.Thus, the proposed circuit of Fig. 1 is useful for realizing single frequency oscillators.

EFFECT OF CURRENT-AND VOLTAGE-TRACKING ERRORS
Taking into account the current-and voltage-tracking errors of the CFOA, namely z Otix, Vx l)y and Vo "VVz, where a 1 t11, It, ll <<1 represents the current tracking error of the CFOA, 13 1 2, 121 <<1 represents the input voltage tracking error of the CFOA and -1 3, ITS31 << 1 represents the output voltage tracking error of the CFOA, the characteristic equation of (1) becomes $2C1C2 qs(G1C 2 + G2C et/G1C1) + GIG2 0 (4) Using (4), it is easy to show that, while the frequency of oscillation of the circuit of Fig. 1 will not be affected by the CFOA nonidealities, the condition of oscillation will be ot3"yG 1C G 1C2 + G2C (5) Thus, the condition of oscillation will be slightly affected by the CFOA current and voltage tracking errors.

EFFECT OF CFOA PARASITICS
Taking into account the CFOA-parasitics, the CFOA can be modelled using the equivalent circuit shown in Fig. 2.This model is obtained by adding a voltage- controlled voltage-source to the plus-type second-generation current-conveyor (CCII+) model used by Svoboda [5].Reanalysis of the structure of Fig. 1, using the CFOA model of Fig. 2, yields the characteristic equation that can be expressed as $2C1C2 qs(GIC 2 + a2c G1C1) -+-G1G2 (G z + sCz)(1 4-RxY1) + RxYIY (6)   Using ( 6), the effect of the CFOA-parasitics on the frequency and condition of oscillations of the circuit of Fig. 1 can be calculated.With C1 >>Cz, C2 >>Cz, G1 ,>>G z, RxG <<1, G2 >>Gz, the frequency and the condition of oscillation can be approximated by From (7) and (8), one can see that while the parasitic resistance R will slightly affect the frequency of oscillation, it has almost no effect on the condition of oscillation.
o 0 SENSITIVITIES The various sensitivity figures are calculated using the sensitivity definition Y dtoo SY to o dy (9) Using (9), the o passive and active sensitivities for the two circuits were calculated and are given by From (11), one can see that the frequency of oscillation of the proposed oscillator circuit is insensitive to the current and voltage tracking errors of the CFOA.

EXPERIMENTAL RESULTS
The proposed sinusoidal oscillator circuit was experimentally tested using the AD844 CFOA.Fig. 3 shows the results obtained with C1 C2 lOOpF, R1 196.

FIGURE 3
FIGURE 3 Measured Frequency of Oscillation with R 196 II, C1 C2 100 PF