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In this communication, a new single-resistance controlled sinusoidal oscillator (SRCO) has been presented. The presented SRCO uses two voltage differencing inverting buffered amplifiers (VDIBAs), one resistor and two capacitors in which one is grounded (GC) and the other one is floating (FC). The proposed structure offers the following advantageous features: 1) independent control of oscillation condition (OC) and oscillation frequency (OF); 2) low passive and active sensitivities and 3) very good frequency stability. The non-ideal effects of the VDIBA on the proposed oscillator have also been investigated. The proposed SRCO has been tested for its robustness using Monte-Carlo simulations. The check of the validity of the presented SRCO has been established by SPICE simulations using 0.18 μm TSMC technology.

In analog signal processing and circuit design, realization of active filters and oscillators has become the important research areas. In reference [

The symbolic notation and equivalent model of the VDIBA are given in _{+} = 0 = I_{−}, I_{z} = g_{m} (V_{+} − V_{−}) and V_{w}_{−} = −V_{z}, where g_{m}, represents the transconductance of VDIBA.

The presented single-resistance-controlled sinusoidal oscillator circuit is shown in

The characteristic equation (CE) of the proposed SRCO of

CE:

s 2 C 1 C 2 + s { C 1 g m 2 − C 2 g m 1 } + g m 2 R 0 = 0 (1)

From Equation (1), the oscillation condition (OC) and oscillation frequency (OF) can be determined as:

OC:

{ C 1 g m 2 − C 2 g m 1 } ≤ 0 (2)

and

OF:

ω 0 = g m 2 C 1 C 2 R 0 (3)

From Equations (2) and (3), it is obvious that OF is independently controllable by resistor R_{0} and OC is independently controllable electronically by transconductance g_{m}_{1}.

Frequency stability may be considered to be an important figure of merit of an oscillator. The frequency stability factor is defined as S F = d φ ( u ) / d u [_{1} = C/2, C_{2 }= C, R_{0 }= R/n and g_{m}_{1} = g_{m}_{2} = 1/R, S^{F} for the proposed SRCO is found to be

S F = 2 2 n (4)

Thus for larger values of n, the presented oscillator circuit enjoys a very good frequency stability.

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 − ε p ( ε p < < 1 ) denotes the voltage tracking error of Z-terminal of VDIBA, the expressions for characteristic equation, CO and FO respectively become:

s 2 { C 1 C 2 + ( C 1 + C 2 + C z ) C z } + s { ( C 1 + C z ) ( 1 R z + β + g m 2 ) + ( C 2 + C z ) ( 1 R 0 + 1 R z ) − β + 2 C 2 ( g m 1 + 1 R 0 ) } + ( 1 R 0 + 1 R z ) ( 1 R z + β + g m 2 ) = 0 (5)

Therefore the expressions for OC and OF are given as:

OC:

{ ( C 1 + C z ) ( 1 + β + g m 2 R z ) R 0 + ( C 2 + C z ) ( R 0 + R z ) − β + 2 R z C 2 ( 1 + g m 1 R 0 ) } ≤ 0 (6)

OF:

ω 0 = R 0 + R z + β + g m 2 R z ( R 0 + R z ) R 0 R z 2 { C z ( C 1 + C 2 + C z ) + C 1 C 2 } (7)

Therefore the active and passive sensitivities can be obtained as:

S C 1 ω 0 = − 1 2 1 1 + C z 2 + C 2 C Z C 1 ( C 2 + C Z ) , S C 2 ω 0 = − 1 2 1 1 + C z 2 + C 1 C Z C 2 ( C 1 + C Z ) , S R 0 ω 0 = − 1 2 { R z R 0 + R z } (8)

S C Z ω 0 = − 1 2 1 1 + C 1 C 2 − C z 2 C z ( C 1 + C 2 + 2 C Z ) , S R z ω 0 = − 1 2 { 2 R 0 + R z ( 1 + β + g m 2 R 0 ) R 0 + R z + β + g m 2 R z ( R 0 + R z ) } (9)

S β + ω 0 = 1 2 1 1 + 1 β + g m 2 R z = S g m 2 ω 0 (10)

Ideally, the various sensitivities of OF with respect to passive elements C_{z}, R_{z}, C_{1}, and C_{2} are found to be

S C z ω 0 = S R z ω 0 = 0 , S C 1 ω 0 = S C 2 ω 0 = − 1 2 (11)

For the typical values of C_{z} = 0.81 pF, R_{z}_{ }= 53 kΩ, β^{+} = 1 along with C_{1} = 0.5 nF, C_{2} = 1.0 nF, R_{0} = 950 Ω, the various sensitivities are found to be S C 1 ω 0 = − 0.391 , S C 2 ω 0 = − 0.276 , S C Z ω 0 = − 0.533 , S R 0 ω 0 = − 0.491 , S β + ω 0 = 0.477 = S g m ω 0 ,

S R Z ω 0 = − 0.0241 which are all low.

_{DD} = 0.9 V D.C. = −V_{SS} and I_{b} was taken 100 µA.

To confirm theoretical analysis, the proposed SRCO was simulated using CMOS VDIBA (as shown in _{1} = 0.5 nF, C_{2} =1.0 nF, R_{0} = 950 Ω. The transconductance of VDIBA was controlled by bias current I_{b}. SPICE generated output waveforms indicating transient and steady state responses are shown in

These results, thus, confirm the validity of the proposed configuration. _{0}. A comparison with other previously known SRCOs using different active building blocks has been given in

The implementation of CMOS VDIBA employing 0.18 μm TSMC technology was used from [

From Equations (8) - (10), this is obvious that the values of various sensitivities of passive and active components are less than half.

This work presents VDIBAs-based SRCO which employs minimum number of passive elements (namely, one resistor, two capacitors) and offers independent control of OF through the resistor R_{0} and OC through the transconductance g_{m}_{1} (thus the circuit enjoys the electronic control of OC), low passive and active sen-

Reference | Active Element | Number of Active Element(s) | Number of GC | Number of FC | Number. of Resistors | Whether OC and OF are Independently Controllable? |
---|---|---|---|---|---|---|

[ | CFOA | 1 | 1 | 1 | 3 | YES |

[ | CC-II (+) | 1 | 1 | 1 | 3 | YES |

[ | CC-II (−) + Buffer | 2 | 2 | 0 | 3 | YES |

[ | PFTFN | 1 | 1 | 1 | 3 | YES |

[ | PNFTN | 1 | 2 | 0 | 4 | NO |

[ | NFTFN + Buffer | 2 | 2 | 0 | 3 | YES |

[ | DVCCC | 1 | 2 | 0 | 3 | YES |

[ | DVCCC | 1 | 2 | 0 | 3/2 | YES |

[ | CDBA | 1 | 1 virtually grounded) | 1 | 3 | YES( only in second topology of |

[ | OTRA | 1 | 1 virtually grounded) | 1 | 3 | NO |

[ | CDTA | 1 | 1 | 1 | 2 | YES |

[ | VD-DIBA | 2 | 2 | 0 | 1 | YES |

[ | VDIBA | 2 | 1 | 1 | 1 | NO |

[ | VD-DIBA | 1 | 2 | 0 | 2 | YES |

[ | VD-DIBA | 1 | 1 | 1 | 2 | YES |

Proposed | VDIBA | 2 | 1 | 1 | 1 | YES |

sitivities and a very good frequency stability. This communication, therefore, added a new application circuit to the existing repertoire of VDIBAs-based application circuits.

The authors gratefully acknowledge Prof. Dr. D. R. Bhaskar, Professor, Department of Electronics and Communication Engineering, Delhi Technological University, Shahbad Daulatpur, Main Bawana Road, Delhi-110042, India, useful suggestions/discussions.

Pushkar, K.L., Singh, G. and Goel,^{ }R.K. (2017) CMOS VDIBAs-Based Single-Resistance-Controll- ed Voltage-Mode Sinusoidal Oscillator. Circuits and Systems, 8, 14-22. http://dx.doi.org/10.4236/cs.2017.81002