common Gate Amplifier Problem

[MahmoudHassan]

Hello
while i was solving problems in Common gate amplifier i found this one
Figure 1 is the problem
Figure 2,3 my solution and small signal model
Figure 4 is the solution manual solution

i doubt that solution manual is not correct because it is supposed that all capacitors must be shorted (i.e as the problem that capacitors are very large) which will simplify the problem too much

i hope you can help me to know what is wrong with my analysis and why solution manual solved it like that
Thanks



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[erikl]

I think your result is not correct, Mahmoud, sorry!

It neglects the relatively low input impedance at the source of this common-gate stage, which is in parallel to R4 and might be comparably lower than this, and the output resistance Ro of M1, as well as the parallel (to RD) load resistors R2 and R3, which are connected to a virtual GND.

Your gain result is in accordance with that one of a common-source stage (at least to 1^st order), and - by this - much too large for a common-gate stage.

At least I think so. I didn't retrace the solution manual solution, however.

 

[MahmoudHassan]

I think your result is not correct, Mahmoud, sorry!

It neglects the relatively low input impedance at the source of this common-gate stage, which is in parallel to R4 and might be comparably lower than this, and the output resistance Ro of M1, as well as the parallel (to RD) load resistors R2 and R3, which are connected to a virtual GND.

Your gain result is in accordance with that one of a common-source stage (at least to 1^st order), and - by this - much too large for a common-gate stage.

At least I think so. I didn't retrace the solution manual solution, however.

first of all thanks a lot for your reply and time really appreciated
i didn't get it i hope you can help me as The problem stated that capacitors are very large which i have to make them short circuits in small signal model , but in solution manual solved as open circuit !!!!
and also what do you mean by " (at least to 1st order) " i didn't get it ?

 

[erikl]

... also what do you mean by " (at least to 1st order) " i didn't get it ?

Means approximately

Can't help you for the rest, sorry!

 

[MahmoudHassan]

Means approximately

Can't help you for the rest, sorry!

Thanks Erikl for your help
Actually i faced the same issue with other problems that have capacitors !
any suggestions will be really appreciated because iam now stuck at this point

 

[FvM]

The connection of R3 and R4 must be a ground node in small signal equivalent circuit, because it's shorted by a capacitor as you mentioned. Knowing this already, what's your problem?

 

[MahmoudHassan]

The connection of R3 and R4 must be a ground node in small signal equivalent circuit, because it's shorted by a capacitor as you mentioned. Knowing this already, what's your problem?

Thanks a lot for trying help me
my problem that in figures shared ,
i shared my small signal model and equations as you said capacitors shorted
but in solution manual i think you put capacitors as open circuit !!! even problem stated that capacitors are very large
i want to know from experts which solution is correct mine or solution manual for mine it is ok for solution manual why ??!

Thanks a lot trying help me really appreciated

 

[FvM]

The solution manual does connect R3 and R4 to ground, as required. I don't understand where you see open circuit.

 

[MahmoudHassan]

what i mean that the common node between R3 and R4 must be connected to ground in small signal model but in solution manual it is not connected to ground ?

 

[FvM]

I didn't clearly understand what's the solution manual diagram. Anyway, if it doesn't conect R3/R4 to ground, it's wrong.

 

[MahmoudHassan]

Thanks a lot , i was afraid that i may missing or misunderstood something
Your help is really appreciated

 

[chuckey]

Vo = Ids X ( Ro// Rd// R3//R2)
Ids = Vi/(I/gm) { R4 drops the input Z but does not change Ids}
so Vi = Ids (1/gm)
so Vo/Vi = Ids X ( Ro// Rd// R3//R2) / Ids (1/gm)
Vo/Vi = ( Ro// Rd// R3//R2) / (1/gm)
Vo/Vi = ( Ro// Rd// R3//R2) X gm
Is that correct?
Frank