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A new voltage-mode quadrature sinusoidal oscillator (QSO) using two voltage differencing-differential input buffered amplifiers (VD-DIBAs) and only three passive components (two capacitors and a resistor) is presented. The proposed QSO circuit offers advantages of independent electronic control of both oscillation frequency and condition of oscillation, availability of two quadrature voltage outputs and low active and passive sensitivities. SPICE simulation results have been included using 0.35 μm MIETEC technology to confirm the validity of the proposed QSO oscillator.

Quadrature sinusoidal oscillators (QSOs) are important blocks in the synthesis of modern transceivers. A QSO provides two sinusoids with a 90˚ phase difference. QSOs are useful in telecommunications for quadrature mixers and single sideband generators [

The symbolic notation and the equivalent circuit model of the VD-DIBA are shown in

( I + I − I z I v V w ) = ( 0 0 0 0 0 0 0 0 0 0 g m − g m 0 0 0 0 0 0 0 0 0 0 1 − 1 0 ) ( V + V − V z V v I w ) . (1)

A straight forward circuit analysis of the circuit of

CE: s 2 C 1 C 2 + s C 1 ( 1 R 0 − g m 2 ) + g m 1 R 0 = 0 . (2)

From Equation (2), the CO and FO are given by

CO:

( 1 R 0 − g m 2 ) ≤ 0 (3)

Figure2. Proposed electronically controllable quadrature sinusoidal oscillator.

FO:

ω 0 = g m 1 R 0 C 1 C 2 . (4)

Thus from Equations (3) and (4), it is clear that CO is electronically controllable by the transconductance g_{m}_{2}, whereas FO is electronically controllable through the transconductance g_{m}_{1}. Therefore both CO and FO are independently controllable by two separate transconductance of VD-DIBAs.

Considering R Z and C Z as parasitic resistance and parasitic capacitance respectively of the Z-terminal of the VD-DIBA, taking the non-idealities into account, namely the voltage of W-terminal V W = ( β + V Z − β − V V ) where β^{+} = 1 − ε_{p} (ε_{p} = 1) and β^{−} = 1 − ε_{n} (ε_{n} = 1) denote the voltage tracking errors of Z-terminal and V-terminal of the VD-DIBA respectively, then the expressions for CE, CO and FO can be given as:

CE:

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

CO:

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

FO:

ω 0 = R 0 + R z − R 0 R z g m 2 β + + R z 2 β + g m 1 R 0 R z 2 ( C 1 + C z ) ( C 2 + C z ) . (7)

The passive and active sensitivities can be expressed as:

S C 1 ω 0 = − 1 2 C 1 C 1 + C z , S C 2 ω 0 = − 1 2 C 2 C 2 + C z , S C z ω 0 = − 1 2 ( 1 C 1 + C z + 1 C 2 + C z ) C z (8a)

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

S g m 1 ω 0 = 1 2 R z 2 β + g m 1 R 0 + R z − R 0 R z g m 2 β + + R z 2 β + g m 1 (8b)

S g m 2 ω 0 = − 1 2 R 0 R z g m 2 β + R 0 + R z − R 0 R z g m 2 β + + R z 2 β + g m 1 ,

S R 0 ω 0 = − 1 2 R z ( 1 + R z β + g m 1 ) R 0 + R z − R 0 R z g m 2 β + + R z 2 β + g m 1 (8c)

S R z ω 0 = − 1 2 ( 1 + 2 R 0 + R z R z + R 0 − R 0 R z β + g m 2 + R z 2 β + g m 1 ) (8d)

In the ideal case, the various sensitivities of ω_{0} with respect to C_{1}, C_{2}, R_{0}, C_{z}, R_{z}, g_{m}_{1}, g_{m}_{2} and β^{+} are found to be

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

Considering the typical values of various parasitic e.g. C_{z} = 0.81 pF, R_{z} = 53 kΩ, β^{+} = β^{−} = 1 along with g_{m}_{1} = 310.477 µƱ, g_{m}_{2} =291.186 µƱ, C_{1} = C_{2} = 10 nF, and R_{0} = 4 kΩ, the various sensitivities are found to be S C 1 ω 0 = − 0.006 , S C 2 ω 0 = − 0.006 , S C Z ω 0 = − 0.987 , S R 0 ω 0 = − 0.533 , S R Z ω 0 = − 0.535 , S g m 1 ω 0 = 0.502 , S g m 2 ω 0 = − 0.0355 , and S β + ω 0 = 0.466 which are all quite low.

Frequency stability is an important figure of merit of an oscillator. The frequency stability factor is defined as S F = d φ ( u ) / d u , where ω / ω 0 is the normalized frequency, and u = φ ( u ) represents the phase function of the open loop transfer function of the oscillator circuit. With C_{1} = C_{2} = C, R_{0} = 1/g_{m}_{2} = 1/g, g_{m}_{1} = ng, S^{F} for the proposed SECO is found to be:

S F = 2 n . (10)

Thus, the new proposed configuration offers very high frequency stability factor larger values of n.

The proposed QSO was simulated using CMOS VD-DIBA (as shown in _{0} = 4 kΩ, and C_{1} = C_{2} = 10 nF. The transconductances of VD-DIBAs were controlled by bias voltages V_{B}_{1}, V_{B}_{2} respectively. The simulated output waveforms for transient response and steady state response are shown in _{o}_{1} and V_{o}_{2}. The generated waveforms relationship within quadrature circuit has been confirmed by Lissajous pattern shown in

implemented using 0.35 µm MIETEC technology. The transistor model parameters used for CMOS VD-DIBA are listed in

In this communication, an electronically tunable voltage-mode quadrature sinusoidal oscillator enabling independent electronic control of frequency of oscillation and condition of oscillation is presented. The proposed QSO circuit employs only two VD-DIBAs, two grounded capacitors and a resistor. The

.MODEL N NMOS (LEVEL = 3; TOX = 7.9E−9; NSUB = 1E17; GAMMA = 0.5827871; PHI = 0.7; VTO = 0.5445549; DELTA = 0; UO = 436.256147; ETA = 0; THETA = 0.1749684; KP = 2.055786E−4; VMAX = 8.309444E4; KAPPA = 0.2574081; RSH = 0.0559398; NFS = 1E12; TPG = 1; XJ = 3E−7; LD = 3.162278E−11; WD = 7.046724E−8; CGDO = 2.82E−10; CGSO = 2.82E−10 CGBO = 1E−10; CJ = 1E−3; PB = 0.9758533; MJ = 0.3448504; CJSW; = 3.777852E−1; MJSW = 0.3508721) |
---|

.MODEL P PMOS (LEVEL = 3; TOX = 7.9E−9; NSUB = 1E17; GAMMA = 0.4083894; PHI = 0.7; VTO = −0.7140674; DELTA = 0; UO = 212.2319801; ETA = 9.999762E−4; THETA = 0.2020774; KP = 6.733755E−5; VMAX = 1.181551E5; KAPPA = 1.5; RSH = 30.0712458; NFS = 1E12; TPG = −1; XJ = 2E−7; LD = 5.000001E−13; WD = 1.249872E−7; CGDO = 3.09E−10; CGSO = 3.09E−10; CGBO = 1E−10; CJ = 1.419508E−3; PB = 0.8152753; MJ = 0.5; CJSW = 4.813504E−10; MJSW = 0.5) |

Transistor | W/L (µm) |
---|---|

M1 - M6 | 14/1 |

M7 - M9 | 14/0.35 |

M10 - M18 | 4/1 |

M19 - M22 | 7/0.35 |

Reference | Active Elements | No. of Passive Components | Electronic Controllability of: | ||
---|---|---|---|---|---|

No. of Grounded C | No. of C + R | CO | FO | ||

[ | 2VD ? DIBA + UGC | 2 | 0 + 0 | NO | YES |

[ | 2CDBA | 1 | 1 + 3 | NO | NO |

[ | 2OTRA | 2 | 0 + 4 | NO | NO |

[ | 2CDBA | 2 | 0 + 3 | NO | NO |

[ | 2VDIBA + 2MOS | 1 | 1 + 0 | YES | YES |

[ | 3CFTA | 2 | 0 + 0 | YES | YES |

proposed | 2VD − DIBA | 2 | 0 + 1 | YES | YES |

proposed QSO is capable of simultaneously providing two explicit quadrature voltage outputs. The condition of oscillation and the frequency of oscillation of the proposed circuit are controllable electronically through separate transconductance of the VD-DIBAs. The workability of the proposed structure has been demonstrated by PSPICE simulations using 0.35 µm MIETEC technology.

Pushkar, K.L. (2018) Electronically Controllable Quadrature Sinusoidal Oscillator Using VD-DIBAs. Circuits and Systems, 9, 41-48. https://doi.org/10.4236/cs.2018.93004