<< Chapter < Page Chapter >> Page >
Introducing the Sah equation, and discussing some properties of this equation.

This equation looks a lot like the I-V characteristics of a resistor! I d is simply proportional to the drain voltage V ds . The proportionality constant depends on the dimensions of the device, W and L as they intuitivelyshould. The current increases as the transistor gets wider, it decreases as it gets longer. It also depends on c ox and μ s , and on the difference between the gate voltage and the threshold voltage V T . Note that if we adjust V gs we can change the slope of the I-V curve. We have made a voltage-controlled resistor!

The MOSFET I-V in the linear regime

Caution is advised with this result however, because we have overlooked something quite important. Lets go back to our picture ofthe gate and the batteries involved in the operation of the MOS transistor. Here we have explicitly shown the channel as a black bandand we have introduced a new quantity, V c x , the voltage along the channel, and a coordinate x , which tells us where we are on the channel relative to the source and drain. Note that once weapply a drain source potential, V ds , the potential in the channel V c x changes with distance along the channel. At the source end, V c 0 0 , as the source is grounded. At the drain end, V c L V ds . We will define a voltage V gc which is the potential difference between the gate voltage and the voltage in the channel.

V gc x V gs V c x
Thus, V gc goes from V gs at the source end to V gs V ds at the drain end.

Effect of V ds on channel potential

The net charge density in the channel depends upon the potential difference between the gate and the channel at each point along the channel , not just V gs V T . Thus we have to modify the equation of another module to take this into account

Q chan c ox V gc x V T c ox V gs V c x V T

This, in turn, modifies the integral relation between I d and V gs .

V c x 0 V ds μ s c ox V gs V T V c x W x 0 L I d

is only slightly harder to integrate than the one before (Now what is the integral of xdx), and so we get for the drain current

I d μ s c ox W L V gs V T V ds V ds 2 2

This equation is called the Sah Equation after C.T. Sah, who first described the MOS transistor operation thisway back in 1964. It is very important because it describes the basic behavior of the MOS transistor.

Note that for small values of V ds , a previous equation and will give us the same I d V ds behavior, because we can ignore the V ds 2 term in . This is called the linear regime because we have a straight-line relationship between the drain current and the drain-source voltage. As V ds starts to get larger however, the squared term will begin to kick in and the plot will start tocurve over. Obviously, something is causing the current to drop off as V ds gets larger. This is because the voltage difference between the gate and the channel is becomingless, which means there is less charge in the channel to provide conduction. We can graphically show this by making the channellayer look thinner as we move from the source to the drain. , and in fact, would make us think that if V ds gets large enough, that the drain current I d should actually start decreasing again, and maybe even become negative!. This does not seem veryintuitive, so lets take a look in more detail at the place where I d becomes a maximum. We can define V dsat as the source-drain voltage where I d becomes a maximum. We can find this by taking the derivative of I d with respect to V ds and setting the derivative to 0.

V ds I d 0 μ s c ox W L V gs V T V dsat
On dropping constants:
V dsat V gs V T
Rearranging this equation gives us a little more insight into what is going on.
V gs V dsat V T V gc L

Questions & Answers

Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
John Reply
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Ummi Reply
omeprazole
Kamara
what
Renee
what is this
Renee
is a drug
Kamara
of anti-ulcer
Kamara
Omeprazole Cimetidine / Tagament For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
Nency Reply
Not really sure
Eli
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
what is anatomy
Oyindarmola Reply
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Oyerinde Reply
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Mohammed Reply
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
Wulku Reply
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
Ali Reply
function of digestive
Ali
the diagram of the lungs
Adaeze Reply
what is the normal body temperature
Diya Reply
37 degrees selcius
Xolo
37°c
Stephanie
please why 37 degree selcius normal temperature
Mark
36.5
Simon
37°c
Iyogho
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
37A c
Wulku
what is anaemia
Diya Reply
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
Diya Reply
how does Lysin attack pathogens
Diya
acid
Mary
I information on anatomy position and digestive system and there enzyme
Elisha Reply
anatomy of the female external genitalia
Muhammad Reply
Organ Systems Of The Human Body (Continued) Organ Systems Of The Human Body (Continued)
Theophilus Reply
what's lochia albra
Kizito
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Introduction to physical electronics. OpenStax CNX. Sep 17, 2007 Download for free at http://cnx.org/content/col10114/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introduction to physical electronics' conversation and receive update notifications?

Ask