Expression of the Current - 11.2 | 11. Revisiting MOSFET (Contd.) | Analog Electronic Circuits - Vol 1
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Academics
Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Professional Courses
Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skillsβ€”perfect for learners of all ages.

games

Interactive Audio Lesson

Listen to a student-teacher conversation explaining the topic in a relatable way.

Introduction to MOSFET Current Expression

Unlock Audio Lesson

Signup and Enroll to the course for listening the Audio Lesson

0:00
Teacher
Teacher

Welcome to today’s session! We’re going to dive into the expression of the current in MOSFETs. Can anyone tell me what parameters we consider when discussing MOSFET current?

Student 1
Student 1

Is it related to the channel dimensions like width and length?

Teacher
Teacher

Exactly! The width (W) and length (L) of the channel significantly impact the current. The more the width, the greater the current. This is because wider channels allow more charge carriers to flow. We have an acronym here: WL for Width-Length dependency. Can anyone tell me the significance of V_GS and V_th in this context?

Student 2
Student 2

V_GS is the gate-source voltage, and V_th is the threshold voltage, right?

Teacher
Teacher

Perfectly right! V_GS must exceed V_th for the channel to conduct. Now, does anyone remember the initial expression for the drain-source current, I_DS?

Student 3
Student 3

Is it proportional to (V_GS - V_th) and V_DS?

Teacher
Teacher

Yes! Remember, I_DS = K Γ— (V_GS - V_th) Γ— V_DS, where K captures device specifics. Well done! Let’s keep thinking about how we can control this current.

Understanding Conductivity in MOSFETs

Unlock Audio Lesson

Signup and Enroll to the course for listening the Audio Lesson

0:00
Teacher
Teacher

Now that we understand the basic equation, let’s explore conductivity. How does excess voltage relate to conductivity?

Student 1
Student 1

Higher excess voltage would increase conductivity, right?

Teacher
Teacher

Exactly! The excess voltage, V_GS - V_th, directly contributes to how effectively carriers can move through the channel. Does anyone remember what happens when we reach higher drain voltages, V_DS?

Student 2
Student 2

We might approach the pinch-off condition?

Teacher
Teacher

That's correct! Pinch-off occurs when V_GS just meets V_th, reducing effective channel length. This is important for high-speed applications. Remember the term PVCβ€”Pinch-off, Voltage, and Current. How does that affect I_DS?

Student 4
Student 4

The current becomes less dependent on V_DS after pinch-off.

Teacher
Teacher

Very well said! Understanding these dependencies will help in your circuit designs.

Influence of Drain Voltage on Current Expression

Unlock Audio Lesson

Signup and Enroll to the course for listening the Audio Lesson

0:00
Teacher
Teacher

Next, let’s discuss the changes to current expression as we adjust V_DS. What do you think happens if V_DS significantly increases?

Student 3
Student 3

We might need to adjust our current equation because the assumptions would change.

Teacher
Teacher

Exactly! When V_DS is similar to V_GS - V_th, we must modify our equations to account for variations in channel conductivity. Do we remember how to approximate for this situation?

Student 1
Student 1

Do we use averages for the voltages across the channel?

Teacher
Teacher

Absolutely! Taking averages helps us refine I_DS, especially as we work toward saturation conditions with the channel disappearing. Keep the acronym AVERAGE in mindβ€”Averaging Variations Ensures Realistic Analyzing Geological effects!

Pinch-off and Saturation Effects

Unlock Audio Lesson

Signup and Enroll to the course for listening the Audio Lesson

0:00
Teacher
Teacher

Let’s wrap up by discussing pinch-off in detail. Can anyone summarize what happens at this point?

Student 2
Student 2

At pinch-off, the channel becomes short, and the current behavior changes.

Teacher
Teacher

Precisely! The current remains relatively constant despite increases in V_DS, which indicates saturation. This is crucial for power control in circuits. It's good to remember the term SAT for Saturation and Its Effects in MOSFETs.

Student 4
Student 4

So, does the slope change in the current graph as we enter saturation?

Teacher
Teacher

"Yes! Initially, it's quadratic and then becomes almost linear in saturation. More terms like QUAD for Quadratic Understanding & Design in MOSFET will assist you throughout.

Introduction & Overview

Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.

Quick Overview

This section discusses the expression of current in MOSFETs as a function of channel dimensions and voltage parameters.

Standard

The section explores the relationship between drain-source current and key parameters like channel width (W), length (L), threshold voltage (V_th), and gate-source voltage (V_GS). It also introduces the effects of varying these parameters on conductivity and the overall current expression.

Detailed

Expression of the Current

This section focuses on understanding how the drain-source current (7) in a MOSFET is dependent on various parameters such as the width (W) and length (L) of the channel, the gate-source voltage (V_GS), the drain-source voltage (V_DS), and the threshold voltage (V_th). The discussion begins with the assumption that the gate-source voltage is greater than the threshold voltage, allowing the channel to exist and conduct current.

The key relationship outlined involves understanding that 7 is proportional to the aspect ratio (W/L), the excess gate-source voltage (V_GS - V_th), and the drain-source voltage (V_DS). The expression can be simplified to 7 = K D7 (V_GS - V_th) D7 V_DS, where K encapsulates certain device parameters such as mobility of electrons and the dielectric constant.

The actual dependence of 7 also considers varying conditions like when the drain voltage becomes comparable to the gate-source voltage, requiring a modified model for accurately predicting current flow. As V_DS approaches V_GS - V_th, termed "pinch-off," the current is modified as the effective channel length is reduced.
Remaining consistent with these fundamental principles, this section provides critical insight into the operating behavior of MOSFETs under different biasing conditions, which is essential for circuit design and analysis.

Youtube Videos

Analog Electronic Circuits _ by Prof. Shanthi Pavan
Analog Electronic Circuits _ by Prof. Shanthi Pavan

Audio Book

Dive deep into the subject with an immersive audiobook experience.

Introduction to Current Expression

Unlock Audio Book

Signup and Enroll to the course for listening the Audio Book

So, welcome back here again the second part of today’s module. What we are looking for is the expression of the current as a function of the W’s and L’s and V and V. V and V of course, they are applied here. And also, just to get an idea that how this current depends on the device parameter.

Detailed Explanation

In this introduction, we are setting the stage for understanding how the current in a MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) is expressed. The terms W (width) and L (length) refer to the dimensions of the transistor, while V represents the gate-source voltage (V_GS) and the drain-source voltage (V_DS). This section emphasizes that the expression we are about to derive is based on these parameters, and we aim to explore how variations in these factors influence the current that flows through the device.

Examples & Analogies

Consider a water hose: The width of the hose (analogous to W) and its length (L) determine how water flows through it. The pressure from the tap (representing V_GS) and any restriction at the end (analogous to V_DS) also influence the water flow rate. Just as adjustments to these factors can change water flow, so too can changes in W, L, and V affect the electrical current in a MOSFET.

Proportional Relationships

Unlock Audio Book

Signup and Enroll to the course for listening the Audio Book

So, what will be the expression of this I_DS? This is a big question. First of all, let me quickly put the biases. For vertical field we do have V_GS here, so that creates vertical field. And let me assume that this V_GS is higher than V_th. This means the channel is existing. Then we apply V_DS, which is providing the lateral field.

Detailed Explanation

This segment discusses the basic assumptions involved in deriving the expression for the drain-source current (I_DS). First, we establish that the gate-source voltage (V_GS) must be higher than the threshold voltage (V_th) in order for a conductive channel to exist. This ensures that the MOSFET is 'on' or conducting. Additionally, the drain-source voltage (V_DS) creates a lateral electric field that influences the flow of current through the channel. Understanding these conditions is crucial as we outline the expression for I_DS.

Examples & Analogies

Imagine turning on a faucetβ€”once you pull the handle (akin to applying V_GS), water starts flowing through a pipe that must be clear (just like the channel in the MOSFET). If the faucet is off (V_GS < V_th), no water flows, regardless of the pressure within the pipe (V_DS).

Proportionality of Current to Device Dimensions

Unlock Audio Book

Signup and Enroll to the course for listening the Audio Book

Intuitively, I_DS is proportional to what? It is proportional to W. If you are having higher length for everything remaining the same, the resistance will increase, and the current will decrease. Conversely, if W is increasing, the current will increase.

Detailed Explanation

This portion establishes a direct proportional relationship between the width (W) of the MOSFET channel and the drain-source current (I_DS). An increase in W leads to lower resistance, thereby allowing more current to flow. On the other hand, if the length (L) of the channel increases (while keeping everything else constant), the resistance to current flow increases, which reduces I_DS. This highlights the significance of the aspect ratio (W/L) in determining the behavior of current in a MOSFET.

Examples & Analogies

Think of W as the width of a river; wider rivers allow more water to flow with less resistance. If a river gets narrower (analogous to a smaller W), there is more restriction, and water flow decreases. Similarly, adjusting W in a MOSFET directly affects how much current can flow.

Impact of Gate Voltage on Current

Unlock Audio Book

Signup and Enroll to the course for listening the Audio Book

The current will be proportional to the conductivity in the channel regions controlled by V_GS - V_th. The excess voltage contributes to the conductivity, increasing I_DS as V_GS increases.

Detailed Explanation

Here, the discussion focuses on the role of voltage beyond the threshold voltage (V_GS - V_th) in increasing conductivity within the MOSFET's channel. Essentially, a larger difference between the gate-source voltage and the threshold voltage allows more charge carriers to be available, thereby increasing the current flow. This aspect indicates how crucial the voltage applied at the gate is in controlling the electrical characteristics of the MOSFET.

Examples & Analogies

Picture adding more and more water pressure to a water balloon. Initially, the water does not fill it much when there isn't enough pressure (V_GS < V_th). Once you apply sufficient pressure (V_GS > V_th), the balloon fills and expands, allowing more water (current) to flow in.

Combining Factors to Form the Current Expression

Unlock Audio Book

Signup and Enroll to the course for listening the Audio Book

So, if I combine all of them, we can say that I_DS is proportional to a constant K times (V_GS - V_th) times V_DS.

Detailed Explanation

In this chunk, we summarize the relationships established previously into a coherent formula for I_DS. The formula states that the drain-source current is directly proportional to the product of the excess gate voltage (V_GS - V_th), the drain-source voltage (V_DS), and a proportionality constant K that encapsulates various device parameters including electron mobility and capacitance per unit area. This puts all our earlier observations together into a single expression that predicts current flow based on specified voltages and dimensions.

Examples & Analogies

This is like calculating how much water will flow through a pipe based on its diameter (W), the pressure difference at the ends (V_GS - V_th), and the length of the pipe (L), taking into account any restrictions or features (represented by K) that affect flow. All these variables combine in a formula to give an accurate prediction of the flow rate.

Valid Conditions for Current Expression

Unlock Audio Book

Signup and Enroll to the course for listening the Audio Book

This equation assumes that V_GS is higher than V_th and that V_DS is much smaller than V_GS - V_th. This assumption is critical for the validity of the derived expression for I_DS.

Detailed Explanation

In this concluding section, we discuss the important conditions under which our expression for I_DS holds true. Specifically, it is crucial that the gate-source voltage remains above the threshold voltage, indicating that the MOSFET is on. Additionally, V_DS must be small compared to the gate drive conditions for the equation to accurately predict current behavior. Without these conditions, one may receive incorrect predictions about current flow.

Examples & Analogies

Returning to our water analogy, think of it like this: if you have a full faucet (V_GS > V_th), you're likely to get a good flow. But if the faucet is partially closed (akin to a large V_DS), then flow might not be as expected. The conditions must be right for a reliable prediction of how much water flows.

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Current Expression: I_DS = K Γ— (V_GS - V_th) Γ— V_DS

  • Effect of Channel Width and Length: I_DS depends directly on the channel width and inversely on length.

  • Influence of Threshold Voltage: V_GS must exceed V_th for current flow.

  • Pinch-off: Occurs when V_GS β‰ˆ V_th, altering current behavior.

  • Saturation Region: Current remains nearly constant regardless of increases in V_DS.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • Example of varying W and L: Increasing the width results in increased current flow while increasing the length decreases it.

  • Example of threshold voltage effects: If V_GS is 3V and V_th is 1V, the excess voltage is 2V, contributing to higher current.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎡 Rhymes Time

  • Current flows when V_GS is bright, above V_th it can ignite!

πŸ“– Fascinating Stories

  • Imagine a narrow road (channel) widening (W) allows more cars (current) to pass through with ease, while a longer road (L) slows down traffic (current).

🧠 Other Memory Gems

  • Remember: 'VGS - VTH' is your line; it dictates how smoothly current flows in kind!

🎯 Super Acronyms

For pinch-off, think PVC

  • Pinch
  • Voltage
  • Current.

Flash Cards

Review key concepts with flashcards.

Glossary of Terms

Review the Definitions for terms.

  • Term: I_DS

    Definition:

    The drain-source current in a MOSFET, dependent on the gate-source and drain-source voltages.

  • Term: V_GS

    Definition:

    The gate-source voltage applied to the MOSFET.

  • Term: V_th

    Definition:

    The threshold voltage, the minimum gate-source voltage required for the channel to form.

  • Term: Pinchoff

    Definition:

    Condition when the channel closes, reducing current with respect to the drain-source voltage.

  • Term: Saturation

    Definition:

    Region where the current through the MOSFET becomes almost constant despite increases in V_DS.