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Chapter 6: Problem 41

Does the current of an enhancement-type MOSFET increase at about the same rate as a depletiontype MOSFET for the conduction region? Carefully review the general format of the equations, and if your mathematics background includes differential calculus, calculate \(d I_{D} / d V_{G S}\) and compare its magnitude.

Short Answer

Expert verified
Based on the differential analysis, the current increase rate for the enhancement type MOSFET is usually greater than the depletion type for the same \(V_{GS}\) region.

Step by step solution

01

Understand enhancement-type MOSFET behavior

An enhancement-type MOSFET stays off until a certain threshold voltage (Vth) is applied. When the gate-source voltage \((V_{GS}) > V_{th}\), it starts to conduct and the drain current (\(I_D\)) increases. The key equation used for this is the piecewise function, \(I_D = K * (V_{GS} - V_{th})^2\) for \(V_{GS} > V_{th}\) and \(I_D = 0\) for \(V_{GS} < V_{th}\).
02

Derive the rate for enhancement-type MOSFET

Let’s use calculus to calculate \(d I_{D} / d V_{GS}\) for enhancement type MOSFET. By taking the derivative of the equation \(I_D = K * (V_{GS} - V_{th})^2\), we get \(d I_{D} / d V_{GS} = 2K * (V_{GS} - V_{th})\). This expresses the rate of change of current with respect to voltage for enhancement-type MOSFET.
03

Understand depletion-type MOSFET behavior

A depletion-type MOSFET is normally on and requires negative \(V_{GS}\) to stop conducting. The corresponding formula for this is \(I_D = I_{DSS} * (1 - \frac{V_{GS}}{V_{GS(off)}})^2\), where \(I_{DSS}\) is the saturation current and \(V_{GS(off)}\) is the cut-off voltage.
04

Derive the rate for depletion-type MOSFET

Using calculus, calculate \(d I_{D} / d V_{GS}\) for depletion-type MOSFET. By taking the derivative, we have \(d I_{D} / d V_{GS} = -2 * I_{DSS} / V_{GS(off)} * (1 - \frac{V_{GS}}{V_{GS(off)})\), which shows how the current changes with voltage for depletion type MOSFET.
05

Compare the magnitudes

By substituting some typical values for K, \(V_{th}\), Idss, and Vgs(off), student can compare the magnitude of \(d I_{D}/d V_{GS}\) for both types of MOSFETs. The comparison would depend on the transistor constants, but typically, the rate of change for enhancement type MOSFET is found to be greater.

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Most popular questions from this chapter

a. What is the significant difference between the construction of an enhancement-type MOSFET and a depletion-type MOSFET? b. Sketch a \(p\) -channel enhancement-type MOSFET with the proper biasing applied \(\left(V_{D S}>0 \mathrm{~V}, V_{G S}>V_{T}\right)\) and indicate the channel, the direction of electron flow, and the resulting depletion region. c. In your own words, briefly describe the basic operation of an enhancement- type MOSFET.

Sketch the transfer characteristics of a \(p\) -channel enhancement-type MOSFET if \(V_{T}=-5 \mathrm{~V}\) and \(k=0.45 \times 10^{-3} \mathrm{~A} / \mathrm{V}^{2}\).

What are the relative advantages of the UMOS technology over the VMOS technology?

Explain in your own words why the application of a positive voltage to the gate of an \(n\) -channel depletion-type MOSFET will result in a drain current exceeding \(I_{D S S}\).

Sketch the transfer and drain characteristics of an \(n\) -channel depletion- type MOSFET with \(I_{D S S}=12 \mathrm{~mA}\) and \(V_{P}=-8 \mathrm{~V}\) for a range of \(V_{G S}=-V_{P}\) to \(V_{G S}=1 \mathrm{~V}\).
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