Amplitude and Quadrature Errors of Two-Integrator Oscillator

In this paper we present the analysis of two-integrator oscillator. The main characteristics of this oscillator are its wide tuning range (about a decade), the inherent quadrature outputs, and the low power requirements in comparison with other inductorless oscillators. Using the transistors nonlinearities to limit the amplitude, allows one to avoid the use of extra circuits for automatic amplitude control and, therefore, also reduces the power requirements of the oscillator. We focus the study on the quasi-linear regime where the outputs are sinusoidal. The motivation and main focus of the research is to determine the impact of the components mismatches on the frequency, amplitude- and phase-error. The equations for the amplitude mismatches and the quadrature error are derived. The theory is validated by simulation using the parameters of standard 130 nm CMOS technology. Simulations confirm the amplitude and phase error equations, and show that the quadrature error can be reduced with no impact on the phase noise. The amplitude and quadrature errors may be reduced increasing the transconductance amplifiers gains. The amplitude mismatch is dependent on the ratio of the transconductances and capacitances mismatches. Therefore, with an independent adjustment of the transconductances, the amplitude mismatch can be eliminated even with a mismatch in the capacitances.