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<p>In this paper we present an algorithm to generate the layout of a pair of devices <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(A\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>A</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(B\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>B</mi> </math></EquationSource> </InlineEquation> for a given matching ratio <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(r\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>r</mi> </math></EquationSource> </InlineEquation> and total unit cell count <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(N\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>N</mi> </math></EquationSource> </InlineEquation> that minimizes the mismatch due to systematic gradient effects. The algorithm relies on simple reflections and rotations of an initial optimized pattern across 4 quadrants. The approach cancels all odd-order systematic gradients and minimizes 2nd order systematic gradients. The method can easily be extended to cancel higher-order even gradient effects. The validity of the proposed algorithm is demonstrated via numerical simulations. Additionally, an electrothermal simulation of a set of layouts is run to further validate the proposed layout generation scheme.</p>

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Gradient Minimization in Layout Patterns for Analog Circuits

  • 期刊论文

  • 发表日期：

    2025年6月28日

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  • Isaac Bruce,
  • Michael Sekyere,
  • Ruohan Yang,
  • Saeid Karimpour,
  • Colin C. McAndrew,
  • Degang Chen

摘要

In this paper we present an algorithm to generate the layout of a pair of devices \(A\) A and \(B\) B for a given matching ratio \(r\) r and total unit cell count \(N\) N that minimizes the mismatch due to systematic gradient effects. The algorithm relies on simple reflections and rotations of an initial optimized pattern across 4 quadrants. The approach cancels all odd-order systematic gradients and minimizes 2nd order systematic gradients. The method can easily be extended to cancel higher-order even gradient effects. The validity of the proposed algorithm is demonstrated via numerical simulations. Additionally, an electrothermal simulation of a set of layouts is run to further validate the proposed layout generation scheme.