UNIVERSITY OF CALIFORNIA
UNIVERSITY OF CALIFORNIA
College of Engineering
Department of Electrical Engineering
and Computer Sciences
| |Midterm 2 |EECS 105 |
|B. E. BOSER |October 26, 2004 |FALL 2004 |
• Closed book, closed notes.
• No calculators.
• Copy your answers into marked boxes on exam sheets.
• Simplify numerical and algebraic results as much as possible.
Up to 5 points penalty for results that are not reasonably simplified.
• Mark your name and SID at the top of the exam and all extra sheets.
• Be kind to the graders and write legibly. No credit for illegible results.
Problem 1 [25 points]
[pic]
Given: μnCox = 200μA/V2, VTN=1V, λn=0.01V-1 @ L=1μm
gmro >> 1
The circuit is biased such that all transistors are in saturation.
a) [10 points] Find numerical values (not expressions) for:
[pic]
[pic]
b) [15 points] Find an algebraic expression for the small signal output resistance (at terminal vOUT) of the circuit as a function of transistor small-signal parameters. Use gmro >> 1 to simplify your result as much as possible:
[pic]
[pic]
Problem 2 [25 points]
[pic]
The above sketch shows a rough approximation of the electron drift velocity versus the electrical field in Silicon. For an NMOS transistor with L=0.1μm, W=10μm, and Cox=5fF/μm2 calculate the following:
a) [10 points] What is the minimum VDS (numerical value) for which current flow is limited by the thermal carrier drift velocity? Assume that the field in the channel is uniform.
[pic]
[pic]
b) [15 points] Find the numerical value of the maximum drain current ID for VGS-VTH=1V. Hint: get the current from the channel charge and its velocity.
[pic]
[pic]
[pic]
Problem 3 [25 points]
[pic]
The circuit shown above is biased so that all transistors are in saturation. Draw a small signal model (label all elements with appropriate symbols, e.g. gm1, ro2) and find an algebraic expression for the small-signal voltage gain av=vout/vin as a function of small-signal parameters (gm’s and ro’s). Use gmro >> 1 to simplify your result.
[pic]
[pic]
[pic]
Problem 4 [23 points]
[pic]
The circuit shown above is biased so that the transistor is in saturation.
a) [8 points] What is the type of this amplifier?
b) [15 points] Find an algebraic expression for the small-signal voltage ratio v2/v1 for is=0 as a function of R1, R2, and transistor small-signal parameters.
Hint: you may find small-signal model very helpful to answer this question.
-----------------------
gm3 = 10000 [pic]0ƒ…Œ?Ž?”—™¥¯´µ¶º¾¿ÁÂÄÝÞíî! " : C _ a § ¨ Ë ê ë ì nrtžðìèäàìÛìÛÖÑìÈ¿·È³ì¯ìÖ󻓴 ³ä³ä³ä³œ³ä’³ìŽäì臃yhlhl5?\?hlμS
ID3 = 1000 μA
Name: ______________________________
SID: ______________________________
Name of student at your left:
____________________________ (1 point)
Name of student at your right:
____________________________ (1 point)
rout = 1/(gm3 + gmb3)
VDS = 0.1 V
Common _Gate_________________________________________
ID = 4.75 mA
v2/v1 = [pic]
Small-signal model (neatness counts) [13 points]:
av = – gm1/gm2
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
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