Lecture_Slides Small Signal Modeling y Parameter Model
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MOS Transistors Yannis Tsividis Small-Signal Modeling y-Parameter Model Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011 1 These slides are based on Y. Tsividis and C. McAndrew, “Operation and Modeling of the MOS Transistor”, Copyright © Oxford University Press, 2011. They are meant to be part of a lecture, and may be incomplete or may not even make sense without the accompanying narration.
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Transcript of Lecture_Slides Small Signal Modeling y Parameter Model
MOS Transistors Yannis Tsividis
Small-Signal Modeling y-Parameter Model
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011 1
These slides are based on Y. Tsividis and C. McAndrew, “Operation and Modeling of the MOS Transistor”, Copyright © Oxford University Press, 2011. They are meant to be part of a lecture, and may be incomplete or may not even make sense without the accompanying narration.
2
𝑣𝑔 𝑡 = 𝑀 cos 𝜔𝑡 + 𝜙
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
𝑣𝑔(𝑡) 𝑖𝑔(𝑡)
𝑖𝑠(𝑡) 𝑖𝑑(𝑡)
𝑖𝑏(𝑡) 𝑣𝑠(𝑡)
𝑣𝑏(𝑡)
𝑣𝑑(𝑡)
𝑉𝑔 𝐼𝑔
𝐼𝑠 𝐼𝑑
𝐼𝑏 𝑉𝑠
𝑉𝑏 𝑉𝑑
𝑉𝑔 = 𝑀𝑒𝑗𝜙
3 Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
𝑦𝑑𝑑 ≡𝐼𝑑𝑉𝑑
𝑉𝑔,𝑉𝑏,𝑉𝑠=0
𝐼𝑑
𝑉𝑑
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
𝑦𝑑𝑔 ≡𝐼𝑑𝑉𝑔
𝑉𝑑,𝑉𝑏,𝑉𝑠=0
𝑉𝑔
𝐼𝑑
4
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
𝑦𝑑𝑏 ≡𝐼𝑑𝑉𝑏
𝑉𝑔,𝑉𝑑,𝑉𝑠=0
𝐼𝑑
𝑉𝑏
5
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
𝑦𝑑𝑠 ≡𝐼𝑑𝑉𝑠
𝑉𝑑,𝑉𝑔,𝑉𝑏=0
𝐼𝑑
𝑉𝑠
6
7
𝐼𝑑 = 𝐼𝑑 𝑉𝑔,𝑉𝑏,𝑉𝑠=0
+ 𝐼𝑑 𝑉𝑑,𝑉𝑏,𝑉𝑠=0
+ 𝐼𝑑 𝑉𝑑,𝑉𝑔,𝑉𝑠=0
+ 𝐼𝑑 𝑉𝑑,𝑉𝑔,𝑉𝑏=0
𝐼𝑑 = 𝑦𝑑𝑑 𝑉𝑑 + 𝑦𝑑𝑔𝑉𝑔 + 𝑦𝑑𝑏𝑉𝑏 + 𝑦𝑑𝑠𝑉𝑠
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
When all voltages are applied simultaneously:
𝑉𝑔
𝐼𝑑
𝑉𝑠
𝑉𝑏 𝑉𝑑
8
𝐼𝑑 = 𝑦𝑑𝑑𝑉𝑑 + 𝑦𝑑𝑔𝑉𝑔 + 𝑦𝑑𝑏𝑉𝑏 + 𝑦𝑑𝑠𝑉𝑠
𝐼𝑔 = 𝑦𝑔𝑑𝑉𝑑 + 𝑦𝑔𝑔𝑉𝑔 + 𝑦𝑔𝑏𝑉𝑏 + 𝑦𝑔𝑠𝑉𝑠
𝐼𝑏 = 𝑦𝑏𝑑𝑉𝑑 + 𝑦𝑏𝑔𝑉𝑔 + 𝑦𝑏𝑏𝑉𝑏 + 𝑦𝑏𝑠𝑉𝑠
𝐼𝑠 = 𝑦𝑠𝑑𝑉𝑑 + 𝑦𝑠𝑔𝑉𝑔 + 𝑦𝑠𝑏𝑉𝑏 + 𝑦𝑠𝑠𝑉𝑠
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
𝑦𝑘𝑙 ≡𝐼𝑘𝑉𝑙
𝑉𝑛=0, 𝑛≠𝑙
𝑉𝑔 𝐼𝑔
𝐼𝑠 𝐼𝑑
𝐼𝑏 𝑉𝑠
𝑉𝑏 𝑉𝑑
Similarly for the other currents:
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𝑦𝑑𝑑 + 𝑦𝑑𝑔 + 𝑦𝑑𝑏 + 𝑦𝑑𝑠 = 𝑦𝑑𝑑 + 𝑦𝑔𝑑 + 𝑦𝑏𝑑 + 𝑦𝑠𝑑 = 0
𝑦𝑔𝑔 + 𝑦𝑔𝑑 + 𝑦𝑔𝑏 + 𝑦𝑔𝑠 = 𝑦𝑔𝑔 + 𝑦𝑑𝑔 + 𝑦𝑏𝑔 + 𝑦𝑠𝑔 = 0
𝑦𝑏𝑏 + 𝑦𝑏𝑑 + 𝑦𝑏𝑔 + 𝑦𝑏𝑠 = 𝑦𝑏𝑏 + 𝑦𝑏𝑑 + 𝑦𝑔𝑏 + 𝑦𝑠𝑏 = 0
𝑦𝑠𝑠 + 𝑦𝑠𝑑 + 𝑦𝑠𝑔 + 𝑦𝑠𝑏 = 𝑦𝑠𝑠 + 𝑦𝑑𝑠 + 𝑦𝑔𝑠 + 𝑦𝑏𝑠 = 0
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
Working as in the case of capacitance parameters, we obtain:
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𝐼𝑑 = 𝑦𝑑𝑑𝑉𝑑𝑠 + 𝑦𝑑𝑔𝑉𝑔𝑠 + 𝑦𝑑𝑏𝑉𝑏𝑠
𝐼𝑔 = 𝑦𝑔𝑑𝑉𝑑𝑠 + 𝑦𝑔𝑔𝑉𝑔𝑠 + 𝑦𝑔𝑏𝑉𝑏𝑠
𝐼𝑏 = 𝑦𝑏𝑑𝑉𝑑𝑠 + 𝑦𝑏𝑔𝑉𝑔𝑠 + 𝑦𝑏𝑏𝑉𝑏𝑠
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
and, keeping three independent equations:
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𝑦𝑚 = 𝑦𝑑𝑔 − 𝑦𝑔𝑑
𝑦𝑚𝑏 = 𝑦𝑑𝑏 − 𝑦𝑏𝑑
𝑦𝑚𝑥 = 𝑦𝑏𝑔 − 𝑦𝑔𝑏
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011
Completely general!
𝐼𝑔
−𝑦𝑔𝑠 −𝑦𝑔𝑑 𝑦𝑚𝑉𝑔𝑠
−𝑦𝑠𝑑
𝑦𝑚𝑏𝑉𝑏𝑠
𝐼𝑑
−𝑦𝑏𝑠 𝑦𝑚𝑥𝑉𝑔𝑏 −𝑦𝑔𝑏 −𝑦𝑏𝑑
𝐼𝑏
𝐼𝑑 = −𝑦𝑔𝑑𝑉𝑑𝑔 − 𝑦𝑠𝑑𝑉𝑑𝑠 − 𝑦𝑏𝑑𝑉𝑏𝑑 + 𝑦𝑚𝑉𝑔𝑠 + 𝑦𝑚𝑏𝑉𝑏𝑠
𝐼𝑔 = −𝑦𝑔𝑑𝑉𝑔𝑑 − 𝑦𝑔𝑏𝑉𝑔𝑏 − 𝑦𝑔𝑠𝑉𝑔𝑠
𝐼𝑏 = −𝑦𝑏𝑑𝑉𝑏𝑑 − 𝑦𝑔𝑏𝑉𝑏𝑔 + 𝑦𝑚𝑥𝑉𝑔𝑏 + 𝑦𝑏𝑠𝑉𝑏𝑠
Transformation of the above equations results in:
Based on Tsividis/McAndrew; Copyright © Oxford University Press, 2011 12
Compare to our complete quasi-static model:
𝑖𝑔
𝐶𝑔𝑠 𝐶𝑚
𝑑𝑣𝑔𝑠
𝑑𝑡
𝑔𝑚𝑣𝑔𝑠
𝑔𝑠𝑑
𝐶𝑔𝑑
𝑖𝑠 𝑖𝑑 𝐶𝑔𝑏 𝐶𝑠𝑑
𝑔𝑚𝑏𝑣𝑏𝑠
𝐶𝑚𝑏
𝑑𝑣𝑏𝑠
𝑑𝑡
𝐶𝑚𝑥
𝑑𝑣𝑔𝑏
𝑑𝑡 𝐶𝑏𝑠 𝐶𝑏𝑑
𝑖𝑏
𝐼𝑔
−𝑦𝑔𝑠 −𝑦𝑔𝑑 𝑦𝑚𝑉𝑔𝑠
−𝑦𝑠𝑑
𝑦𝑚𝑏𝑉𝑏𝑠
𝐼𝑑
−𝑦𝑏𝑠 𝑦𝑚𝑥𝑉𝑔𝑏 −𝑦𝑔𝑏 −𝑦𝑏𝑑
𝐼𝑏
