- #1

Granger

- 168

- 7

## Homework Statement

I'm studying the following circuit with a MOSFET

[![enter image description here][1]][1] [1]: https://i.stack.imgur.com/gEEdQ.png

## Homework Equations

3. The Attempt at a Solution [/B]

Now for analyzing this circuit my book came out with various equations (which I totally understand and have no doubts about it).

Because the gate current is zero we have

$$V_G=V_{DD} \frac{R_2}{R_1+R_2}$$

Assuming the MOSFET is working on saturation we also have

$$I_D=k(V_{GS}-V_t)^2$$

And applying KVL:

$$V_{GS}=V_G-R_SI_D$$

Substituting equation (3) on equation (2) we have

$$I_D=k(V_G-R_SI_D -V_t)^2$$Now comes to the point I'm not understanding. To show us the dependence of the drain current over the threshold voltage, the book takes the derivative of the expression:

$$\frac{dI_D}{dV_t}=\frac{d}{dV_t}k(V_G-R_SI_D -V_t)^2$$

and then it writes

$$\frac{dI_D}{dV_t}=\frac{-2\sqrt{kI_D}}{1+2R_S\sqrt{kI_D}}$$

How on Earth did they go from equation (5) to equation (6) by taking the derivative. What kind of substitution are they making?