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hey my lecturer put this example up for an exam tomorrow, could someone please explain how he gets to the 3rd line? is he using factorization?

$V_{\mathrm{dsb}}=V_{\mathrm{gsb}}-V_{\mathrm t}$

$V_{\mathrm{dsb}}=V_{\mathrm{dd}}-(R_{\mathrm d}/2)K_n(V_{\mathrm{gsb}}-V_{\mathrm t})^2$

$V_{\mathrm{gsb}}=V_{\mathrm t}+(\sqrt{2K_{\mathrm n}R_{\mathrm d}V_{\mathrm{dd}}+1}-1)/K_{\mathrm n}R_{\mathrm d}$

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    I formatted the equations. It was rather non-trivial to guess what you meant; please check that everything is as it should $b$e. You can right-click on the equations and select "Show Source" to see how to do the formatting so you can do it yourself next time.2011-09-22

1 Answers 1

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The first equation states that the expression being squared in the second equation is $V_{\mathrm{dsb}}$. Thus the second equation becomes

$V_{\mathrm{dsb}}=V_{\mathrm{dd}}-(R_{\mathrm d}/2)K_nV\;_{\mathrm{dsb}}^2\;.$

This is a quadratic equation for $V\;_{\mathrm{dsb}}$. Substituting one of its two solutions into the first equation yields the third equation.

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    sorry about the formatting, thanks for the help it just wasn't clicking, and thanks for the formatting help2011-09-22