ACTIVE-ONLY SINUSOIDAL OSCILLATOR WITH ELECTRONICALLY-TUNABLE FULLY-UNCOUPLED FREQUENCY AND CONDITION OF OSCILLATION

A new active-only sinusoidal oscillator is presented. The oscillator circuit uses two internally compensated operational amplifiers, two plus-type second-generation current conveyors and three operational transconductance amplifiers. The proposed circuit enjoys the attractive features of totally uncoupled frequency and condition of oscillation, low sensitivities, electronic tunability and integratability.

Active-only resistorless-capacitorless sinusoidal oscillators using two OAs only have been reported in the literature (Abuelmaatti and  Almansoury, 1986; Bhat and Shah, 1989).While there is no control on the condition of oscillation, and consequently the amplitude of oscil- lation, these oscillator circuits suffer from the additional disadvantage of the need to change the d.c.supply of the whole circuit in order to change the frequency of oscillation.
An active-only sinusoidal oscillator circuit is reported in (Abuel- maatti and Al-Zaher, 1998).This circuit was obtained by converting an RLC resonator into an RLM resonator by scaling all the im- pedances of the RLC resonator by s/o where M is a FDNC char- acterized by Z(s)--Ms2.In this paper, it will be shown that active only sinusoidal oscillators can be directly obtained from an RLC resonator comprising an inductor, a capacitor and two resistors.First, new active-only simulators will be proposed for grounded inductors and capacitors.Then, these new simulators will be combined with active- only simulated grounded positive and negative resistances to obtain a sinusoidal oscillator circuit.

PROPOSED CIRCUITS
Consider the circuit shown in Figure l(a).Using standard notations, the OTA can be characterized by i=g,,e(V-V) where g,,,k = I,BCk/2Vr is the transconductance of the kth OTA, l.Bce is its auxiliary bias- current, Vr is the thermal voltage and v and v are the input voltages of the OTA.The plus-type second-generation current-controlled current- conveyor (CCCCII) can be characterized by (, O, V.,.V,R,.i.,. and iz , .where R,.= Vr/2Io and Io is the bias current of the CCCCII.

Assuming internaly compensated OAs with open-loop gain of
Ae--Be/s, where Be is the gain-bandwidth product of the kth OA, routine analysis yields the input impedance given by sRxl Zinl (1) Bi Thus, the circuit of Figure l(a) realizes a lossless grounded inductor Leq--Rx/B.It is worth mentioning here that the circuit of Figure l(a) can be obtained from the circuit of Figure 3 of Khan et al., 1992,  simply by replacing the OTA by the CCCCII.The advantages of using the CCCCII instead of the OTA are as follows: a.For the conventional bipolar OTA the value of g,,, is IBias/2VT, while I/R,.for the CCCCII is 21Bi,,s/Vr.biasing current /Bias, the transconductance of the OTA will be 4 times less than that of the CCCCII.This means that an OTA implementation may result in a higher power consumption.
b.Because of the use of high values of currents, the maximum fre- quency usable for an OTA-based implementation will be reached sooner than that for a CCCCII based implementation.
The plus-type second-generation current-conveyor (CCII) can be characterized by iy--0, I/'.,.V.v and iz i... Routine analysis shows that the input impedance of the circuit of Figure (b) can be expressed as

Zinl
(2) Thus, the circuit of Figure l(b) realizes lossless grounded capacitor Ceq g,,,2B2.It is worth mentioning here that the OTA in the circuit of Figure l(b) can be replaced by a CCCCII with its y-and z-terminals connected to ground, and its x-terminal connected to the z-terminal of the CCII.It is interesting to note also that if the parasitic input re- sistance of the CCII of Figure l(b) is taken into consideration, then the input impedance will be formed of a series combination of the capacitor of Eq. ( 2) and a resistor R.,.. Minimizing this resistance is possible using the composite second-generation current-conveyor with reduced para- sitic resistance (Fabre and Barthelemy, 1994).
Combining the circuits of Figure yields a sinusoidal oscillator circuit with frequency of oscillation given by 2 090 BIB2 (3) Leq Ceq gin2 Rxl This oscillator circuit suffers from the disadvantage of having no condition of oscillation and consequently no control on the amplitude of oscillation.This can be avoided by introducing two OTAs config- ured as grounded positive and negative resistances as shown in Figure 2. Thus the condition of oscillation of the circuit of Figure 2 will be given by gin3 g,,4 (4) From Eqs. (3) and (4) it appears that the frequency of oscillation and the condition of oscillation are totally uncoupled, that is while the frequency of oscillation is controlled by a set of parameters, the con- dition of oscillation is controlled by a completely different set of parameters.This property is very attractive for electronic tuning of the frequency and the amplitude of oscillation.Moreover, it appears that while R.,.t, g,,,2, g,,,3 and gn,4 are temperature dependent, the frequency V( 4) and the condition of oscillation are temperature insensitive.Finally, it is interesting to note that the circuit can support two low-output im- pedance quadrature, voltages.From Eq. (3) it is easy to show that the sensitivities of the parameter O9o are: S'g,) Sg,n4 0 all of which are small.

SIMULATION RESULTS
The sinusoidal oscillator circuit of Figure 2 was simulated using the PSPICE circuit simulation program.The OA 741 with corner fre- quencies f 10Hz, f2 3MHz, input resistance Rinpu --400k output resistance Routput--200 and DC gain--100000, the OTA macromodel [Wu, 1994] and the current conveyor macromodel [Svoboda, 1994] were used in simulation.Figure 3 shows typical output waveforms obtained with 1/Rxl gin2 gin3 lmA/V, gin4 1. ImA/V and the DC supply voltage--5V.Figure 4 shows the output spectrum of the waveforms of Figure 3. From Figure 3 it is easy to see that the voltages CF based oscil lator Date/Time 04129/100 09'20:50  Temperature: 27.0 V(2) and V(4) are in quadrature.Figure 5 shows the variation of the frequency of oscillation with the parameter I/R., while g,,,z= gin3 mA/V, g,,,4 1. mA/V.

CONCLUSION
A new active-only sinusoidal oscillator with totally uncoupled fre- quency and condition of oscillation has been presented.5.0MHz 6.0MHz 7.0MHz 8.0MHz Frequency FIGURE 4 Spectrum of the output waveforms of Figure 3.
only inductor and capacitor with OTA-based grounded positive and negative resistances, the new oscillator circuit was obtained.
In addition to using only active devices for its realization, the new circuit enjoys the following advantages: 1. Totally uncoupled frequency and condition of oscillation.
2. Low sensitivities of the frequency of oscillation to the gain- bandwidth products of the OAs, the transconductances of the OTAs and the parasitic resistance of the CCCCII. 3. Despite the temperature dependence of the transconductances of the OTAs and the parasitic resistance of the CCCCII, the fre- quency of oscillation and the condition of oscillation are tem- perature insensitive. 4. The circuit supports two low output-impedance quadrature vol- tages.
The new os- cillator circuit is obtained directly from the RLC resonator without recourse to the classical approach of obtaining an RLM circuit from the RLC resonator.Direct realization of the new oscillator circuit required the development of a new active-only grounded inductor and a new active-only grounded capacitor.Combining these new active