On the quadrature accuracy of in-phase coupled quadrature LC oscillator

In this article, closed-form equations are proposed for phase and amplitude errors of an in-phase coupled quadrature LC oscillator. First of all, the injected current from coupling network to switching one is analytically calculated in a novel approach. Then, fundamental equations are obtained to derive phase and amplitude errors which are results of mismatches of the tank's inductors, capacitors and resistors. The analysis shows that the LC tank's phase of this oscillator has a negligible deviation from zero that is desirable and causes low phase noise. Also, the study indicates that in-phase coupling of this structure generates an injection current that reduces the output current magnitude. In the following, a mechanism is proposed to compensate the phase error, using intentional mismatch in tail currents. Moreover, In contrast to previous works, there is not a considerable trade-off between phase error and phase noise; meaning phase noise is almost stable while phase error dramatically decreases. Next, Many simulations have been done in TSMC 0.18 pm to evaluate the proposed analytical equations and efficiency of the presented approach. Finally, all of these tests confirm the high accuracy of equations and capability of the mentioned technique.