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Plotting MOS I-V

Module by: Bill Wilson. E-mail the author

Summary: Plotting MOS I-V, and sketching the I-V behavior.

Now we use two of the equations ((Reference) and (Reference)) that we found in the discussion about MOS Regimes to calculate a set of Vdsat Vdsat and Idsat Idsat values for various value of Vgs Vgs . (Note that Vgs Vgs must be greater than VT VT for the two equations to be valid.) When we get the numbers, we build a little table.

Once we have the numbers, then we sketch a piece of graph paper with the proper scale, and plot the points on it. Once the Idsat Idsat , Vdsat Vdsat points have been determined, it is easy to sketch in the I-V behavior. You just draw a curve from the origin up to any given point, having it "peak out" just at the dot, and then draw a straight line at Idsat Idsat to finish things off. One such curve is shown in Figure 3. And then finally in Figure 4 they are all sketched in. Your curves probably wont be exactly right but they will be good enough for a lot of applications.

Figure 1: Results of calculating Vdsat Vdsat and Idsat Idsat .
V gs V gs V dsatV V dsat V V dsatmAV dsat mA
3 1 0.44
4 2 1.76
5 3 3.96
6 4 7.04
7 5 11

There is a particularly easy way to measure by kk and VT VT for a MOSFET. Let's first introduce the schematic symbol for the MOSFET, it looks like Figure 5. Let's take a MOSFET and hook it up as shown in Figure 6.

Since the gate of this transistor is connected to the drain, there is no doubt that V gs V ds V gs V ds is less than VT VT . In fact, since V gs = V ds V gs V ds , their difference, is zero. Thus, for any value of Vds Vds , this transistor is operating in its saturated condition. Since V gs = V ds V gs V ds , we can rewrite a previous equation derived equation from the section on MOS transistor as

I d =k2 V ds V T 2 I d k 2 V ds V T 2
(1)

Now let's take the square root of both sides:

I d =k2( V ds V T ) I d k 2 V ds V T
(2)

So if we make a plot of I d I d as a function of Vds Vds , we should get a straight line, with a slope of k2 k 2 and an x-intercept of VT VT .

Because of the expected non-ideality, the curve does not go all the way to VT VT , but deviates a bit near the bottom. A simple linear extrapolation of the straight part of the plot however, yields an unambiguous value for the threshold voltage VT VT .

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