Plot transistor characteristics Id vs. Vds

[VinnyCee]

Homework Statement

Assume the circuit pictured below:

http://img259.imageshack.us/img259/3443/problem2bwz3.jpg [Broken]

The transistor follows these rules:

$$I_D\,=\,0$$ if $$V_{GS}\,\le\,V_T$$

$$I_D\,=\,g_m\,\left(V_{GS}\,-\,V_T\right)\,\left(\frac{V_{DS}}{V_{DS, SAT}}\right)$$ if $$V_{GS}\,\ge\,V_T\,$$ and $$\,0\,\le\,V_{DS}\,\le\,V_{DS, SAT}$$

$$I_D\,=\,g_m\,\left(V_{GS}\,-\,V_T\right)$$ if $$V_{GS}\,\ge\,V_T\,$$ and $$\,V_{DS}\,\ge\,V_{DS, SAT}$$

$$I_G\,=\,0$$ at all times


The question: Plot the transistor characteristics Id vs. Vds for Vds = 0 to 5V and Vgs = 1 to 5V in 0.25V steps.

Homework Equations

KCL, KVL, v = iR, the transistor rules above.

The Attempt at a Solution

I did KCL at node Vd and node Vs.

Vd) $$\frac{V_{out}\,-\,V_{cc}}{R_2}\,+\,g_m\,\left(V_{GS}\,-\,V_T\right)\,\left(\frac{V_{DS}}{V_{DS, SAT}}\right)\,=\,0$$

Vs) $$\frac{V_S}{R_1}\,-\,g_m\,\left(V_{GS}\,-\,V_T\right)\,\left(\frac{V_{DS}}{V_{DS, SAT}}\right)\,=\,0$$

I don't know how these help me if I solve them for Vout ot Vs or whatever. The problem before this one had the exact same circuit diagram with different transistor rules. The previous problem did not have the last fractional term for the middle region of operation for the transistor. This made a graph that looked like this:

http://img264.imageshack.us/img264/5963/homework5problem1aeg7.jpg [Broken]

However, I know that the same graph for these new transistor rules is not just straight lines again. Each line in this new graph of Id vs. Vds is supposed to start out at the origin and linearly slope upwards to the straight lines in the graph from the previous problem (above). The problem is that I don't know what to graph or how to go about getting the equations for it. Please help!

 

[mjsd]

the key here is to know what is V_T, V_DS,SAT, g_m do you know what they are? are they given in the question? if you know them, then the equation relating I_D and V_DS are given to u, so somply plot them.
for example, when V_gs is less than threshold V_T, draw a flat/straight line I_D=0, when it enters the triode region, draw that sloped straight line, then after satuation another horizontal line (but not zero) etc.. each value of V_gs will give a slightly different curve.. observe that the slope, and the saturated value changes with V_GS.