weak inversion in analog and digital circuits - Lund Institute of ...

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