CMOS Small signal model: Rout calculation

cmos small signal model

Hi,

Can anyone explain me how Rout is calculated for the circuit shown in the attached figure (circuit.jpg).

I have the solution (answer.jpg); but want to know how it is calculated.

Thanks in anticipation.
Cheers,

Kiran

rout + cmos

For calculating the output resistance, all inputs and DC bias sources are deactivated (replaced by short circuit if voltages ).This would cause a short between the gate and source of M1 (at small signal analysis) so it would be replaced by rds1 .For M2 both its gate and bulk are connected to ground so the upper 2 current sources can be considered as one current source = gm(1+n)vgs where n=gmb/gm .
vgs would be equal to -Iout*rds1 .Applying KVL : vout=Iout *rds1+(Iout-gm(1+n)*(-Iout*rds1))*rds2 = Iout*(rds1+(1+gm(1+n)*rds1)*rds2)
= Iout*(rds1+rds2+gm(1+n)rds1*rds2) ,Rout=vout/Iout .

cmos rout

Hi,

Thank you for your quick response.
You have made it soo simple to understand.

I am new to edaboard.Am not sure if i can continue a new question with the same Subject line.

My question: "How do one make a choice between Large Signal Analysis & Small signal analysis and what are their practical usage"

Thanks & Best Regards,

Kiran Kumar S.

cmos small signal model rout

Small signal analysis ,as its name implies, is used for input signals of very small amplitudes .It is based mainly on dividing voltages and currents into bias voltages and currents and small signal ones .Then, equations of transistors are linearized (expanding the equations into polynomials and considering only the first order terms and neglecting higher powers) thus the linearized model is achieved (the one containing the voltage controlled current source gm*vgs) .For this solution to be valid ,higher power terms should be very small considered to the linear term, else non linearity occurs and harmonics of the signal may get significant .
Large signal solution is used for signals of large amplitude specially when it causes your transistor to go from certain mode of operation to another (e.g: saturation to triode or cutoff) .A very famous case is calculating the slew rate of an amplifier .
For more details ,you can refer to "design of analog CMOS integrated circuits "by Razavi, chapters 9(p326) and 13 .

cmos small signal analysis

Hi,

Thank you for your response.

Will go through the book by Razavi and revert for any clarifications.

Best Regards,

Kiran