Intuitive Understanding of Flicker Noise Reduction via Narrowing of Conduction Angle in Voltage-Biased Oscillators

Abstract

This brief aims to intuitively explain and numerically verify the observed phenomenon of flicker noise reduction in oscillators of reduced conduction angle (i.e., in class-C), which has been presented in literature but never properly explained. The flicker phase noise in a voltage-biased oscillator capable of operating in class-B and class-C is compared and numerically verified using a commercial simulation model of TSMC 28-nm CMOS. We illustrate how narrowing the conduction angle can suppress the 1/f noise up-conversion by decreasing 1/f noise exposure to the asymmetric rising and falling edges of oscillation waveform. The effects of implicit common-mode tank in the class-C operation is also discussed. We further clarify ambiguities among several simulation methods of impulse sensitivity function (ISF) based on periodic small-signal analysis (PAC or PXF), which is a key tool in understanding the flicker noise upconversion. A clearer ISF simulation method based on positive sidebands of PXF is proposed.

A −193.6 dBc/Hz FoMT 28.6-to-36.2 GHz Dual-Core CMOS VCO for 5G Applications

“…In this way, an impedance match is realized between the cross-couple pair and the output buffer, increasing the output power. As indicated, the VCO second harmonic tank impedance at the cross-couple pair source terminal is real, about 70 , increasing the symmetry of the signal [7]- [12]. Moreover, with the source degeneration effect, the second harmonic current into the LC tank will be suppressed.…”

“…To illustrate the improved signal symmetry, with the PSS and PXF simulations Fig. 4 shows the discrete I ds noise at 10 kHz offset and the effective non-normalized impulse sensitivity function (ISF) which is the product of the non-normalized ISF, h ds (t), and I ds noise, I noise respectively [12]. As indicated, the VCO conduction angle is 180 degree, and benefiting from the physical symmetry and the improved signal symmetry, the proposed dual-core VCO ISF is symmetrical.…”

Oscillator Flicker Phase Noise: A Tutorial

“…Class-C oscillator was first introduced in [72] with a thorough analysis of its thermal PN mechanism. However, the theory explaining its excellent flicker PN (see [73]- [76] showing surprisingly good 1/f 3 PN) was not revealed until [49]. In contrast to "symmetrising" the oscillating waveform by V H2 [48], narrowing of conduction angle could decrease the flicker current noise exposure to the asymmetric waveform caused by the 2nd (in nMOS-only class-C) or 3rd (in complementary class-C [77]) harmonic current entering the nonresistive terminations.…”

“…shows the simulated plots of V GS , I 1/f,rms (obtained, for example, fromFig. 2), V DS , and h DS (see[49]) of the Conceptual models of waveform-shaping of V DS due to I H2 entering (a) inductive, (b) resistive, or (c) capacitive terminations at 2ω 0 ; and due to I H3 entering (d) capacitive or (e) resistive terminations at 3ω 0 (Conditions: |V H0 | = 1V, |V H1 | = 1V, |V H2 | = 0.2V, |V H3 | = 0.1V).…”

“…The positive sidebands of periodic transfer function (PXF)[53] provide a fast and accurate way to calculate h DS (t)[49] (see also[54]-[56]). …”