Time-domain thermal noise simulation of switched capacitor circuits and delta-sigma modulators

Investigation of Phase Noise of Ring Oscillators With Time-Varying Current and Noise Sources by time-scaling Thermal Noise

“…[22]. It is seen that as I (t ) increases by 1.76 (=2.3mA/1.3mA) and phase noise at 10 MHz offset decreases roughly by (1:76) (= -8 dB) a) The variance of oscillator phase noise goes down as the cube of the factor , the rate at which is increasing with respect to time.…”

“…Therefore, extracting the expression for the mean cell delay from (23), substituting and equating the resulting expression to 1 we can solve for (24) Now, we comment on the condition . Since , referring to (22) this condition means the different delay cells are so designed that at time equal they all have the noisevariance parameter as the case when . Finally, if from (23), we extract the expression for the delay cell variance, evaluate the derivative explicitly, substitute , , and (24) in the resulting expression, and normalize by dividing by the mean period, , we obtain the normalized oscillator variance, denoted as (25) where when , the case when we have a constant drift.…”

“…We assume the SDE that is used for FPT calculation of the delay cells in this family is all given by (22) When , (22) is identical to (12) and this delay cell becomes the one described in Fig. 2 with biased in triode region.…”

“…The expression of , given in (17), is then generalized to the expression for , by replacing expression for in (17) with the expression for as given in (25) (26) From (25), we can state that, for ring oscillators using different delay cells in the family described by the SDE given in (22), and which have the same oscillation frequency. [22].…”

An 8-channel CMOS low-noise fast readout IC for CZT X-ray detectors designed by time-domain Hspice noise simulation

“…These three noise sources are modeled in the time-domain with the random number [10], [11]. Shot and thermal noise sources are a white noise in the frequency-domain, so they can be modeled as a Gaussian distribution of amplitude in the time-domain [10], [11]. Random number sets for these white noise sources are generated and made as time-domain noise sources in the Hspice simulator by constructing a series combination of piecewise linear sources.…”