ENEE 303H Fall 2009 HW2 YHC 10/08/09
1.
(a)
Since VGDn=0 < VTOn and VDGp=0 < |VTOp|
(or VDSn > VGSn-VTOn and VSDp > VSGp-|VTOp|)
Besides, if VGSn > VTOn and VSGp > |VTOp|,
then MOSFETs will work in saturation region.
Since VDD > 2|VTOp|> 0, so VDD-VSS=2VDD=VSGp+VGSn > 4|VTOp|,
and from the symmetry property of this circuit, we know
that this requirement should be satisfied.
(b)
Assume MOSFETs work in saturation region,
Vout=VDD-VSGp=-VDD+VGSn
IDp =(KPp/2)*(Wp/Lp)*(VDD-Vout-|VTOp|)^2
IDn =(KPn/2)*(Wn/Ln)*(VDD+Vout-VTOn)^2
because the currents which flow into gates are zero,
so IDp=IDn
and let x=sqrt((KPp*Wp/Lp)/(KPn*Wn/Ln))= 1.07
Vout=(VDD*(x-1)-|VTOp|*x+VTOn)/(1+x)=0.0337*VDD-0.147(V)
(which is close to 0)
Example: if VDD=5 V, then Vout=21(mV)
check:
VGSn=VDD+Vout=5.02(V) > VTOn,
VSGp=VDD-Vout=4.98(V) > |VTOp|,
so MOSFETs indeed work in saturation region.
(c)IDn =(KPn/2)*(Wn/Ln)*(VDD+Vout-VTOn)^2=
184.86(uA/V^2)*(1.0337*VDD-1.447)^2 (A)
(d)since the gates and sources of M3 and M1 are tied
together, respectively, to get the same drain current as
M1, just make sure M3 works in saturation region.
VDS3>=VGS-VTOn (note that lambda is assumed to be 0),
so VD>=Vout-VTOn=0.0337*VDD-1.447 (V)
For example, VD can be equal to Vout in this problem.
Spice:
VDD
M2
M4007P
5Vdc
M3
VD
out
0.021Vdc
M4007N
0
VSS
-5Vdc
M1
0
M4007N
NAME
MODEL
ID
VGS
VDS
M_M3
M4007N
2.56E-03
5.02E+00
5.02E+00
M_M1
M4007N
2.56E-03
5.02E+00
5.02E+00
M_M2
M4007P
-2.56E-03 (A)
-4.98E+00 (V)
-4.98E+00 (V)
2.
(a)
VCC1
U2 7
3
0Vdc
Vd
+
10Vdc
V+
OS2
5
6
OUT
2
-
4
uA741
0
out
1
OS1
V-
0
10Vdc
VEE1
0
10V
5V
0V
-5V
-10V
-10V
V(U2:OUT)
-8V
-6V
-4V
-2V
0V
2V
4V
6V
V_Vd
Magnitudes of saturation values are very close to but
smaller than VCC (here VEE=-VCC).
(b)Vd=V+-V-=V+-Vin=Vout*R1/(R1+R2)-Vin, so
Vout=(Vd+Vin)*(1+R2/R1)
8V
10V
Vin increases
15V
10V
5V
0V
-5V
-10V
-15V
-10V
V(U2:OUT)
-8V
-6V
3 * V(Vd:+) + V(VCC1:+)
-4V
-2V
3 * V(Vd:+) - V(VCC1:+)
0V
3 * V(Vd:+)
V_Vd
2V
4V
6V
8V
10V
slope of load line =(1+R2/R1)
(c)(d)
R2
10k
R1
10k
VCC
U1 7
3
+
0
V+
OS2
OUT
2
Vin
-
uA741
4
OS1
V-
10Vdc
5
6
1
0
10Vdc
0
VEE
0
4.907V
0V
-10.00V
0V
10V
5V
0V
-5V
-10V
0s
V(U1:OUT)
2ms
V(Vin:+)
4ms
6ms
8ms
10ms
12ms
14ms
16ms
Time
10V
5V
0V
-5V
-10V
-10V
V(U1:OUT)
-8V
-6V
-4V
-2V
0V
2V
4V
V(Vin:+)
|saturation values|~=VCC=10(V)
width~=2*|saturation values|*(R1/(R1+R2)~=10(V)
6V
8V
10V