Spectral theory analysis of UWB-oscillations in frequency sinthesizers based on phase-locked loops

In this report a general theory of phase-locked loop (PLL) for N-dimensional UWB-signals (for example radar and optical signals) is given. On the first step a discretization method for solving differential equations of the PLL systems is presented. It is shown that there are a lot of zones of synchronous in discretized PLL and a technical realization of this device (in PLL with samples). A spectral theory of analysis of oscillations in PLL with samples is given. It is shown a lot of different physical properties in PLL with samples. The effect of shape of the input signals (harmonic signals, splines and atomic functions) at the border zones of operating modes being entered into PLL with samples is examined.