Controllable Sinusoidal Oscillators Employing VDIBAs

Two new electronically controllable sinusoidal oscillators each employing two Voltage Differencing Inverting Buffered Amplifiers (VDIBAs), two capacitors, and a single resistor have been proposed. The presented oscillators offer independent electronic control of Condition of Oscillation (CO) and Frequency of Oscillation (FO), and low active and passive sensitivities. The effect of non-idealities of the VDIBAs on the proposed oscillators is also investigated. The validity of the proposed structures has been confirmed by SPICE simulation with TSMC 0.18 μm process parameters.


Introduction
Sinusoidal oscillators have the wide range of applications in signal processing, instrumentation and measurement, control systems, and communications.Recently, number of oscillators, have been proposed by the various researchers, see [1], [2], [3], [4], [5], [6], [7], [8], [9] and [10], and the references cited therein.In [11], authors proposed electronically controllable sinusoidal oscillator employing CMOS VD-DIBAs in which the CO is controlled through a resistance, whereas FO is electronically controllable by the transconductance of the VD-DIBA.A fully uncoupled electronically controllable sinusoidal oscillator employing VD-DIBAs was presented in [12], where CO and FO both are electronically controllable through a separate transconductance of the VD-DIBAs but the circuit uses four passive elements (two capacitors and two resistors).In reference [13], a fully uncoupled electronically controllable sinusoidal oscillator was presented employing four Current Controlled Current Conveyors (CCCIIs) and two capacitors.Two VDIBAs based single resistance controlled oscillator with two capacitors and a resistance has been proposed in [14], where only CO is electronically controllable.Thus, the purpose of this article is to propose two new sinusoidal oscillators having electronic control of both CO and FO by separate transconductance of the VDIBAs.This feature is very attractive for realizing current-controlled oscillators as FO can be adjusted independently without disturbing CO, whereas the flexibility of being able to control CO independently is useful in amplitude stabilization.The proposed structures also offer low active and passive sensitivities.The feasibility of the proposed sinusoidal oscillators has been confirmed by SPICE simulation with TSMC 0.18 µm process parameters.

The Proposed New Configurations
Many new active building blocks such as VDBA, CD-DIBA, etc. were introduced for the first time in [15].It may be noted that VDIBA [10] is a modified form of VDBA introduced in [15], not all possible variants of the various active building blocks were mentioned to save the space.Thus, VDIBA, a four terminal active building block with electronic tuning, was subsequently generated [10] based upon the methodology of [15].The symbolic notation and equivalent model of the VDIBA are shown in Fig. 1(a) and Fig. 1(b), respectively [10].
Using standard notations, the voltage-current relations of VDIBA can be described by the following set of equations: Figure 2 shows the proposed new sinusoidal oscillators with independent electronic control of CO and FO. V-Vw- Fig. 2: Proposed sinusoidal oscillators with electronic control of both CO and FO.
A routine circuit analysis of the circuits in Fig. 2 yields the following Characteristic Equation (CE), CO, and FO for both the oscillators: CO: From Eq. (3) and Eq. ( 4), it is seen that CO is electronically controllable by the transconductance g m2 , where as FO is electronically controllable through the transconductance g m1 .Thus both CO and FO are independently electronically controllable by two separate transconductances.

Non-Ideal Analysis and Sensitivity Performance
Let R z and C z denote the parasitic resistance and parasitic capacitance of the Z-terminal of VDIBA.Taking the non-idealities into account, namely the voltage of W-terminal V w − = (−β + V z ), where β + = 1− p ( p << 1) denotes the voltage tracking error, then the expressions for CE, CO and FO, respectively, become: • For the circuit given in Fig. 2(a) is CE in Eq. ( 5), CO in Eq. ( 6) and FO in Eq. ( 7).
The various active and passive sensitivities of FO are given by: • For the circuit of Fig. 2(a): CO: FO: CO: FO: . (18) • For the oscillator of Fig. 2(b): . (26) In the ideal case, the various sensitivities of FO with respect to R 0 , R z , C 1 , C 2 , g m1 , g m2 , g m2 , and C z for both the oscillators are found to be: Considering the typical values of various parasitic as given in [10], e.g.C z = 0.367 pF, R z = 131.93kΩ, R w = 42.36Ω, β + = 1, g m1 = 600 µS, and g m2 = 704.7 µS along with C 1 = C 2 = 10 nF, and R 0 = 3.333 kΩ, the various sensitivities are found to be: • For the circuit of Fig. 2(a (29)

SPICE Simulation Results
To confirm theoretical analysis, the proposed oscillators were simulated using CMOS VDIBA (as shown in Fig. 3).The CMOS VDIBA is implemented using 0.18 µm TSMC real transistor models which are listed in Tab. 2. Table 1 shows the aspect ratios of transistors used in Fig. 3.The passive elements were selected as The transconductances of VDIBAs were controlled by the bias currents I b1 = 100 µA and I b2 = 110 µA, respectively.PSPICE generated output waveforms indicating transient and steady state responses of circuits in Fig. 2 are shown in Fig. 4 and Fig. 5, respectively.These results, thus, confirm the validity of the proposed configurations.
Figure 6 shows the output spectrum of circuits shown in Fig. 2; whereas the Total Harmonic Distortions (THD) for both circuits are found to be 1.0542 % and 1.049 %, respectively.Figure 7 shows the variation of frequency with the transconductance g m1 for both circuits in Fig. 2.  Tab.2: 0.18 µm TSMC CMOS model parameters.

M3
Table 3 shows the comparison with other previously known oscillators using different active building blocks.

Conclusion
In this paper, two new circuit configurations employing two VDIBAs along with a minimum number of passive elements (i.e. two capacitors and only one resistor) have been presented.The proposed oscillators offer independent electronic control of both CO and FO, and have low active and passive sensitivities.The validity of both oscillators was established by SPICE simulations with a CMOS VDIBA architecture implementable in 0.18 µm TSMC CMOS technology.

Fig. 7 :
Fig. 7: Variation of frequency with gm 1 for both the circuits of Fig. 2.
Tab. 3: Comparison with other previously known fully uncoupled sinusoidal oscillators.