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

[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.

Homework Equations

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?

 

[rude man]

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.

Homework Equations

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 μC_oxW/L and VT are constants. VT = 1V in your case. A typical value for μC_oxW/L might be 0.025 A/V².

 

[pc2-brazil]

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 μC_oxW/L and VT are constants. VT = 1V in your case. A typical value for μC_oxW/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.

 

[mfb]

To get a single value of I_DS for specific V_GS, I think you have to assume that V_DS is large enough to saturate the MOSFET.

 

[pc2-brazil]

To get a single value of I_DS for specific V_GS, I think you have to assume that V_DS 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?

 

[rude man]

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!