# Characteristics of MOSFET: How Does i_{DS} Vary with v_{GS} in the ON State?

• pc2-brazil
In summary: Vds does not increase i_{DS} beyond some value v_{LD} (where v_{LD} is the linear region crossover point).
pc2-brazil

## Homework Statement

A specific type of MOSFET has $V_T = -1\ \rm V$. The MOSFET is in the ON state when $v_{GS} \geq V_T$. The MOSFET is in the OFF state when $v_{GS} < V_T$.
a) Graph the $i_{DS}$ versus $v_{GS}$ characteristics of this MOSFET.

## The Attempt at a Solution

My doubt concerns part a. I will use the switch-resistor (SR) model (the ON state of the MOSFET is modeled as a resistance $R_{ON}$ between the drain and the source). So, the graph of $i_{DS}$ versus $v_{GS}$ would have $i_{DS} = 0$ for all $v_{GS} < V_{T}$.
But what about the case where $v_{GS} \geq v_T$? The problem is that I don't know how $i_{DS}$ varies as a function of $v_{GS}$.
I know that $i_{DS} = \dfrac{v_{DS}}{R_{ON}}$; if this value doesn't vary with $v_{GS}$, then, for $v_{GS} \geq v_T$ the graph would have just a horizontal line with y-value $i_{DS} = \dfrac{v_{DS}}{R_{ON}}$.
What am I missing?

pc2-brazil said:

## Homework Statement

A specific type of MOSFET has $V_T = -1\ \rm V$. The MOSFET is in the ON state when $v_{GS} \geq V_T$. The MOSFET is in the OFF state when $v_{GS} < V_T$.
a) Graph the $i_{DS}$ versus $v_{GS}$ characteristics of this MOSFET.

## The Attempt at a Solution

My doubt concerns part a. I will use the switch-resistor (SR) model (the ON state of the MOSFET is modeled as a resistance $R_{ON}$ between the drain and the source). So, the graph of $i_{DS}$ versus $v_{GS}$ would have $i_{DS} = 0$ for all $v_{GS} < V_{T}$.
But what about the case where $v_{GS} \geq v_T$? The problem is that I don't know how $i_{DS}$ varies as a function of $v_{GS}$.
I know that $i_{DS} = \dfrac{v_{DS}}{R_{ON}}$; if this value doesn't vary with $v_{GS}$, then, for $v_{GS} \geq v_T$ the graph would have just a horizontal line with y-value $i_{DS} = \dfrac{v_{DS}}{R_{ON}}$.
What am I missing?

You need the equations for i as a function of Vds and Vgs. The most common way is to graph i vs. Vds so you'll have a family of curves, one for each Vgs where usually Vgs varies from 0 to some max. number like 10V in 2V increments (i.e. 6 curves). The Vgs = 0 curve is of course the i = 0 axis.

There are three regions of operation for the MOSFET. I am attaching a pdf file for you. Use the "square law" equations at the top of page 1 and assume μCoxW/L and VT are constants. VT = 1V in your case. A typical value for μCoxW/L might be 0.025 A/V2.

#### Attachments

• MOS equations.pdf
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rude man said:
You need the equations for i as a function of Vds and Vgs. The most common way is to graph i vs. Vds so you'll have a family of curves, one for each Vgs where usually Vgs varies from 0 to some max. number like 10V in 2V increments (i.e. 6 curves). The Vgs = 0 curve is of course the i = 0 axis.

There are three regions of operation for the MOSFET. I am attaching a pdf file for you. Use the "square law" equations at the top of page 1 and assume μCoxW/L and VT are constants. VT = 1V in your case. A typical value for μCoxW/L might be 0.025 A/V2.

Thank you for the help, but, actually, the book I'm using doesn't present the square law model in the chapter where it asks this problem. So, I think I should be able to graph the approximate behavior of the MOSFET only by using the SR model (the MOSFET acts like a resistor $R_{ON}$ in its ON state, for sufficiently small values of $V_{GS}$).

By the way, the book is "Foundations of Analog and Digital Circuits" by Agarwal and Lang. This problem is from Chapter 6.

To get a single value of IDS for specific VGS, I think you have to assume that VDS is large enough to saturate the MOSFET.

mfb said:
To get a single value of IDS for specific VGS, I think you have to assume that VDS is large enough to saturate the MOSFET.

What exactly do you mean by saturating the MOSFET?

In this situation, would I have a single value of $i_{DS} = \dfrac{v_{DS}}{R_{ON}}$ for $v_{GS} \geq V_T$, which would then be plotted as a horizontal line in the $i_{DS}$ versus $v_{GS}$ graph?

pc2-brazil said:
What exactly do you mean by saturating the MOSFET?

In this situation, would I have a single value of $i_{DS} = \dfrac{v_{DS}}{R_{ON}}$ for $v_{GS} \geq V_T$, which would then be plotted as a horizontal line in the $i_{DS}$ versus $v_{GS}$ graph?

On the contrary, I think what's intended here is not the saturated region but the 'linear' region. (The saturated region is when Vsd > (Vgs + VT). In that region, increasing Vds does not materially affect i if Vgs is held constant). The linear region is where i decreases with Vds for a given Vgs.

It's confusing nomenclature since the linear region is where the device is used as an on/off switch, which is thought of as the device being "saturated". I.e. Vds is about as low as it can go which is what you want when the device is "on". It's 'saturated' in the sense of minimum Vds which also implies minimum Ron.

The plot you need is i vs. Vds for various values of Vgs. For each value of Vgs, the value of i/Vds is approximately constant & varies only with Vgs. These values of i/Vds = 1/Ron. You will find that i/Vds increases as Vgs increases.

PS - com jeito vai! Eu era Carioca entre 1956-58!

Last edited:

## What is a MOSFET?

A MOSFET (Metal Oxide Semiconductor Field Effect Transistor) is a type of transistor that is commonly used in electronic devices. It is a three-terminal device that can be used for switching or amplifying electronic signals.

## What are the main characteristics of a MOSFET?

The main characteristics of a MOSFET include its low input impedance, high output impedance, and high current-carrying capability. It also has a high input-to-output isolation, which makes it useful for amplifying weak signals without affecting the input signal.

## How does a MOSFET work?

A MOSFET works by controlling the flow of current between its source and drain terminals using an electric field. When a voltage is applied to the gate terminal, it creates an electric field that either allows or blocks the flow of current between the source and drain terminals, depending on the type of MOSFET (n-type or p-type).

## What are the advantages of using MOSFETs?

MOSFETs have several advantages over other types of transistors, including their low power consumption, high switching speed, and ability to handle high currents. They also have a high input impedance, which makes them less likely to load or affect the input signal.

## What are the applications of MOSFETs?

MOSFETs are used in a wide range of electronic devices, including computers, smartphones, and power supplies. They are also commonly used in amplifiers, motor control circuits, and switching circuits. Additionally, MOSFETs are used in integrated circuits (ICs) to perform various functions in electronic devices.

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