ACTIVE-ONLY SINUSOIDAL OSCILLATOR CIRCUITS

Two new active-only sinusoidal oscillator circuits are proposed. The first circuit uses one 
current feedback operational amplifier (CFOA) and four operational transconductance 
amplifiers (OTAs). The second circuit uses only four OTAs. Without using any external 
passive elements, voltage (or current) control of the frequency and condition of 
oscillation, of the two circuits, can be achieved by adjusting the bias currents of the 
OTAs. The proposed circuits enjoy low sensitivities.


INTRODUCTION
At present, there is a growing interest in designing capacitor-less/ resistor-less active-filters using only active-elements, such as operta- tional amplifiers (OAs) and operational transconductance amplifiers (OTAs).This is attributed to their integratability, programmability and wide frequency range of operation (Abuelmaatti and Alzaher,  1997; Tsukutani etal., 1996).
Active-only resistor-less/capacitor-less sinusoidal oscillator circuits using two operational amplifiers have, also, been reported (Abuelmaatti and Almansoury, 1986; Bhat and Shah, 1989).The main dis- advantage of these oscillators, is that there is no control on the condition of oscillation.Moreover, the frequency of oscillation can be controlled only by changing the dc supply of the whole circuit.
In this paper, new capacitor-less/resistor-less active-only sinusoidal oscillator circuits are presented.The first circuit uses four OTAs and one CFOA, and the second circuit uses only four OTAs.Both circuits enjoy independent current(voltage)-control of the frequency and the condition of oscillation.

PROPOSED CIRCUIT
Figure shows the proposed circuits.OTAs and CFOAs are nonideal devices.Figure 2 shows the simplified models of the OTA (Urbas and Osiowski, 1982) and the CFOA (Svoboda, 1994).Using the models of Figure 2, the equivalent circuits of the oscillator circuits of Figure 1, can be represented by the circuits of Figure 3. (2) and Y3 gm3 q-"A---t-sC3 (3) where Cl Col q--Co4 RI Ril//Rol//Ro4//Ry C2 Ri2 q-Co2 R2 Ri2//Ro2 is the transconductance of the ith OTA with IABCi the auxiliary bias current of the ith OTA and Vr is the thermal voltage.
Using Figure 3(a) the characteristic equation of the oscillator circuit of Figure (a) can be expressed as FIGURE 2 Simplified equivalent circuits for (a) the OTA; Urbas and Osiowski, 1982  (b) the CFOA; Svoboda, 1994.where and fl represent the current-and voltage-tracking errors of the CFOA.Assuming that R. Y2 << l, combining Eqs. ( 1)-( 4 With 1/R (( gml, l/R3 (( gin3 and l/R2 (( gm2, Eqs. ( 5) and ( 6) From Eqs. ( 5)-( 8) it is easy to see that the frequency of oscillation can be controlled by adjusting gin2 without disturbing the condition of oscillation, and the condition of oscillation can be controlled by ad- justing C2 without disturbing the frequency of oscillation.Thus, the circuit of Figure (a) enjoys independent control of the frequency and the condition of oscillation.(15) From Eqs. ( 12)-( 15) it is easy to see that the frequency of oscillation can be controlled by adjusting gml and/or gin4 without disturbing the condition of oscillation, and the condition of oscillation can be con- trolled by adjusting gin2 and/or gm3 without disturbing the frequency of oscillation.Thus, the circuit of Figure.l(b) enjoys independent control of the frequency and the condition of oscillation.
From Eqs. ( 7) and ( 14) it is easy to show that the sensitivities of the parameter O9o are Thus, all the Oo-sensitivities, of the circuits of Figure 1, are small.

Simulation Results
The sinusoidal oscillator circuits of Figure were simulated using the PSPICE circuit simulation program.The OTA macromodel of Figure 2(a) with Ri-65 kf, Ro-63 M, Co--7.5 pF and CFOA macromodel of Figure 2(b) with R. 50f, Ry 10Mf, Rt--3 M, Ct 4.5 pF, fl were used in simulation.To avoid the possible latch-up and to limit the amplitude of oscillation, two anti-parallel biased-diodes were connected between the output term- inal of the oscillator circuit and the ground.The results reported here were obtained with 4-2 V biasing voltage for the diodes.
The results obtained from the oscillator circuit of Figure l(a) with gm!--gm2 gm3--0.1 mA/V,g,,,4 1.45 mA/V are shown in Figure 4(a).Using Eq. ( 7) the calculated frequency of oscillation is 2.77 MHz and the simulated frequency obtained from Figure 4(a) is 2.742 MHz.It appears that the simulated and calculated results are in good agreement.This justifies the approximations made in obtaining Eq. ( 7).
The results obtained from the oscillator circuit of Figure l(b) with gm! --gm-6 mA/V, gm3 gm4 7 mA/V are shown in Figure 4(b).Using Eq. ( 14) the calculated frequency of oscillation is 79.4 MHz and the simulated frequency obtained from Figure 4(b) is 77.6 MHz.It appears that the simulated and calculated results are in good agree- ment.This justifies the approximations made in obtaining Eq. ( 14).  .1 mA/V, gm4-1.45mA/Vand (b) the oscillator circuit of Figure l(b) with gml gm2 6 mA/V, gm3 gm4 7 mA/V.However, the output impedance of this circuit is high.This can be solved using the on-chip unity-gain buffer available with the OTA.
The first circuit uses an additional CFOA and enjoys a low output impedance terminal.While its frequency of oscillation can be adjusted using the auxiliary bias current of an OTA without disturbing the condition of oscillation, the condition of oscillation cannot be adjusted using the auxiliary bias current of an OTA.
Figure2, the equivalent circuits of the oscillator circuits of Figure1, can be represented by the circuits of Figure3. Figure 3(a) shows the equivalent circuit of the oscillator circuit of Figure (a) with r gm + -, + sCI FIGUREProposed active-only oscillator circuits.

FIGURE 3
FIGURE 3 Equivalent circuits for the proposed active-only oscillator circuits of Figure 1.

Figure 3
Figure 3(b) shows the equivalent circuit of the oscillator circuit of Figure (b) with

CONCLUSION
Two new active-only sinusoidal oscillator has been presented.The first circuit, of Figure l(a), uses one current feedback operational amplifier and four operational transconductance amplifiers.The second circuit, of Figure (b), uses only four operational transconductance amplifiers.No external passive elements are used.The second oscillator circuit enjoys the following advantages: a. independent current control of the frequency and the condition of oscillation.b. low active and passive sensitivities of the frequency of oscillation.

FIGURE 4
FIGURE 4 Simulation results obtained fronl (a) the oscillator circuit of Figure l(a) with gml --gm2-gm3