Differential gain of 3-stage amp

[perplexabot]

Homework Statement

Find the differential gain int terms of small signal parameters of the attached image.

Homework Equations

I don't think we need any equations. Just some basic mosfet knowledge.
Not going to draw the small signal circuit, because it would take a long time.

The Attempt at a Solution

My attempt at the question is attached along with the schematic. When comparing my answer to
the answer in the solutions, I am missing a factor of (1+gm(ro6 || ro7))^-1
Where || means "in parallel." I am really close but it looks like I am missing a critical part. Thank you for your help.

 

[NascentOxygen]

Hi perplexabot. Do you not have image software that will allow you to rotate images so they are the right way up? My monitor is light enough for me to rotate it by 90 degrees, but quite precarious to balance in that state.

 

[perplexabot]

Hi perplexabot. Do you not have image software that will allow you to rotate images so they are the right way up? My monitor is light enough for me to rotate it by 90 degrees, but quite precarious to balance in that state.

Hey, I am sorry about that, I am using my sisters Mac, and I have no idea how to use it. Can you not rotate it yourself?

EDIT: For some reason, after rotating it on my sisters mac and saving it. It still will not upload correctly. I apologize for the inconvenience.

 

[NascentOxygen]

 

[perplexabot]

Hahahahaha. Thanks for that NascentOxygen.
My friend was kind enough to point out my problem. Turns out the third stage's (class A output stage) output resistance is not ro7 || ro6, this is due to the fact tha Vgs of M6 is not zero, so the dependent current source in the small signal hybrid pi model conducts current, hence I needed to take that into account when calculating output resistance. That is where the extra factor comes in.

Thank you.