dirac16
Member level 5
I want to work out the probability density function of a single inverter in case of mismatch and device jitter. This paper (https://ieeexplore.ieee.org/document/7063035) considers a long chain of inverters and writes the following equations to describe the stochastic nature of the inverter.
According to the paper, the delay of each delay cell, Tdi (i=1,2,…N), is different and follows a Gaussian distribution with a nominal delay Td_nom that depends on process corner, supply voltage, and temperature, and a standard deviation σmis determined by the device matching characteristics of the process. This is described by equation (1).
In other hand, Tdi also experiences a dynamic random variation and has a Gaussian probability density function (PDF) with a standard deviation σjit that is mainly due to device noise. This is described by equation (2). However this doesn't look alright to me. First note that equation (1) has the form of a density function. What you see in the 2nd equation is a bit weird as the exp argument takes the density function Tdu and subtracts it from the time t. There seems to be a flaw in their derivation of the inverter's PDF. Anyway what's the correct form of the second equation?
According to the paper, the delay of each delay cell, Tdi (i=1,2,…N), is different and follows a Gaussian distribution with a nominal delay Td_nom that depends on process corner, supply voltage, and temperature, and a standard deviation σmis determined by the device matching characteristics of the process. This is described by equation (1).
In other hand, Tdi also experiences a dynamic random variation and has a Gaussian probability density function (PDF) with a standard deviation σjit that is mainly due to device noise. This is described by equation (2). However this doesn't look alright to me. First note that equation (1) has the form of a density function. What you see in the 2nd equation is a bit weird as the exp argument takes the density function Tdu and subtracts it from the time t. There seems to be a flaw in their derivation of the inverter's PDF. Anyway what's the correct form of the second equation?