Help me solve this cascode problem!

Discussion in 'Homework Help' started by daviddeakin, Oct 17, 2013.

  1. daviddeakin

    Thread Starter Active Member

    Aug 6, 2009
    207
    27
    I thought I'd post this n the homework section as it's more likely to get an answer here, although I haven't been in school for quite a while!

    I want to find the output noise current of a cascode, using the attached equivalent circuit. The problem is to find i in terms of i2, i4 and gm. But I end up going in a circle! Where am I going wrong?

    My solution:
    i = i1 + i2 + gm.V

    But:
    V = -i3.R2 = -(i-i4)R2 = (i4-i).R2

    Substituting this into the previous expression:
    i = i1 + i2 + gm.(i4-i).R2

    But:
    i1 = i - i2 - gm.V = i - i2 - gm.(i4-i).R2

    Substituting this into the previous expression:
    i = i - i2 - gm.(i4-i).R2 + i2 + gm.(i4-i).R2

    Hence:
    i = i
    :eek:
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    You need another independent equation that relates i, i1, R1 & R3 to the control voltage V.
     
    daviddeakin likes this.
  3. daviddeakin

    Thread Starter Active Member

    Aug 6, 2009
    207
    27
    AhA! So using:

    V = (i4-i).R2 = i.R3 + i1.R1

    But: i1 = i - i2 - gm.V = i - i2 - gm.(i4-i).R2..........................1

    Hence: V = i.R3 + (i - i2 - gm.(i4-i).R2).R1............................2


    Solution:
    i = i1 + i2 + gm.V

    Sub in 2:
    i = i1 + i2 + gm.(i.R3 + (i - i2 - gm.(i4-i).R2).R1)

    Sub in 1:
    i = (i - i2 - gm.(i4-i).R2) + i2 + gm.(i.R3 + (i - i2 - gm.(i4-i).R2).R1)

    Hence:
    i = [R2.i4 + R1.i2 + gm(R1.R2.i4)] / [R1 + R2 + R3 + gm(R1.R2)]

    :D
     
  4. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    Yep - looks correct.
     
Loading...