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This paper presents a third-order quadrature sinusoidal oscillator (TOQSO) using two voltage differencing buffered amplifiers (VDBAs), three capacitors and a resistor. The new topology provides two quadrature voltage outputs. The condition of oscillation (CO) and frequency of oscillation (FO) are electronically independently controllable by the separate transconductance of the VDBAs. The workability of the proposed TOQSO is confirmed by SPICE (Version 16.5) simulation using Taiwan semiconductor manufacturing company (TSMC) 0.18 μm process parameters.

An oscillator is a very important basic building block, which is frequently used in electrical and electronics engineering applications. Among several types of sinusoidal oscillators, the quadrature oscillators are widely used because they can offer sinusoidal signals with 90˚ phase difference, for example, in telecommunications for quadrature mixers and SSB generators [

V o V i n = T 1 ( s ) T 2 ( s ) = − a 3 s ( a 0 s 2 + a 1 s + a 2 ) (1)

where T 1 ( s ) = 1 a 0 s 2 + a 1 s + a 2 and T 2 ( s ) = − a 3 s

or T 1 ( s ) = − 1 a 0 s 2 + a 1 s + a 2 and T 2 ( s ) = a 3 s

To produced sustained oscillations, V_{o} = V_{in} and hence the characteristic equation can be denoted as

a 0 s 3 + a 1 s 2 + a 2 s + a 3 = 0 (2)

The CO and FO can be deduced from Equation (2) as follows:

CO : a 0 a 3 = a 1 a 2 (3)

FO : ω 0 = a 3 a 1 = a 2 a 0 (4)

The symbolic notation and equivalent model of the VDBA are shown in

current relations of VDBA can be described by the following matrix.

( I p I n I z V w ) = ( 0 0 0 0 0 0 0 0 g m − g m 0 0 0 0 β 0 ) ( V p V n V z I w ) (5)

where β is a non-ideal voltage gain of VDBA. The value of β in an ideal VDBA is unity and g_{m} is the transconductance of the VDBA.

The expression for characteristic equation (CE) of the circuit of

CE : s 3 C 1 C 2 C 3 + s 2 ( C 1 C 2 R 0 ) + s ( C 2 g m 1 R 0 ) + g m 1 g m 2 R 0 = 0 (6)

The condition of oscillation and the frequency of oscillation can be given as

CO : g m 2 R 0 ≤ C 2 C 3 (7)

FO : ω 0 = g m 1 R 0 C 1 C 3 (8)

The relationship between V_{o}_{1} and V_{o}_{2} can be obtained as:

V o 1 V o 2 = − j ω C 2 g m 2 = ω C 2 g m 2 e j − 90 ∘ (9)

From Equation (9) it is evident that V_{o}_{1} and V_{o}_{2} are in quadrature.

The sensitivity is an important performance criterion of any circuit structure. The sensitivities of ω_{0} with respect to active and passive elements are given by

S C 1 ω 0 = S C 3 ω 0 = S R 0 ω 0 = − 1 2 , S g m 1 ω 0 = 1 2 (10)

It may be easily observed from Equation (10) that all sensitivities are lower than unity in magnitude, for the proposed third-order quadrature oscillator. It ensures that the sensitivity performance is good.

To confirm theoretical analysis, the proposed TOQSO was simulated using CMOS VDBA (as shown in _{1} = 1.0 nF and C_{2} = 1.0 nF, and R_{0} = 1.66 kΩ. The transconductances of VDBAs were controlled by the bias currents. SPICE generated output waveforms indicating transient and steady state responses of circuit of

Transistor | W (µm) | L (µm) |
---|---|---|

M1-M4, M10, M11, M15, M16 | 7 | 0.35 |

M5, M6 | 21 | 0.7 |

M7, M8 | 7 | 0.7 |

M9 | 3.5 | 0.7 |

M12-M14 | 14 | 0.35 |

shown in _{o1} and V_{o2} are found to be 2.55% and 0.48% respectively. The THD at output V_{o2} is very small.

A new voltage-mode third order quadrature sinusoidal oscillator with independent electronic control of both CO and FO using two VDBAs, three capacitors and a resistor is introduced. The CO can be electronically controlled by transcoductance (g_{m}_{2}) of VDBA_{2} without affecting FO. FO can also be electronically adjusted by transcoductance (g_{m}_{1}) of VDBA_{1} without affecting CO. The proposed TOQSO offers low sensitivities. The circuit exhibits good high frequency performance. One can design TOQSO with single VDBA. Workability of the proposed configuration is verified by SPICE simulation using 0.18 µm TSMC technology.

Pushkar, K.L. (2017) Voltage-Mode Third-Order Quadrature Sinusoidal Oscillator Using VDBAs. Circuits and Systems, 8, 285-292. https://doi.org/10.4236/cs.2017.812021

KCL at node 1:

i z 1 = g m 1 ( v p 1 − v n 1 ) = v z 1 s C 1

g m 1 ( v p 1 − v n 1 ) = v z 1 s C 1 (a)

KCL at node 2:

i z 2 = g m 2 ( 0 − v n 2 ) = v z 2 s C 2

− g m 2 v z 1 = v z 2 s C 2 , (b)

KCL at node 3:

v n 1 ( s C 3 + 1 R 0 ) = v z 2 s C 3 + v z 1 1 R 0 (c)

From Equations ((a)-(c)), we will gate CE.