Fully Uncoupled Electronically Controllable Sinusoidal Oscillator Employing VD-DIBAs Data

Recently, voltage differencing-differential input buffered amplifiers (VD-DIBA)-based electronically controllable sinusoidal oscillator has been presented that it does not have the capability of complete independence of frequency of oscillation (FO) and condition of oscillation (CO) as well as electronic control of both CO and FO. In this article, a new fully-uncoupled electronically controllable sinusoidal oscillator using two VD-DIBAs, two grounded capacitors and two resistors has been proposed which offers important advantages such as 1) totally uncoupled and electronically controlled condition of oscillation (CO) and frequency of oscillation (FO); 2) low active and passive sensitivities; and 3) a very good frequency stability factor. The effects of non-idealities of the VD-DIBAs on the proposed oscillator are also investigated. The validity of the proposed formulation has been confirmed by SPICE simulation with TSMC 0.18 μm process parameters.


Introduction
Sinusoidal oscillators find various applications in signal processing, instrumentation, measurement, communication and control systems.The class of single resistance controlled oscillators (SRCOs) using different active element(s)/device(s) has been of particular interest during the last four decades because of their applications in variable frequency oscillators.However, in these SRCOs, electronic control of CO and FO can be obtained by replacing the respective controlling resistor(s) with FET based or CMOS voltage controlled resistor(s).A careful inspection of the available SRCOs reveals that while many oscillators enjoy independent single element control of CO and FO, the class of fully uncoupled oscillators has not been considered adequately in the literature.In fully uncoupled oscillator circuits CO and FO are determined by two completely different sets of active and/ or passive components, that is none of the active and/or passive components appeared in CO are involved in FO and vice versa.This feature is very useful for realizing voltage controlled oscillators as FO can be controlled independently without disturbing CO, whereas the flexibility of being able to control CO independently is advantageous to incorporate amplitude stabilization.In the recent past, number of fully-uncoupled sinusoidal oscillators employing different active element(s)/devices has been introduced see [1][2][3][4][5][6][7] and the references cited therein.In references [1][2][3][4][5] the CO and FO of the proposed oscillators are adjustable through resistors (the electronic tunability can be established by replacing one of the grounded resistors by JFETs/MOSFETs [8,9]), whereas in case of oscillators presented in references [6,7], both CO and FO are electronically controllable.The VD-DIBA was introduced by Biolek, Senani, Biolkova and Kolka in [10] since then it has been found to be a useful new active building block in realizing all voltage-mode pass filters [11], inductance simulation [12], universal biquad filter [13] and an electronically controllable sinusoidal oscillator [14].Although the paper presented by the authors in [14] employs two VD-DIBAs, two grounded capacitors and one grounded resistor but this circuit does not have the capability of complete independence of CO and FO as well as electronic control (only FO is electronically controllable).Therefore, the purpose of this paper is, to propose a new fully uncoupled electronically controllable sinusoidal oscillator employing two VD-DIBAs, two grounded capacitors and two resistors, which offers 1) fully uncoupled and electronically controlled CO and FO, 2) low active and passive sensitivities, and 3) a very good frequency stability factor.The feasibility of the proposed oscillator has been demonstrated by SPICE simulation with TSMC 0.18 μm process parameters.

The Proposed Fully Uncoupled Oscillator
The schematic symbol and behavioral model of the VD-DIBA are shown in Figures 1(a) and (b) respectively [11].The VD-DIBAs can be described by the following set of equations: Assuming that the VD-DIBAs are characterized by Equation ( 1), the characteristic equation (CE) of Figure 2 can be given by: From this CE, the CO and FO can be found as: Therefore, from Equations (3) and ( 4) it is clear that FO and CO are fully decoupled and electronically controllable i.e.FO is independently controllable by transconductance 2 m g of the VD-DIBA(−), whereas CO is also electroni controllable through the transconductance 1 m cally g of VD-DIBA(+).

Non-Ideal Analysis
f VD-DIBA i.e.R Z and C Z , Considering the parasitics o the parasitic resistance and the parasitic capacitance of the Z-terminal respectively.Taking the non-idealities into account, namely the voltage of W-terminal e voltage tracking rs of Z-terminal and denote th erro V-terminal of the VD-DIBA (+/−) respectively, then the expression for CE becomes: From Equation (5), the CO and FO can be given by: ivities of 0 2 The sensit  with respect to active and passive elements are calculated as: An inspection of Equation ( 8) reveals that the a and passive sensitivities of 0 ctive  are found to be low.

Frequency Stability
Frequency stability is an important figure of merit for an F y sinusoidal oscillator.Using the definition of the frequency stability factor S as given in [5,8]  is the normalized frequency and    u denotes the phase of the open-loop transfer function), with ng , the S F of this oscillator is found to be 2 n .Thus the new proposed oscillator circuit offers very high frequency stability f oscillator circuit has been simu lated using the CMOS-based VD-DIBA [14].The variomponent 7 K I B7 = 30 μA.The transconere controlled through the and actor for larger values of n.

Simulation Results
The From SPICE simulations {Figures 3(a) and (b)}, the oscillations are observed to be quite stable and the frequency of generated sine wave was found as 731.88 KHz.The THD of the output waveform was found as 1.159%.

Concluding Remarks
A new si idal oscillator with fully decoupled and electronically controllable both frequency of oscillation and condition of oscillation has been presented.The new oscillator configuration also enjoy 1) low active and passive sensitivities and 2) a very good frequency stability fact r values of n.T obustness of the roposed oscillator circuit has been confirmed by the

Figure 1 .
Figure 1.(a) Schematic symbol; (b) Behavioral model of proposed sinusoidal ous c values used were C 1 = C 2 = 0.05 nF, R 1 = 1.6 Ω and R 2 = 10 K, the CMOS VD-DIBA was biased with ±1 V D.C. power supplies with I B1 = I B2 = I B3 = I B4 = I B5 = I B6 = 150 μA and ductances of VD-DIBAs w respective bias currents.The SPICE generated output waveforms indicating transient and steady state responses are shown in Figures 3(a) and (b) respectively.

Figure 4 Figure 3 .
Figure 3. (a) Transient output waveform; (b) Steady state response of the output.

Figure 4 .
Figure 4. Result of Monte-Carlo simulation of oscillator circuit of Figure 2.