NEW ELECTRONICALLY-TUNABLE OSCILLATOR CIRCUIT USING ONLY TWO OTAs

The potentials of the operational transconductance amplifier (OTA) as an integrated circuit building block alongwith its applications in generating all finite linear circuits were introduced early by Bialko et al. [1]. The OTAs have many attractive features. For example, they require just a few or even no resistors for their internal circuitry, provide highly linear electronic tunability of its transfer gain and have more reliable high-frequency performance. Over the past few years, a number of schemes have been developed for realizing OTA-based sinusoidal RC-oscillators [2-8]. Most of these circuits use two OTAs in combination with a number of grounded and floating capacitors and resistors. From a practical point


INTRODUCTION
The potentials of the operational transconductance amplifier (OTA) as an integrated circuit building block alongwith its applications in generating all finite linear circuits were introduced early by Bialko et al. [1].The OTAs have many attractive features.For example, they require just a few or even no resistors for their internal circuitry, provide highly linear electronic tunability of its transfer gain and have more reliable high-frequency performance.
Over the past few years, a number of schemes have been developed for realizing OTA-based sinusoidal RC-oscillators [2][3][4][5][6][7][8].Most of these circuits use two OTAs in combination with a number of grounded and floating capacitors and resistors.From a practical point 190 M.T. ABUELMA'ATTI AND M. H. KHAN of view an oscillator circuit is attractive if (1) a single-element control of the frequency of oscillation is possible without disturbing the condition of oscillation and (2) a single element control of the condition of oscillation is possible without disturbing the frequency of oscillation.Most of the oscillator circuits available in [2-8] do not enjoy these two attractive features simultaneously.
The major intention of this paper is to present a new OTA-based oscillator circuit.The proposed circuit uses two OTAs, two grounded capacitors, a buffer and one floating resistor and enjoys independent control of the frequency and the condition of oscillation.

PROPOSED CIRCUITS
Consider the oscillator structure shown in Figure 1.Assuming an ideal OTA, routine analysis of the circuit yields its characteristic equation given by where and so-1/C2R2 + 1/CER (2) Equation (1) generates a pair of complex conjugate poles with a small positive real part.These poles, ap +jwp, are given by crp -c0/2 (4) and (4/30 c)1/2/2 (5) Obviously, if a, > 0, wp will be the frequency of oscillation of the circuit.From ( 2) and ( 4) one can see that for ap > 0, it is required that and R1 > IRzl (7) Also, from (4) and ( 5) one can see that if cry, 0 /, then the frequency of oscillation of the circuit will be From ( 6)-( 8) one can see that obtaining oscillation from the circuit of Figure is feasible subject to realising R2 as a negative resistance.
Realising a negative resistance is straightforward using an operational transconductance amplifier [9]. Figure 2 shows a modified version of the proposed circuit of Figure with R2 realised using an OTA.Using (2)-( 8) it is easy to show that the frequency of oscillation and the condition of oscillation of the circuit of Figure 2 will be W2o gml/C2C3R1 (9) and gm2R1 (10) From ( 9) and (10) one can see that the condition of oscillation and the frequency of oscillation are totally uncoupled.Thus, while the  frequency of oscillation can be adjusted by tuning gml without disturbing the condition of oscillation, the condition of oscillation can be adjusted by tuning gm2 without disturbing the frequency of oscillation.And since the transconductance gain of the OTA (gmi) is linearly proportional to the amplifier bias current I.aBci of the OTA then the frequency of oscillation and the condition of oscillation can be independently adjusted by changing the amplifier bias currents.Moreover if these currents are obtained from the output of digital-to- analog converters (DACs) then digital programming of the frequency of oscillation and the condition of oscillation is feasible.

EXPERIMENTAL RESULTS
The circuit of Figure 2 was tested using the LM 13600 OTA.This chip contains two OTAs and two buffers.Thus the circuit of Figure 2 requires only one IC chip.The results obtained are shown in Figure 3. Good quality sinusoidal oscillations were obtained.From Figure 3 one can see that the measured and calculated results are in good agreement.

CONCLUSION
In this paper a new OTA-based RC oscillator circuit has been presented.The circuit uses two OTAs, one buffer, one resistor and two grounded capacitors.Thus it can be realised using one IC chip (the LM13600).The circuit enjoys independent control of the frequency and the condition of oscillation.
It is worth mentioning here that fully integrable, entirely OTA- based oscillator can be obtained, at the cost of two extra OTAs, by simulating the resistor R1 by two OTAs.Alternatively, from an IC implementation viewpoint R could be a resistor either external to the chip or can be a part of a feedback electronic circuit used to stabilise (or control) the amplitude of oscillation.

FIGURE 2
FIGURE 2 Modified version of Figure with R2 realised as a negative resistance -1/gm2.

FIGURE 3
FIGURE 3 Measured and calculated results obtained from Figure 2 with: C1 Ca 10 nf R1 10 k, IB2 4 gA