Evaluation of the pole expressions of nano-scale multistage amplifiers based on equivalent output impedance

Several frequency compensation schemes have been proposed to stabilize multistage amplifiers with negative feedback. The performance of these amplifiers can be analyzed by inspecting their input-output transfer function as representation of their frequency response. With many circuit elements affecting the output response, it is relatively difficult to obtain the real transfer function of multistage amplifiers based on only the original small-signal expressions. Instead, certain techniques such as Miller's theorem are used to approximate important parameters such as DC gain and dominant pole. These methods are not generally helpful for approximating the nondominant poles which have a critical role on the loop stability of nano-scale amplifiers. With this issue in mind, this work proposes a systematic methodology to achieve the pole expressions of multistage amplifiers with frequency compensation. The key in the proposed technique is to model the equivalent impedance of the compensation loop at the output. The effectiveness of the proposed approach has been verified through comparison between the transfer functions obtained from theory and those transfer functions found in the literature.