How can I find the Vm of a pseudo nmos inverter? Since I dont know the Vds of neither of my transistors I cant determine in which region they are.
The circuit and some parameters are in that link. Wn = 9u is missing there tho.
EDIT1:
LTSpice Netlist
M1 N002 N003 0 0 T15DN l=0.6u w=9u
M2 N001 0 N002 N001 T15DP l=0.6u w=3u
V1 N001 0 5V
V2 N003 0 5V
.model NMOS NMOS
.model PMOS PMOS
.lib C:\PROGRA~2\LTC\LTSPIC~1\lib\cmp\standard.mos
.include T15D_models.txt
.dc V2 5 0 0.1
.backanno
.end
T15D_models.txt
.MODEL T15DN NMOS LEVEL=3 PHI=0.7 TOX=9.5E-09 XJ=0.2U TPG=1
+ VTO=0.7 DELTA=8.8E-01 LD=5E-08 KP=1.56E-04
+ UO=420 THETA=2.3E-01 RSH=2.0E+00 GAMMA=0.62
+ NSUB=1.40E+17 NFS=7.20E+11 VMAX=1.8E+05 ETA=2.125E-02
+ KAPPA=1E-01 CGDO=3.0E-10 CGSO=3.0E-10
+ CGBO=4.5E-10 CJ=5.50E-04 MJ=0.6 CJSW=3E-10
+ MJSW=0.35 PB=1.1
.MODEL T15DP PMOS LEVEL=3 PHI=0.7 TOX=9.5E-09 XJ=0.2U TPG=-1
+ VTO=-0.95 DELTA=2.5E-01 LD=7E-08 KP=4.8E-05
+ UO=130 THETA=2.0E-01 RSH=2.5E+00 GAMMA=0.52
+ NSUB=1.0E+17 NFS=6.50E+11 VMAX=3.0E+05 ETA=2.5E-02
+ KAPPA=8.0E+00 CGDO=3.5E-10 CGSO=3.5E-10
+ CGBO=4.5E-10 CJ=9.50E-04 MJ=0.5 CJSW=2E-10
+ MJSW=0.25 PB=1
Best Answer
If we are looking for the voltage where Vin=Vout we can first assume (but we don't know it for sure) that MP is in the linear region. So we take the equation for the linear region (which I'm too lazy to type in) and set Vds to (5V-Vin) and Vgs to 5V.
Then we look at MN, since Vin=Vout it will be in saturation. Therefore we use the equation for saturation. We set Vgs to Vin.
Since the drain current for both transistors is the same, we can equate the two expressions and solve for Vin.
In a final step we check our assumption, that MP is indeed in linear region.
Update:
If you want your hand calculation to match with your simulation you have to use a simpler model.
The text in blue is my "hand calculation" and it agrees perfectly.
Please note that due to the condition Vin = Vout I am allowed to connect the output to the input.