Help in deriving Zin small-signal expression

[Wimberleytech]

Is it possible to derive the absolute numerical value of lambda(λ) from the mosfet model files ? Could anyone show how to do so ?

Do you mean: run a simulation of a mosfet using the model file and from the results, calculate lambda?  Yes you can get an approximation at an operating point.  Not sure that is what you are asking, however.  If not, ask again in a different way.

BTW, unless it is a homework problem, trying to get the "exact" value of lambda (CLM parameter) is a useless exercise.

Alternatively, could I just use https://github.com/imr/ngspice/blob/master/examples/xspice/table/modelcards/modelcard.nmos#L38 directly ?

The lambda in that model is NOT the "channel length modulation" parameter.

Besides, what does  TOXE = 1.8E-009  actually give ?  1.8*10^(-9) ? I asked this because I saw  LC = 5E-9  in the same file

yes,  1.8E-009  is   1.8*10^(-9)

[promach]

How do we obtain the channel length modulation parameter, lambda from https://github.com/imr/ngspice/blob/master/examples/xspice/table/modelcards/modelcard.nmos ?

The lambda in that model is NOT the "channel length modulation" parameter.

Then what is that lambda for ?

[promach]

No matter how I measure the output impedance, the result can never come any close to the following theoretical calculation. Could anyone point out if my output impedance test circuit setup is wrong ?

https://github.com/imr/ngspice/blob/master/examples/xspice/table/modelcards/modelcard.pmos

Code: [Select]

*CMOS inverter

.PARAM V_SUPPLY = 3.3
.PARAM V_OUT = 2
*.PARAM INP_FREQ = '#INP_FREQ#'
*.PARAM INP_PERIOD = '1/INP_FREQ'
*.PARAM NO_PERIODS = '4'
*.PARAM TMEAS_START = '(NO_PERIODS-1)*INP_PERIOD'
*.PARAM TMEAS_STOP = '(NO_PERIODS)*INP_PERIOD'
.PARAM AC_POINTS = 10
.PARAM AC_START = 1000
.PARAM AC_STOP = 1E6

*** *** SUPPLY VOLTAGES *** ***
VDD VDD 0 'V_SUPPLY'
VSS VSS 0 0

*** *** INPUT SIGNAL *** ***
VSIG IN VSS 0
** VSIG IN VSS AC 1 DC 'V_SUPPLY/2'

*** *** CIRCUIT UNDER TEST *** ***
MP OUT IN VDD VDD P1 W=2U L=2U
MN OUT IN VSS VSS N1 W=1U L=2U

** CL OUT VSS 3p
** RIN IN VSS 1G

CIN IN VSS 1E9
Rf OUT IN 1E9
** Lf OUT IN 1E-12
** The input can be either biased with a DC source, or a DC feedback circuit. Using a DC feedback circuit (RC, inductor, whatsoever) makes only sense if there's no DC voltage source, see [url]https://www.edaboard.com/showthread.php?377214-Noise-in-CMOS-Inverter&p=1617292&viewfull=1#post1617292[/url] 

*** *** ROUT TEST SIGNAL WITH FIXED 1A CURRENT AND VARIABLE TEST VOLTAGE (VOUT) *** ***
*VOUT VOUT 0 'V_OUT'
*** *** IOUT flows into the output of the circuit under test, so negative terminal node of this current source is OUT instead of VSS
IOUT VSS OUT AC 1

*** *** ANALYSIS *** ***
*.AC dec 'AC_POINTS' 'AC_START' 'AC_STOP'
*.TRAN 'INP_PERIOD/1000' 'NO_PERIODS*INP_PERIOD'
*
*.PROBE TRAN V(IN)
*.PROBE TRAN V(OUT)
.OPTION POST PROBE ACCURATE
.include modelcard.nmos
.include modelcard.pmos

.control
*AC dec 'AC_POINTS' 'AC_START' 'AC_STOP'
AC dec 10 1000 1E6

let ROUT=OUT/abs(i(VSS))
plot ROUT
print ROUT > ROUT.log
.endc

.END

[promach]

@Wimberleytech

I have solved the ASCO problems with a simple CMOS inverter.  https://github.com/promach/frequency_trap/tree/development/optimization/inv

Now I am coming back to solve the ASCO optimization for output impedance of asymmetric differential pair.

1. How should I set the DC operating points for this asymmetric differential amplifier pair ?
2. For DC analysis, should I connect the IN and OUT to a feedback circuit which is the CMOS inverter in this case ?
3. Do I do the same for AC simulation for output impedance after determining the DC operating points ?