Noise optimization in operational transconductance amplifier filters

A general framework for evaluating nonlinearity, noise and dynamic range in continuous‐time OTA‐C filters for computer‐aided design and optimization

“…As shown in Figure 3, the noise of a CMOS transconductor with value g m can be described by an equivalent input-referred noise-voltage source, v n , whose spectral density, S n ( f ), can be modelled as [36] where the thermal noise component, S t , and the flicker-noise component, S f , depend on the transconductor topology and on biasing. We shall assume that noise sources associated with different OTAs are statistically independent.…”

“…The literature contains several intuitive ideas on calculating noise, and attempts to solve noise problems for specific filters [36][37][38][39]. In contrast, this section provides complete, explicit, and easily evaluated formulas based on a general approach to noise analysis, and using matrix description as presented in Section 2, originally presented in [41].…”

“…Assuming ideal, that is, lossless and, therefore, noiseless capacitors, the output noise of any OTA-C filter is a combination of the noise contributions of all its transconductors. As shown in Figure 3, the noise of a CMOS transconductor with value g m can be described by an equivalent input-referred noise-voltage source, v n , whose spectral density, S n ( f ), can be modelled as [36] S n ( f ) Figure 4. Let G mx denote one of the filter transconductors (i.e.…”

“…. , N c (36) where N c is the number of constraints, c j is the j constraint function (e.g. total capacitance of the filter) which is dependent on matrices describing the filter and optimization variables, while m j and M j are minimum and maximum values of c j (which may be finite or infinite).…”

“…A large number of research papers have been published which deal with improving performance of the OTA-C filters focusing on the dynamic range, THD, and noise [8][9][10][11][12][22][23][24][25][26][27][28][29][30]. Some of the papers include estimation of dynamic range [4,31], nonlinear distortion using Volterra series approach [32-34] and harmonic injection method [35], as well as noise [36][37][38][39]. In this paper, based on the matrix description of the general OTA-C filter class [1], the estimation of nonlinear distortion, noise, and dynamic range has been proposed.The most challenging task for the analog design engineers is to have efficient tools for nonlinear distortion and noise analysis, in particular, tools that can be embedded into computer-aided filterdesign systems.…”