More on the Impulse Sensitivity Functions of CMOS Differential LC Oscillators

Abstract

The effective ISFs of differential LC oscillators are derived under the assumption that the drain-to-source current is linearly dependent on the gate-to-source voltage for transistors operated in saturation. Moreover, a new interpretation of phase noise is given by examining the real vector diagram of the carrier signal, upon which the noise voltage induced by the impulse noise current is superimposed. The distinct feature of our vector diagram lies in that the noise voltage is always parallel with the horizontal axis. From the Fourier transformations of the derived effective ISFs, the phase noise of differential LCoscillators can be formulated with physical meanings in the frequency domain. The proposed theory can well describe the translation of the noise spectra when the noises from the LC-tank, the switching transistors, and the tail current source are converted into the phase noise. Theoretical predictions from our formulas agree well with the simulation results.