# Why does this MOSFET turn on initially in saturation?

• CoolDude420
In summary, according to Razavi's book "Analog CMOS Integrated Circuits", transistor M1 will turn on in saturation regardless of the values of Vdd and Rd. This is because the condition for saturation, VDS > VGS - VTH, simplifies to Vout > Vin - VTH. This proves that the transistor will turn on in saturation. On a characteristic curve graph, the output voltage will lie on the load line for RD, and at the point where it is just switching on, it must be in the saturation region.
CoolDude420

## Homework Statement

Razavi's book (Analgoue CMOS Integrated Circuits) says that that "as Vin approaches Vth, M1 begins to turn on, drawing current from Rd and lowering Vout. Transistor M1 turns on in saturation regardless of the values of Vdd and Rd."

Why is that? I mean that the condition for saturation is (assuming Vgs > Vth) is:
For Saturation:
$$V_{DS} > V_{GS} - V_{TH}$$
Simplifies to:
$$V_{out}>V_{in} - V_{TH}$$

How does that prove it will turn on in saturation?

## The Attempt at a Solution

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Personally, I look at the characteristic curves rather than the formulae, but either way is ok.

When the mosfet is cut off, what is the output voltage?
And the input voltage?
Now, as the input voltage rises, at what level does the mosfet start to turn on?
What is the output voltage just before or just as the mosfet starts to turn on?

Otherwise, on a ID vs VDS graph of characteristic curves, draw in a load line for RD (any nominal value will do.) The output voltage will lie on the load line. Look at the point where it is just switching on. What region must it be in?

## 1. Why does a MOSFET turn on initially in saturation when a voltage is applied?

The MOSFET, or metal-oxide-semiconductor field-effect transistor, has a gate, source, and drain. When a voltage is applied to the gate, it creates an electric field that allows current to flow from the source to the drain. This current is initially constrained by the size of the channel between the source and drain, resulting in saturation.

## 2. What is the difference between initial saturation and long-term saturation in a MOSFET?

Initial saturation occurs when a voltage is first applied to the gate of a MOSFET, and the current is limited by the size of the channel. Long-term saturation, on the other hand, can occur when the MOSFET is continuously operating and the channel becomes depleted of charge carriers, limiting the current that can flow through.

## 3. How does the threshold voltage affect initial saturation in a MOSFET?

The threshold voltage, also known as the gate-source voltage, is the minimum voltage required to turn on the MOSFET. When this voltage is applied, it creates the initial electric field that allows current to flow from the source to the drain, resulting in initial saturation.

## 4. Why is initial saturation important in MOSFETs?

Initial saturation is important because it determines the initial current flow through the MOSFET when a voltage is applied. This can affect the overall performance and efficiency of the MOSFET in its intended application.

## 5. Can a MOSFET be prevented from initially turning on in saturation?

Yes, the initial saturation of a MOSFET can be prevented by applying a gate-source voltage higher than the threshold voltage. This will create a stronger electric field, allowing more current to flow through the channel and preventing initial saturation.

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