# 1ECE 584, Summer 2002Brad Noble Chapter 3 Slides Early Voltage in MOSFETs Due to channel length modulation:

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1ECE 584, Summer 2002Brad Noble Chapter 3 Slides Early Voltage in MOSFETs Due to channel length modulation:

2ECE 584, Summer 2002Brad Noble Chapter 3 Slides Saturation Voltage V pinchoff = V DS,sat = V GS – V TH –Separates resistive from saturation region The drain current is given by Solving for V DS,sat : Good to solve for quiescent voltage-current.

3ECE 584, Summer 2002Brad Noble Chapter 3 Slides Ex: Find V DS,sat for an NFET

4ECE 584, Summer 2002Brad Noble Chapter 3 Slides Variations in V TH Across Channel We assume V TH is constant across channel THIS IS NOT TRUE! Depletion region is thick at S and thin at D. C ox C dep inversion layer Gate oxide capacitance Depletion cap, function of x

5ECE 584, Summer 2002Brad Noble Chapter 3 Slides Notes on PFETs PFETs typically have a shape factor 3 or 4 times larger than NFETs Body effect can be eliminated in PFETs by tying the n-well to V DD –Need 6  m spacing between n-wells to isolate. –Dr. Engel always does this on input devices, not always elsewhere.

6ECE 584, Summer 2002Brad Noble Chapter 3 Slides Weak Inversion What really happens if V GS < V TN ? In digital design, I DS = 0. We call it “weak inversion” or W.I. I DS is primarily due to I drift in strong inversion and I diffusion in weak inversion.

7ECE 584, Summer 2002Brad Noble Chapter 3 Slides Modes of Inversion I DS = I drift + I diffusion If V GS > V TN the channel has been inverted. To be more precise, we can say the channel has been “strongly inverted” (S.I.) due to an abundance of carriers in the channel. Inversion is independent of whether the FET is in the linear or saturation region.

8ECE 584, Summer 2002Brad Noble Chapter 3 Slides Weak Inversion I diffusion Drain is more reverse biased than source: To find I diff, compute gradient Because no carriers are lost as they travel from S to D, current is the same for all x and gradient is not a function of x. Note: This is not really true due to recombination, but its close!

9ECE 584, Summer 2002Brad Noble Chapter 3 Slides W.I. Surface Potential

10ECE 584, Summer 2002Brad Noble Chapter 3 Slides Deriving Weak Inversion I DS

11ECE 584, Summer 2002Brad Noble Chapter 3 Slides W.I. FET As Exp. Law Dev. S must be big for device to be useful. If V DS = 100mV, can be neglected. For W.I. v DS,Sat  100mV Looks like a BJT

12ECE 584, Summer 2002Brad Noble Chapter 3 Slides Inversion Coefficient Let Shape factor as a function of  : Lets you chose shape to match inversion mode.  < 0.1 Weakly Inverted (W.I.)  > 10 Strongly Inverted (S.I.) 0.1 <  < 10 Moderately Inverted (M.I.)

13ECE 584, Summer 2002Brad Noble Chapter 3 Slides Ex. Using Inversion Coeff.

14ECE 584, Summer 2002Brad Noble Chapter 3 Slides Small Signal Analysis

15ECE 584, Summer 2002Brad Noble Chapter 3 Slides Ex: Quiescent Point Question: How many digits are significant?

16ECE 584, Summer 2002Brad Noble Chapter 3 Slides Small Signal Model Limits Suppose the previous circuit is the input device of an amplifier. Small-signal model holds as long as the deviations are small

17ECE 584, Summer 2002Brad Noble Chapter 3 Slides Taylor Series Expansion Taking a Taylor expansion of one variable:

18ECE 584, Summer 2002Brad Noble Chapter 3 Slides Small Signal Model Params

19ECE 584, Summer 2002Brad Noble Chapter 3 Slides Example: Small Signal Analysis

20ECE 584, Summer 2002Brad Noble Chapter 3 Slides Small Signal Low-Freq Model

21ECE 584, Summer 2002Brad Noble Chapter 3 Slides Ex: Find g m and r O

22ECE 584, Summer 2002Brad Noble Chapter 3 Slides Transconductance: W.I. & M.I. What is g m for a weakly inverted FET? What is g m for a moderately inverted FET? Not in textbooks!

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