Noise analysis of a CMOS inverter using the Itô stochastic differential equation

The noise-free CMOS inverter is described by a first- order non-linear differential equation that can be regarded as a standard case in electronic circuits from the system-theoretic viewpoint. In lieu of the noise-free CMOS inverter, this paper explains the stochastic CMOS inverter at the low power supply voltage. The method of this paper utilizes the Kolmogorov-Fokker-Planck equation for the noise analysis of the CMOS inverter. In this paper, first we develop the CMOS inverter Itô Stochastic Differential Equation (SDE). Secondly, a system of two-coupled state estimation equations is derived. The numerical experimentations are demonstrated for the noise analysis of the CMOS inverter circuits as well.

[1]  Y. Tsividis.  Operation and modeling of the MOS transistor , 1987 .

[2]  Kaushik Roy,et al.  Robust ultra-low power sub-threshold DTMOS logic , 2000, ISLPED'00: Proceedings of the 2000 International Symposium on Low Power Electronics and Design (Cat. No.00TH8514).

[3]  David Blaauw,et al.  Ultralow-voltage, minimum-energy CMOS , 2006, IBM J. Res. Dev..

[4]  K. Ragini.  ULTRA LOW POWER DIGITAL LOGIC CIRCUITS IN SUB-THRESHOLD FOR BIOMEDICAL APPLICATIONS , 2009 .

[5]  Saibal Mukhopadhyay,et al.  Leakage current mechanisms and leakage reduction techniques in deep-submicrometer CMOS circuits , 2003, Proc. IEEE.

[6]  Peng Xu,et al.  Stochastic Behavior of a CMOS Inverter , 2007, 2007 14th IEEE International Conference on Electronics, Circuits and Systems.

[7]  J. Fellrath,et al.  CMOS analog integrated circuits based on weak inversion operations , 1977 .

[8]  Abderrahmane Haddad,et al.  Estimation theory with applications to communications and control , 1972 .

[9]  RoyKaushik,et al.  Robust subthreshold logic for ultra-low power operation , 2001 .

[10]  P. Kloeden,et al.  Numerical Solutions of Stochastic Differential Equations , 1995 .

[11]  Kaushik Roy,et al.  Robust subthreshold logic for ultra-low power operation , 2001, IEEE Trans. Very Large Scale Integr. Syst..

[12]  José E. Franca,et al.  Design of Analog-Digital VLSI Circuits for Telecommunications and Signal Processing , 1993 .

[13]  Harish Parthasarathy,et al.  Dynamics of a stochastically perturbed two-body problem , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[14]  K. RAGINI,et al.  ULTRA LOW POWER DIGITAL LOGIC CIRCUITS IN SUBTHRESHOLD FOR BIOMEDICAL APPLICATIONS , 2009 .