Frequency‐domain behavioural noise analysis of analogue phase‐locked loops

Abstract

A frequency-domain approach for phase noise analysis of integer-N multiplier-type phase-locked loops (PLLs), based on the conversion matrix approach, is introduced that can take all non-linearities in the loop into account. It can also characterise all kinds of power spectral densities and correlation between variables and all aspects of phase noise-to-phase noise or amplitude noise-to-phase noise (AN–PN) conversions. The noise transfer between various sidebands is also taken into account. This is especially important for characterising the folding of the voltage-controlled oscillator's phase noise which results in the phase noise augmentation at small frequency offsets. Unlike the linear phase-domain models, the stochastic phase noise local maxima at large offset frequencies are also accurately characterised. Giving the phase/amplitude noise spectra of various PLL blocks, this approach computes the resulting output phase noise spectrum. The validity of the new approach is verified by comparing its results with those of a numerical time-domain stochastic simulation. The proposed method has far much faster runtimes, independent of the time constants in the system, compared to the corresponding time-domain methods that allow a convenient simulation-based design of PLLs especially at radio frequencies.