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 />
With bipolar transistors:<br />
+<br />
+<br />
I i<br />
V BEi<br />
[15]<br />
+ <strong>and</strong> - directions <strong>of</strong> BEi (any sequence)<br />
∑V BEi = ∑V BEi<br />
with: VBEi = UT ln I +<br />
i<br />
Isi ∏I i ∏I si<br />
+<br />
=<br />
+<br />
+<br />
+<br />
∏I i ∏I si<br />
+<br />
= λ<br />
TRANSLINEAR CIRCUITS<br />
With MOS transistors <strong>in</strong> <strong>weak</strong> <strong><strong>in</strong>version</strong>:<br />
∑(VGi - VSi ) = ∑(VGi - VSi )<br />
+<br />
V Gi<br />
n<br />
with:<br />
-V Si = U T ln I i<br />
I D0i<br />
CSEM, E. Vittoz, 2003<br />
V Gi<br />
I i -1<br />
I i<br />
V Si<br />
common substrate<br />
• Otherwise: separate wells connected to<br />
sources to impose V Si = 0<br />
• Precision degraded by VT0 mismatch<br />
page 18<br />
[16,17]<br />
• If + <strong>and</strong> - are alternated then: pairs <strong>of</strong> equal<br />
VGi both sides <strong>of</strong> equation:<br />
V Gi ⇒ V Gi /n for each pair,<br />
<strong>and</strong> then