Steve, I disagree that a PLL with just a phase comparator and VCO is not particularly useful as "something has to be done to establish the DC operating point." A plain vanilla PLL will find its DC operating point just fine, as long as the necessary VCO input voltage is within the range of the phase detector's average output voltage. But, without the addition of the second integrator, it has zero frequency error but non-zero phase error. In many cases this is just fine. The other problem with the bare-bones PLL is that it has no filtering to reduce sidebands (VCO jitter) on account of the phase detector's output, which is usually an AC waveform of some variety. The addition of either the second integrator (making it a type II control loop), and/or low-pass filtering inside the loop, are what could cause closed-loop instability if not designed well, as well as the second- or higher-order closed-loop response which can be somewhat oscillatory depending on damping factor. We usually analyze them as if they are second-order loops even if the transfer function is higher order. Regards, Andy > Parthal, it is the natural frequency of the typical second-order transfer > function of the closed loop. Phase comparator gain is in volts / radians, > while VCO gain is in radians / second / volt. Given only DC gain, the > system is first order and unconditionally stable yielding > V/S/V. Unfortunately, it is not particularly useful as something has to be > done to establish the DC operating point. In most implementations an > integrator serves this purpose, adding a second order to the transfer function. ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List FAQ wiki page is located at: http://si-list.org/wiki/wiki.pl?Si-List_FAQ List technical documents are available at: http://www.si-list.org List archives are viewable at: //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu