Plot transistor characteristics Id vs. Vds

[VinnyCee]

Homework Statement

Assume the circuit pictured below:

http://img259.imageshack.us/img259/3443/problem2bwz3.jpg

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 timesThe 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

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.

 

[piercas]

I would approach this problem by first understanding the characteristics of a transistor and how it operates. A transistor is a three-terminal semiconductor device that can amplify or switch electronic signals. It consists of a source (S), a drain (D), and a gate (G) terminal.

In this circuit, the transistor is being used as a voltage-controlled current source, where the gate voltage (Vgs) controls the current flowing from the source to the drain (Id). The transistor rules given in the problem statement describe how the drain current (Id) is affected by the gate-source voltage (Vgs) and the drain-source voltage (Vds).

To plot the transistor characteristics Id vs. Vds, we need to vary the drain-source voltage (Vds) and observe the corresponding drain current (Id) at different gate-source voltages (Vgs). This can be done by setting Vgs at different values from 1V to 5V in 0.25V steps, and then measuring the corresponding Id at Vds ranging from 0V to 5V.

Using the given transistor rules, we can plot the characteristics by following these steps:

1. For Vgs < Vt (threshold voltage), the transistor is in the OFF state and the drain current (Id) is 0. Hence, the graph will start from the origin for all values of Vgs.

2. For Vgs > Vt, the transistor is in the ON state and the drain current (Id) is given by the equation: Id = gm(Vgs - Vt)(Vds/Vds,sat), where gm is the transconductance parameter and Vds,sat is the saturation voltage.

3. For 0 ≤ Vds ≤ Vds,sat, the drain current (Id) varies linearly with Vds, with a slope of gm(Vgs - Vt).

4. For Vds > Vds,sat, the drain current (Id) remains constant at gm(Vgs - Vt)Vds,sat.

5. Repeat steps 2-4 for different values of Vgs (1V, 1.25V, 1.5V, etc.) and plot the corresponding Id vs. Vds curves on the same graph.

The resulting graph will have a similar shape to the one shown in the previous problem, but with different slopes for each curve. The graph will also show the three distinct regions of operation of the

 

[piercas]

I would first clarify the problem by asking for more information. Specifically, I would want to know the values of the different parameters in the transistor rules, such as V_T, g_m, and V_DS,SAT. Without these values, it is impossible to accurately plot the transistor characteristics.

Once I have all the necessary information, I would use the transistor rules to calculate the values of I_D for different values of V_DS and V_GS. Then, I would plot these points on a graph with V_DS on the x-axis and I_D on the y-axis. I would repeat this process for different values of V_GS, using a different color or symbol for each curve.

The resulting graph would show the transistor characteristics for different values of V_GS, with each curve representing a different V_GS value. From this graph, we can see how the transistor behaves for different voltage inputs and how it transitions between different regions of operation. This information can be useful in designing and analyzing circuits using transistors.