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Identifying and 3D Displaying Poles and Zeros in Analog Circuit Transfer Functions: Bode Surfaces

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Abstract

A new technique is developed that extends the normal Bode plots from two-dimensional to three-dimensional, including the \(\sigma \) axis into the plots. By utilizing MATLAB, it is shown how the Bode plots of a transfer function in an analog circuit can turn into a 3D Bode surface. In general, a tool is developed that integrates WinSpice and MATLAB so that in a comprehensive AC analysis Bode surfaces are directly generated for any given circuit transfer function. The technique is shown to be ideal to identify, and hence subsequently to extract, the poles and zeros of a transfer function. The applications can be extended into exploring feedback theory, analog filter design and stability analysis of control systems in high-performance circuits. Examples particularly for analog CMOS circuits are worked out that demonstrate some of the capabilities of the tool.

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Notes

  1. \(\mathrm{}_{i}(\mathrm{t})\) or \(\mathrm{q}_{o}(\mathrm{t})\) can represent either voltage or current.

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Authors and Affiliations

  1. Department of Electrical Engineering, Northern Illinois University, DeKalb, IL, 60115, USA

    Reza Hashemian, Mounika Vanga & Mahmoud Rahat

Authors
  1. Reza Hashemian
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  2. Mounika Vanga
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  3. Mahmoud Rahat
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Correspondence to Reza Hashemian.

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Hashemian, R., Vanga, M. & Rahat, M. Identifying and 3D Displaying Poles and Zeros in Analog Circuit Transfer Functions: Bode Surfaces. Circuits Syst Signal Process 36, 2473–2485 (2017). https://doi.org/10.1007/s00034-016-0418-0

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  • DOI: https://doi.org/10.1007/s00034-016-0418-0

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