Middlebrook extra element theorem

1. Middlebrook extra element theorem

I am going through Middlebrook and Voperians work on the extra element theorem. I succeed to prove the extra element theorem with Z open, Z short, gm-->0 (dependent current source), A-->0 (dependent voltage source).

What I can't seem to figure out is how to prove the EET for dependent sources with gm --> infinity or A--> infinity. Does anyone have a proof?

For reference the EET for dependent sources with gm -->∞ and A -->∞ is:

H(s) = (H|gm=inf) * (1 + ( 1/(gm*Tn) ) / (1 + (1/(gm*Td) )

or

H(s) = (H|A=inf) * (1 + (1/(A*Tn) ) / (1 + (1/(A*Td) )

Edit: I used the following reference from R W Erickson site which shows how the EET is proved. But it is only for impedance. Would be great if someone can outline a similar proof for dependent sources with gain set to infinity: •

2. Re: Middlebrook extra element theorem

Anyone familiar with Middlebrook EET and NEET techniques? Would be great to get a discussion on these going.. --[[ ]]--