Current based MOS models

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Current based MOS models

• Johan Vanderhaegen
• Bob Brodersen

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Problem statement

• A long time ago, in a galaxy far, far away, the
  quadratic model was useful for analog design.
• (VGS-VT)ws 2nVth 100 mV
• (VGS-VT)sv 4nLCoxvsat / KP µ L
• Low power design requires modeling of the
  moderate inversion region

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How bad is it ?
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Apparently not so bad
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Analog design

• IDS(VGS,VDS) matters for digital design, not for
  analog
• Bias currents are set relatively accurately
• gm is the primary goal (gain, GBW, noise)
• Conclusion gm(I) matters for analog design
• Error(Quadratic model) up to 50

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Quadratic model
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Modeling moderate inversion

• Models based on physics model either strong
  inversion or weak inversion
• Reason simple model requires either diffusion
  current or drift current to be dominant
• Interpolation models relatively accurate in all
  regions
• e.g.

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General Small Signal Models

• Table look-up
• Interpolation model 1
• Interpolation model 2

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Interpolation models
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Interpolation models
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Current based design

• Interpolation models have one variable, the
  normalized current IDS/IDS0 or channel inversion
• The channel length L and normalized current I
  dimensionless span the design space completely
  (assuming gm is given)
• Normalized current also determines
• frequency behavior
• noise
• distortion

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EKV model
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EKV model
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EKV model
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Distortion
For a single transistor
For a diff pair with tail current I