In this article, our study of I/V characteristics is not derived for derivation, but only to give us a clearer understanding of the working state of MOS tubes, which can be more concise and refined in subsequent expressions. Therefore, it focuses on the working state of MOS tubes (mainly on NMOS tubes, and PMOS. In fact, in many cases, there is an extra negative sign. You can analyze it by yourself), how to judge the working state, and draw the I/V characteristics in each state according to mathematical formulas.

**Conductivity**

We can see that a capacitive plate will be formed between the gate and the substrate, and then the VG voltage rises, and the charge accumulated in the gate metal plate begins to increase. When the charge is so large that it forms a channel, D and S will be turned on. At this time, our VG is the so-called “threshold voltage” and VTH voltage. We continue to improve the VG when the charge density in the channel continues to increase, causing the leakage current to increase further. Well, then the VTH we just mentioned is a qualitatively analyzed quantity. Next, we will directly give the calculation formula of VTH in semiconductor physics: Among them, It is the voltage value of the difference between the work function of the polysilicon gate and the substrate. The Nub inside is the doping concentration of the substrate, q is the electron charge, ni is the intrinsic carrier concentration of silicon, Qdep is the charge in the depletion zone, and Cox is the gate oxide layer capacitor per unit area. Of course, it is impossible for us to use the above mathematical formula for actual calculation because these parameters are difficult to test these parameters.

**I/V curve function relationship**

First of all, we still assume that VG is added to the gate of the NMOS tube, the source S is grounded, and a VD voltage is added to the leakage pole, and then according to the following formula:

Well, regardless of the derivation process, we can directly get the mathematical function expression of NMOS’s leakage current ID:

That is to say, at this time, our current is related to the values of carrier mobility, unit length capacitance, VGS, VTH, and VDS (parabolic equation). We find a bias derivative about VD for the ID and make it 0. At this time, we can see that we want the ID to get the maximum value, and the ID is

We believe that for everyone who has studied analog circuits, I have a little impression of the value of ID and max at this time. What is the current of NMOS tube saturation, that is to say, when VD=VGS-VTH, the current of our NMOS tube will tend to stabilize, that is, to reach the Saturation state.

Here we need to pull out the two parameters in the above formula separately

**1) **Our VGS-VTH, which is the famous “over-drive voltage”. How to put it? For the sake of visual understanding, our VG can be turned on as soon as we reach VTH, but we continue to add the voltage (that is, VG-VTH still has leftovers). At this time, is it driven? It flew up, so there is nothing wrong with our understanding of the driving voltage (let’s understand it this first. In fact, this statement is still a little worth studying).

**2)** Our W/L, which is the “width-to-length ratio” we mentioned in our daily work. In the above formula, the maximum output current of the whole MOS tube can be changed by adjusting the aspect ratio. In the subsequent blog posts, we will also discuss the impact of the aspect ratio on trans conductivity, noise, linearity, etc. Well, so far, we have discussed three current and voltage states.

**1) **When VG is less than VTH, our pipe cuts off, which is what I call the cut-off zone, and the current is 0;

**2)** When VG is greater than VTH and VDS ≥VGS-VTH, the tube is in the saturation zone with a current of:

**3)** When VG is greater than VTH and VDS Well, that’s all.

**Cross-guided expression**

This part of the content is lazy and does not repeat its basic origin. It directly makes a partial differential division of the input voltage according to the above current formula, that is, when the tube is in the saturation zone.

When the tube is in the triode region (linear region):

Through the size of the cross-guide, we can know the ability of the pipe to dial thousands of kilograms, that is to say, VGS can change the ID of our door slightly. gm is the value of the ability to measure these four or two kilograms.

How to quickly judge the working status of the NMOS tube

Here is the workspace part of the NMOS tube above. From the figure above, we can know:

**1.** Let’s look at the horizontal coordinates. When VGS is less than VTH, that is, the vertical dotted line is left, and the pipe is cut off and is in the cut-off zone;

**2.** When the horizontal axis VGS is greater than VTH, the oblique dotted line is VD=VGS-VTH, the oblique dotted line is greater than VGS-VTH above, and the pipe is in the saturation, that is, the saturation zone;

**3. **Continue to look at the horizontal axis VGS greater than VTH, the oblique dotted line is VD=VGS-VTH, the VDS below the oblique dotted line is less than VGS-VTH, and the tube is in Triode, that is, the triode region or the linear region;

Well, now we should be clear about the distinction between the workspaces. So let’s add a concept that when our MOS is used for switching, what is its value when it is turned on? How much resistance is turned on at this time? Well, let’s find the answer to this question by ourselves or discuss it in the group.

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