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I am new to this site so I apologize if this post doesn't belong here or anything.

I am trying to solve a quadratic on Matlab. This is relating to my electrical engineering circuits course where I have to determine the drain current. All the values are given except $I_D$ and $V_S$. $V_S$ is broken up using ohms law to reduce to 1 unknown variable to be dealt with.

I want to separate the polynomial terms shown above where $I_D2$ is representing $x^2$ etc. My plan was to use the "roots([x^2, x, c])" function to determine $I_D$. Hoping for someone to help me out since there is still an unknown in the equation.

  • I'm confused, Vs is broken up using ohms law so there is only 1 variable to solve for, so I don't understand why you can't solve the polynomial? Is it possible for you to write and clearly identify which of the above formulas you are trying to solve? (Also, if you don't get a good answer here, try re-writing it real nice and posting on stack overflow) –  Nov 24 '15 at 20:31
  • Have you tried newton's method? Or do you need an analytical solution? – Paul Nov 24 '15 at 22:04

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Starting from $$ I_{D} = \tfrac{1}{2} k'_n \,(V_{OV})^2 $$ and substituting the definitions in the question, we get $$ \begin{aligned} I_D & = \tfrac{1}{2} k'_n \,(V_{GS} - V_{t})^2 \\ & = \tfrac{1}{2} k'_n \,(V_G - V_S - V_{t})^2 \\ & = \tfrac{1}{2} k'_n \,(V_G - I_D\,R_S - V_{t})^2 \\ & = \tfrac{1}{2} k'_n \,\left[(V_G - I_D\,R_S)^2 - 2(V_G - I_D\,R_s)\,V_t + V_{t}^2\right] \,. \end{aligned} $$ Define $$ \alpha := V_G - I_D\,R_S $$ and express $I_D$ in terms of $\alpha$: $$ I_D = \frac{1}{R_S}(V_G - \alpha) \,. $$ With these definitions, $$ \frac{1}{R_S}(V_G - \alpha) = \tfrac{1}{2} k'_n \,\left(\alpha^2 - 2\alpha\,V_t + V_{t}^2\right) \,. $$ Define $$ \beta := \tfrac{1}{2} k'_n\,R_S \,. $$ Then $$ V_G - \alpha = \beta \left(\alpha^2 - 2\alpha\, + V_{t}^2\right) \,. $$ Reorganize $$ \beta\,\alpha^2 + (1 - 2\beta\,V_t)\alpha + (\beta V_t^2 - V_G) = 0 $$

Set up the polynomial in Matlab and find its roots:

beta = 0.5*knp*RS
p = [beta (1 - 2*beta*Vt) (beta*Vt^2 - VG)]
alpha = roots(p)
ID1 = 1/RS*(VG - alpha(1))
ID2 = 1/RS*(VG - alpha(2))
Biswajit Banerjee
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