weak inversion in analog and digital circuits - Lund Institute of ...
weak inversion in analog and digital circuits - Lund Institute of ...
weak inversion in analog and digital circuits - Lund Institute of ...
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Weak <strong><strong>in</strong>version</strong><br />
CONTINUOUS MODELS WEAK-STRONG INVERSION<br />
a. From charge analysis [7,8]:<br />
V P -V S,D<br />
U T<br />
b. Interpolation formula:<br />
IF , R<br />
= 1 + 4<br />
I<br />
-1<br />
S<br />
I F , R<br />
I S<br />
CSEM, E. Vittoz, 2003<br />
+ln<br />
IF , R<br />
1 + 4<br />
I<br />
-1<br />
S<br />
cannot be <strong>in</strong>verted to express I F , R (V P ,V S,D )<br />
VP -VS,D = ln<br />
2UT 2 (1 + e )<br />
Both converge asymptotically towards:<br />
I F , R<br />
I S<br />
I F , R<br />
I S<br />
VP -VS,D = e U for VP -VS,D «UT (<strong>weak</strong> <strong><strong>in</strong>version</strong>)<br />
T<br />
⎛<br />
= ⎝<br />
V P -V S,D<br />
2U T<br />
⎛<br />
⎝<br />
2<br />
for V P -V S,D »U T (strong <strong><strong>in</strong>version</strong>)<br />
2<br />
page 8<br />
• Only 3 parameters: V T0 , n (<strong>in</strong>side V P ) <strong>and</strong> I S (or β) to model the current<br />
from <strong>weak</strong> to strong <strong><strong>in</strong>version</strong>.<br />
[9]
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