how to find the Rin of the self-bias cascode current-mirror

HI, all guys

how to find the Rin of the self-bias cascode current-mirror from the negative viewpoint?
it is just the Figure5.4-4 in ALLEN's book, and there is a sentence like this "duo to negative feedback ,the equivalent input resistance is approximately r+1/gm."

hope for ur reply!

Re: how to find the Rin of the self-bias cascode current-mir

Hi,
I dont have allens book but i'll try to explain the -ve feedback conceept. if we assume that the o/p voltage of the cascode (drain of CG(common gate) MOS) is raised, then due to finite o/p resistance of the MOS, current would increase. This would inturn increase the drain voltage of the CS MOS. this would decrease the overdrive of the CG MOS hence effectively bringing back the o/p current to its original value. This can be viewed as a -ve feedback due to drop across the DS of the bottom transistor of the cascode.
bye

Re: how to find the Rin of the self-bias cascode current-mir

dear timer,
i can't follow you. it is the Figure, could you tell it again?
why can't the picture display correctly? who can tell me why? thanks advanced!

Re: how to find the Rin of the self-bias cascode current-mir

Hi wanily1983,

Thanks for putting up the ckt.
Now let us consider that node 1 was grounded. looking in from 1, we would only see a resistor. If we increase node 1 by V volts, I into node 1 would increase by V/r.

Now in the ckt. you have put up, if we increase V, the overdrive of the top MOS (on left side) will increase hence increasing the current. This current also flows thru bottom transistor. Now to sustain higher current the overdrive of bottom transistor has to increase by (delta I)/gm. this increases the voltage of the bottom side of the resistor r. Hence the test current injected into node 1 decreases. This can be viewed as a -ve feedback. bottom node 2 of r is tracking voltage on top. Hence i/p resistance is r plus the extra (1/gm) due to this feedback.

bye

Re: how to find the Rin of the self-bias cascode current-mir

hi, timer
could Rin calculate used with feedback theory? assume the node 2 is output node, then we can regard R as a thunt-thunt feedback resistance. then analysis this circuit use the classic feedback theory, in the input node,connect the node 2 to ground, in the output node, connect the node 1 to ground. Rin(OPEN LOOP)=R,
the Rin(close loop)=Rin(open loop)/(1+Aloopgain), then the Rin(close loop) will smaller than R. this is contrast to the results in the ALLEN's book, what's the error in my analysis?

Re: how to find the Rin of the self-bias cascode current-mir

hi ,
Rin = R +( (gm3*rds3)*rds1 + 1/gm) ~ R + 1/gm
hope I am clear.
have a nice day!

Re: how to find the Rin of the self-bias cascode current-mir

hi, jps
you said "Rin = R +( (gm3*rds3)*rds1 + 1/gm) ~ R + 1/gm ", but (gm3*rds3)*rds1>>R(or 1/gm), can you explain this?

Re: how to find the Rin of the self-bias cascode current-mir

hi wanily,
sorry, i have made a mistake in my post. Replace "Now let us consider that node 1 was grounded" by "Now let us consider that node 2 was grounded". I dont know how you could possibly use classical feedback theory. Its easier to write down the small signal model and get the resistance. for an intuitive feel, the explanation i've given might be quite ok.

hi jps,
about that formula you have posted, something seems wrong. If we neglect CLM assume rds is infinty, then according to your formula, the resistance would go to infinty which is not true.

hi, timer
i know it is easy to calculate Rin using small-signal analysis, but what puzzled me is why i can't use the feedback theory to calculate it?

i think it can regard as a typical negative feedback circuit then analyze it.