A general theory of phase noise in electrical oscillators

Abstract

The authors thank the correspondents for their note. The c 2 0 =2 correction term, while valid, rarely plays an important role in the final result because normally c 2 0 =2 is much smaller than 0 2 rms . The worst case scenario (which does not normally happen) is constant impulse sensitivity function (ISF). In this case, 0rms = c0. Correction to "A 0.5-V 74-dB SNDR 25-kHz Continuous-Time Delta-Sigma Modulator With a Return-to-Open DAC"Kong-Pang Pun, Shouri Chatterjee, and Peter KingetIn the above paper [1], a mistake in the schematic diagram of the 0.5-V operational transconductance amplifier (OTA) (Fig. 11) was discovered by Prof. Dr. Martin Schubert of FH Regensburg, University of Applied Sciences, Regensburg, Germany. The original OTA circuit diagram shows two series combinations of a 5-k resistor and a 20-pF capacitor connecting the outputs of the first stage to the inputs of the second stage, which is incorrect. The correct OTA schematic is shown in Fig. 1 below. The RC combinations are connected between the inputs and outputs of the second stage for Miller compensation with right-half-plane zero cancellation and the first and second stages are directly coupled. We apologize for this error.

Analyses and techniques for phase noise reduction in CMOS Colpitts oscillator topology

“…Accurate analysis of the behavior of oscillators has been the subject of intense investigation [4][5][6][7][8]. An effective method for providing qualitative and quantitative predictions of PN in integrated oscillators is based on the impulse sensitivity function (ISF) [9]. In [10,11], the authors addressed how to derive accurate evaluations of the ISF in relation to simulation settings.…”

Wake-up Receiver Based Ultra-Low-Power WBAN

“…There is a clear trade-off between power consumption and LO phase noise that has been discussed in literature [32,33]. Therefore, in ultra-low-power receivers, the LO phase noise cannot be neglected.…”

“…The receivers may have high noise figures and I/Q imbalance, since performance is traded for low power consumption. For example, there is a clear trade-off between the local oscillator power consumption and its phase noise [32,33].…”

Modelling and Discretization of Circuit Problems

“…phase noise is considered from a parameter dependency point of view and an averaging technique is described that works well on (but is also restricted to) finite time intervals and is of interest in behavioural modeling. In [112] a less accurate, but faster phase noise model is described that neglects the occurrence of α at the right-hand side in (20.42).…”