Calculate impedance of a feedback circuit with Blackman's technique

[LvW]

I must admit that - up to now - I didn`t need Blackman`s theorem. So, I took this opportunity to become familiar with it.
If somebody is still interested to see how it woks for the present task, here is the solution:

The impedance Z between two points of a feedback system is:
Z=ZD(1+Tsc)/(1+Toc)
with ZD=Impedance between both points without feedback , and
Tsc=Loop gain magnitude with a short across the selcted points; Toc=Loop gain magnitude with an open circuit across both points.

For the present case: We need the resistance between the pos. opamp input (point 1) and ground (point 2).

Therefore: ZD=R and
Tsc=0 because A=0 (both opamp input terminals at ground potential) and |Toc|=A*0.1*gm*R.

This gives

Z=R*(1+0)/(1+A*0.1*gm*R)=R/(1+A*0.1*gm*R)
(confirmed by symbolic analyzer, see my previous post)

 

[rude man]

I must admit that - up to now - I didn`t need Blackman`s theorem. So, I took this opportunity to become familiar with it.
If somebody is still interested to see how it woks for the present task, here is the solution:

The impedance Z between two points of a feedback system is:
Z=ZD(1+Tsc)/(1+Toc)
with ZD=Impedance between both points without feedback , and
Tsc=Loop gain magnitude with a short across the selcted points; Toc=Loop gain magnitude with an open circuit across both points.

For the present case: We need the resistance between the pos. opamp input (point 1) and ground (point 2).

Therefore: ZD=R and
Tsc=0 because A=0 (both opamp input terminals at ground potential) and |Toc|=A*0.1*gm*R.

This gives

Z=R*(1+0)/(1+A*0.1*gm*R)=R/(1+A*0.1*gm*R)
(confirmed by symbolic analyzer, see my previous post)

Thanks for your research! Only thing I would point out is that g_m is a strong function of V_gs = 0.1AV where V is the quiescent + amp input voltage ("point 1"). So the operating point of the circuit still has to be solved for, then g_m = 2k(0.1AV - V_T) can be determined. Of course, you'd need k also.

 

[LvW]

Yes, of course. My calculation (blindly) assumes an operating point in the linear FET region.

 

[rude man]

Yes, of course. My calculation (blindly) assumes an operating point in the linear FET region.

OK. Now you'd be subject to V_ds modulation but I'd say enough of this, thanks for enlightening us all on the (in?)famous Blackman method!
r m

 

[The Electrician]

Waxterzz, are you going to try get a result with the Vtest/Itest method?

 

[NascentOxygen]

This has been a fine, collaborative effort. Well done, all contributors!

 

[LvW]

Yes - and caused by an interesting question from the OP (forcing us - includiung me - to remember and apply Blackmans rule).

 

[rude man]

Yes - and caused by an interesting question from the OP (forcing us - includiung me - to remember and apply Blackmans rule).

@ LvW - just as a final note - the fact that the upper FET can operate as a cascode connection (by suitably setting its gate bias) you can indeed operate the lower FET in the linear mode while keeping Vds essentially constant - meaning your assumption of operating in the linear mode while keeping g_m constant, is fully validated.
Over and out!
rm

 

[LvW]

rude man - thank you for this final remark.