CMOS-RC Colpitts Oscillator Design Using Floating Fractional-Order Inductance Simulator

Abstract

This paper deals with CMOS fractional-order inductance (FoL) simulator design and its utilization in 2.75 thorder Colpitts oscillator providing high frequency of oscillation. The proposed floating FoL is composed of two unity-gain current followers (CFs), two inverting voltage buffers, a transconductor, and a fractional-order capacitor (FoC) of order 0.75, while the input intrinsic resistance of CF is used as design parameter instead of passive resistor. The resulting equivalent inductance value of the FoL can be adjusted via order of FoC, which was emulated via 5 th-order Foster II RC network and values optimized using modified least squares quadratic method. In frequency range 138 kHz-2.45 MHz the L  shows ±5 degree phase angle deviation. Theoretical results are verified by SPICE simulations using TSMC 0.18 μm level-7 LO EPI SCN018 CMOS process parameters with ±1 V supply voltages.

Adjustable Multiphase Sinusoidal Oscillator with Fractional–Order Elements

“…2 (b) is shown the dependence of the values of g m2 on frequency. Note that values of the g m2 are dependent only on frequency as is obvious from substitution the equation C α = C eq ω 1−α to (8). These analysis are very helpful in case of selecting the initial values of the oscillator parameters.…”

“…For fractional-order oscillator design presented in this paper, the FOC approximation through suitable and fully sufficient RC network [15] is used. The approximation of the FOE is dependent on selected type of the RC structure, number of the RC sections, type of the calculation method, value of the α, and frequency band of the approximation validity [7], [8], [15]. The Foster I, Foster II, Cauer I, and Cauer II are types of RC structures most often used to approximate the FOC.…”

“…The Foster I, Foster II, Cauer I, and Cauer II are types of RC structures most often used to approximate the FOC. In case of calculation of the values of passive parts in the selected RC structure, the Oustaloup's or CFE (Continuous Fraction Expansion) methods are most commonly used [7], [8], [15].…”

“…Fractional-order oscillators are characterized by arbitrary phase shift of output signals in multiples of απ/2, where the parameter α is non-zero positive number in range from 0 < α < 1 [8]. Note that standard oscillators provide phase shift of output signals only in multiples of π/2.…”

“…The paper [8] presents fractional-order Colpitts oscillator based on CMOS transconductors providing two voltage outputs. The simple proposal of the fractional-order oscillator with two voltage outputs based on differential voltage current conveyor transconductance amplifier (DVCCTA) and variable gain amplifier (VGA) employing impedance converter is presented in paper [9].…”