File: g:/coursesS11/303/final_home_sols.doc RWN 05/16/11
a) For 1mA, VGS  VTOn  IT/β where β  KP W ; VGS=1.3+2.3258 = 3.626
2 L
for 4007N which when referenced to ground gives the gate voltage of -1.374
b) Set IT=IDMn1+IDMn2 for both Mn1 & Mn2 in saturation. This gives
IT/β  (Vi  Vout  VTOn) 2  (Vdd  Vout  VTOn) 2
n
This is an ellipse but only a portion of it is valid for the transistors in saturation.
Squaring gives a quadratic equation for Vout-VTOn with Vi as a parameter; the
solution requires the choice of minus sign as seen by choosing Vi=0.
The solution is:
Vout(Vi)  VTOn  ( 1 )(Vi  Vdd)  ( 1 ) (2 IT )  (Vdd  Vi) 2
2
2
β
n
Valid when Mn1 is in saturation, Vioff=2.674<Vi<Visat=4.152
c) Mathcad plot of Vout for the calculated saturation region using 4007 parameters.
1.7
1.66
1.62
1.58
1.54
Vout ( Vi) 1.5
1.46
1.42
1.38
1.34
1.3
2.67 2.82 2.97 3.12 3.27 3.41 3.56 3.71 3.86
Vi
d) PSpice circuit
4
4.15
dd
M4007P
Vdd
Mp
5Vdc
Mn1
0
Mn2
in
Vi
M4007N
M4007N
out
tail
0Vdc
-5Vdc
Vss
0
MT
gate
VG
M4007N
ss
-1.374Vdc
0
PSpice runs:
Vout versus Vi
1.8V
1.7V
Input transistor calculated: off below Vioff = 2.674, saturated above Visat = 4.152;
1.6V
1.5V
1.4V
1.3V
-5.0V
V(OUT)
-4.0V
-3.0V
-2.0V
-1.0V
0.0V
1.0V
2.0V
3.0V
4.0V
5.0V
V_Vi
For the input transistor, Mn1, the left portion of the following top curve is VDS, the
bottom is VGS-VTO and the middle is Vout. Here Mn1 is calculated to be in saturation
from Vioff = 2.674 to Visat = 4.152 but seen from the curve to go up to
Visat_Spice=3.87
4.0V
2.0V
0V
below Vi = 4, for Vi top curve =VDS, bottom curve =VGS-VTOn
-2.0V
-4.0V
-6.0V
-8.0V
-5.0V
V(OUT)
-4.0V
-3.0V
-2.0V
V(Mn1:d)-V(Mn1:s)
V(in)-V(OUT)-1.3
-1.0V
0.0V
1.0V
2.0V
3.0V
4.0V
5.0V
V_Vi
For tail current, top = VDS, bottom = VGS-VTO showing MT stays in saturation
7.0V
6.0V
For Itail, top = VDS, bottom = VGS-VTO
5.0V
4.0V
3.0V
2.0V
-5.0V
-4.0V
V(gate)-V(ss)-1.3
-3.0V
V(OUT)-V(ss)
-2.0V
-1.0V
0.0V
1.0V
2.0V
3.0V
4.0V
5.0V
V_Vi
PSpice plot showing Vout within the saturation region of Mn1
1.7V
1.6V
1.5V
1.4V
1.3V
2.7V
2.8V
V(OUT)
3.0V
3.2V
3.4V
3.6V
3.8V
4.0V
4.1V
V_Vi
f) Comparing the PSpice run with the calculation we see that the turn on voltage Vioff is
about the same but that the transition voltage has a small difference undoubtedly due to
the Early effect since the 4007 models are level one (for which the equations used are
valid)
2.5V
2.0V
<-- VDS
1.5V
1.0V
<-- VGS-VTOn
0.5V
0V
-0.5V
2.6V
2.8V
3.0V
V(Mn1:d)-V(Mn1:s)
V(in)-V(OUT)-1.3
3.2V
3.4V
V_Vi
3.6V
3.8V
4.0V