A State-Space Approach to Intermodulation Distortion Estimation in Fully Balanced Bandpass <formula formulatype="inline"><tex>$G_{m}$</tex></formula>&ndash;<formula> <tex>$C$</tex></formula> Filters With Weak Nonlinearities

A general weak nonlinearity model for LNAs

“…The model uses simple closed-form expressions to describe the total output distortion for both narrowband and wideband application, which is just linear combination of the nonlinear coefficients of each transistor and terminal AC gains. In fact this general model can also be applied to [10] where a state-space approach is used to get low complexity analytic expressions of distortions for different fully balanced band Gm-C filters…”

Miller Theorem for Weakly Nonlinear Feedback Circuits and Application to CE Amplifier

“…However, in the authors' opinion, these tools often lead to analytical relationships too difficult to be exploited during the design phase. To overcome this problem, other approaches have been proposed such as that in [4]- [6] or the authors' one, which exploits the phasor notation in the frequency domain [11]- [13]. Although the approach based on phasors demonstrated its strengths in contests such as feedback amplifiers [11] and particularly in two-or three-stage amplifiers [12], [13], a great complication may still arise when nonlinearity is generated also by feedback blocks.…”

Matrix Methods for the Dynamic Range Optimization of Continuous-Time $G_{m}$-$C$ Filters

“…Regarding the impact of distortion, different techniques have been reported; for instance, those presented in [4]- [9]. Proposals in [4], [5] are based on frequency-domain calculation using Volterra series which, although powerful, tend to be very cumbersome as the filter order increases.…”

“…In [6], [7] nonlinearities of individual transconductors are propagated by means of partial transfer functions to the output, where the contributions are summed to estimate the overall distortion behavior of the filter. Finally, [8], [9] use time-domain analysis and state-space modelling for the evaluation of harmonic and intermodulation distortion in filters with no floating capacitors. None of these approaches provides the simple, general and systematic matrix manipulation techniques which are available for noise.…”

“…Also, they are useful to calculate the relative sensitivities of the filter transfer function with respect to the matrices in the representation (1). They can be easily obtained using the Hadamard product as 3 (9) where the sensitivities are defined as . Up to now, it has been assumed that transconductances remain constant with frequency.…”