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Analysis of Stability in Multistage Feedforward Operational Transconductance Amplifiers using Successive One-Pole Approximation

Taeju Lee

TL;DR

This work addresses the stability challenges of high-gain wideband OTAs implemented with multistage feedforward paths in deep CMOS nodes. It introduces SOPA, a systematic method that applies successive one-pole approximations to each substage to analyze and design for stability from 2- to 4-stage OTAs, including how large feedforward transconductances create Zeros that cancel poles. The key contribution is a generalized stability framework and explicit conditions (e.g., $g_{mF(k-1)}/g_{m(k)}$ must be significantly large) that guide the scaling of stage count and transconductance ratios, along with demonstrations of how decoupling capacitors $C_d$ and Miller capacitors $C_m$ influence phase margin. The findings highlight the tradeoffs between gain, bandwidth, phase margin, and practical constraints (bias, power, area) when increasing the number of stages, and provide design guidance for achieving stable, high-gain wideband OTAs in modern CMOS processes.

Abstract

This paper presents analysis results of the operational transconductance amplifiers (OTAs) that combine feedforward paths and multistage amplifiers to achieve high-gain wideband operation as well as frequency compensation. To analyze multistage feedforward OTAs and provide an intuitive design method, the successive one-pole approximation (SOPA) is used for each substage of a multistage feedforward OTA. Using SOPA, the stability analysis is carried out from the two-stage feedforward OTA to the four-stage feedforward OTA in this work.

Analysis of Stability in Multistage Feedforward Operational Transconductance Amplifiers using Successive One-Pole Approximation

TL;DR

This work addresses the stability challenges of high-gain wideband OTAs implemented with multistage feedforward paths in deep CMOS nodes. It introduces SOPA, a systematic method that applies successive one-pole approximations to each substage to analyze and design for stability from 2- to 4-stage OTAs, including how large feedforward transconductances create Zeros that cancel poles. The key contribution is a generalized stability framework and explicit conditions (e.g., must be significantly large) that guide the scaling of stage count and transconductance ratios, along with demonstrations of how decoupling capacitors and Miller capacitors influence phase margin. The findings highlight the tradeoffs between gain, bandwidth, phase margin, and practical constraints (bias, power, area) when increasing the number of stages, and provide design guidance for achieving stable, high-gain wideband OTAs in modern CMOS processes.

Abstract

This paper presents analysis results of the operational transconductance amplifiers (OTAs) that combine feedforward paths and multistage amplifiers to achieve high-gain wideband operation as well as frequency compensation. To analyze multistage feedforward OTAs and provide an intuitive design method, the successive one-pole approximation (SOPA) is used for each substage of a multistage feedforward OTA. Using SOPA, the stability analysis is carried out from the two-stage feedforward OTA to the four-stage feedforward OTA in this work.
Paper Structure (7 sections, 10 equations, 10 figures, 2 tables)

This paper contains 7 sections, 10 equations, 10 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. GENERAL CONSIDERATION
  3. Stability Analysis using SOPA
  4. Analysis of Two-Stage Feedforward Structure
  5. Analysis of Three-Stage Feedforward Structure
  6. Analysis of Four-Stage Feedforward Structure
  7. Conclusion

Figures (10)

  • Figure 1: (a) Miller compensation using $C\textsubscript{m}$. (b) Addition of $R\textsubscript{z}$ to remove the RHP zero.
  • Figure 2: (a) Two-stage feedforward OTA and (b) its Bode plots.
  • Figure 3: (a) Fully differential two-stage feedforward OTA, (b) its bias block, and (c) the common-mode feedback used in the output stage.
  • Figure 4: (a) Approximation from the two-pole system to the one-pole system without (or with) $C\textsubscript{d}$. (b) Successive one-pole approximation (SOPA).
  • Figure 5: (a) Three-stage feedforward OTA and (b) its approximated schematic.
  • ...and 5 more figures