Low Voltage current source Analysis

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ccw27

Full Member level 5
symbolic circuit solver

Anyone tried to solve the output impedance of this low voltage tail current source?
https://amesp02.tamu.edu/~sanchez/pubs/LV-Tail-Current.pdf

I tried using Blackman's formula but did not have much success. Any suggestion on how to go about it will be appreciated.

Thanks

ccw27

Full Member level 5
This is what I got using Blackmans formula:

Rout(a=0)=ro2
Rout(short)=-A*gm1*(ro1||RoB)
Rout(open)=-A(gm1*(ro1||RoB)-gm2*ro2)

Rout=Rout(a=0) [1+Rout(short)]/[1+Rout(open)]
Rout=ro2*[1-A*gm1*(ro1||RoB)]/[1-A(gm1*(ro1||RoB)-gm2*ro2)]

Actually I believe the expression is somewhat the same if you simplify it, maybe there is a sign error somewhere.

Full Member level 6
I made an approx. analysis and found it to be almost:

A*Rob

I am not quite sure this is correct though.

venkateshr

Member level 3
I think it is -Rob.

a negative resistance ckt. i didnt use any blackman's theorm or other thing. strgtfwd analysis.anyway thanks for the good ckt.

there is small correction . resistance is Ro1 || -Rob . i forgot the o/p imp of the mos.

pixel

Very useful circuit, whoose idea is to make equal Vds voltages of two pmos, which results in ideal current matching. Amplifier is just used to set DC voltage gate voltage of current current mirror gate. So I see this circuit like ideally matched current mirror.
If you want to calculate resistance you can to put at node X Itest current generator and find Vx (R=Vx/Ix). If A is high, negative feedback makes that Vtest=V+=V-. As a result of matching, both pmos will have same current, and output resistances, and through RoB will also flow current Ix, which makes V-=-RoB*Ix.
Then Rout=-RoB.
In the case of finite amplifier gain, I have used symbolic circuit solver Syrup for Maple.
Rout=-ro*(ro+RoB+A*gm*ro*RoB)/(gm*ro^2*A-ro-RoB)

pixel

You have two feedback loops (one positive and one negative), and I think that Blackman theorem can not help you.

ccw27

Points: 2

venkateshr

Member level 3
can you please tell me waht that blackman's theorem is ? I am very curious to know that.

ccw27

Full Member level 5
Just check Gray Meyer book

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