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This is a practice problem in deriving the transition frequency function for mos and part of the set of questions is to determine the pole and zero frequency expression but this transfer function i derived is kinda different from what i'm used to from the previous lectures. I usually see this form: enter image description here

But my derived transfer function looks a little different.

enter image description here

Could somebody guide me how to derive them?

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  • \$\begingroup\$ By reading your i_0/i_i expression I though that gap between C_g d and C_g s meant they were different variables/parameters and read it as \$ G(s) = \frac{g_m -s C_g d}{s(C_g s+C_g d)} \$ \$\endgroup\$
    – jDAQ
    Dec 12, 2020 at 6:26
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    \$\begingroup\$ Factor out the coefficients of \$s\$. For example, \$C_g\$ in the denominator. \$\endgroup\$
    – AJN
    Dec 12, 2020 at 7:05
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    \$\begingroup\$ If you're referring to the s term in the denominator, let \$P_1=0\$ \$\endgroup\$
    – Chu
    Dec 12, 2020 at 7:59
  • \$\begingroup\$ @jDAQ sorry about that, my handwriting does suck \$\endgroup\$
    – user266967
    Dec 12, 2020 at 8:52

1 Answer 1

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If you look closely in the generic transfer function, the \$s\$ operator is single, everywhere, and there is a gain parameter. So try to isolate those from your t.f.:

$$\begin{align} \dfrac{g_m-sC_{gd}}{s(C_{gs}+C_{gd})}=\dfrac{-C_{gd}\left(s-\dfrac{g_m}{C_{gd}}\right)}{(C_{gd}+C_{gs})\left(s-\dfrac{0}{C_{gd}+C_{gs}}\right)}=-\dfrac{C_{gd}}{C_{gd}+C_{gs}}\dfrac{s-\dfrac{g_m}{C_{gd}}}{s-0} \end{align}$$

Which is a pure integrator -- that makes sense, since you have no resistive elements, only capacitors and a current source. Notice the denominator now shows the zero valued pole (as mentioned by Chu).

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  • \$\begingroup\$ whats a zero valued pole and how does it relate to an integrator? Is that the same as a pole at the origin? \$\endgroup\$
    – user266967
    Dec 12, 2020 at 9:54
  • \$\begingroup\$ Yes. Pole at origin. \$\endgroup\$
    – AJN
    Dec 12, 2020 at 11:25
  • \$\begingroup\$ Is it right that the zero frequency = -Cgd/gm and the pole frequency = Cgd + Cgs? Because we had a graded exercise based on this and when i used zero freq to be -Cgd/gm, i got it wrong, also pole freq = 1/Cgd+Cgs is also wring which i dont understand. \$\endgroup\$
    – user266967
    Dec 12, 2020 at 13:03
  • \$\begingroup\$ @Rein Try to compare the last part of the formula above with your generic transfer function: \$\small{A}\frac{s-z}{s-p}\$. What similarities do you see? Which one can be \$z\$, which one \$p\$, and which one \$A\$? \$\endgroup\$ Dec 13, 2020 at 9:17
  • \$\begingroup\$ Thanks Chu! I actually figured things out and got perfect scores! \$\endgroup\$
    – user266967
    Dec 14, 2020 at 5:17

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