Abstract
In the previous chapter, the quadrature oscillator with active coupling was analysed. The disadvantages of this coupling are the increase of the noise and power dissipation. In this chapter, we analyse the passive coupling which is an alternative method that diminishes these disadvantages. The quadrature RC-oscillator with capacitive coupling is studied. The capacitive coupling is noiseless and requires a small area. Since the coupling capacitors do not add noise, the phase noise improved in 3 dB (due to the coupling), with a marginal increase of the dissipation power, and the figure-of-merit (FoM) comparable to that of the best state-of-the-art RC-oscillators. Contrarily to what may be expected, with the increase of the coupling capacitances (stronger coupling) the oscillation frequency increases. We present a theory that explains this behaviour and derive the equations for calculation of the frequency, phase error and amplitude mismatch. These calculations are validated by simulation. The theory shows that both phase and amplitude error are reduced with the increase of the coupling factor. Moreover, the phase error is proportional to the amplitude mismatch, indicating that an automatic phase-error minimization based on the amplitude mismatch reduction is possible. The theory shows also that the phase noise has a low sensitivity to the coupling factor. We also study bimodal oscillations and phase ambiguity, for this type of coupling and compare it with other works. To validate the theory, a 2.4-GHz quadrature voltage-controlled oscillator (QVCO) based on two RC-oscillators with capacitive coupling was fabricated, in UMC 130 nm CMOS process.
Published Version
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