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The midterm exam for the eecs 105 course at the university of california, berkeley, taught by prof. A. Niknejad during the fall 2003 semester. The exam covers various topics related to electrical engineering, including lcr circuits, resistor networks, diffusion resistors, and bode plots.
Typology: Exams
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University of California, Berkeley Fall 2003 EECS 105 Prof. A. Niknejad
Helpful hints appear at the end of the exam.
L R
0V v s^ ( t )^ +
1V
v o( t )
2.5 5 7.5 10 12.5 15 17.5 20 ωτ
(a) Is the damping factor ζ greater than or less than unity?
(b) Qualitatively, describe the effect of decreasing the capacitance of the circuit.
(c) If it is desired to obtain a critically damped response, find the value of the series resistance R if
(d) If the circuit is now driven with a sinusoidal voltage source of frequency ω = ω 0 , find an expression for the power dissipation in the resistor R?
60
30
40
15
The sheet resistances of the region are R^1 = 10kΩ/sq, R^2 = 50kΩ/sq, R^3 = 30kΩ/sq.
(c) The same sample is now heated to extend the diffusion region. It is known that the diffusion region grows uniformly by 5μ, so the device now has a length of L = 110μ, a width W = 15μ, and a thickness that increases by 5μ. Calculate the resistance of the diffusion resistor.
(a) write the transfer function.
(b) Draw the phase response assuming all poles and zero occur in the left half plane (in the provided graph).
(b) The denominator for the transfer function is a second order function. What is the Q of the denominator of the transfer function?
(c) What happens at frequency ω =
LC? Explain qualitatively the operation of the circuit at this frequency.
Useful Equations:
An electron has 1.602C of charge. A complex number z = x + jy can be written in polar coordinates as z = rejθ^ where r^2 = x^2 + y^2 and tan(θ) = y/x.
The magnitude of a complex ratio z = (^) wv can be simplified by taking the magnitude of the numerator divided by the denominator: |z| = (^) ||wv||. The phase is the difference of the phase of the numerator and the denominator: ∠z = ∠v − ∠w.
The impedance transfer function is defined as the ratio of the voltage to the current: Z = V /I. Similarly, the admittance is Y = I/V.
The average power dissipated can be computed in terms of phasors:
P = Re(
) = Re(
A second order system can be written in the following canonical form:
(j
ω ω 0
)^2 + (j
ω ω 0
)2ζ + 1
where ω 0 is the natural frequency (also called the natural resonant frequency) and ζ is the damping factor.
The electrical conductivity of a metal is given by the following expression
σ = q^2
N +τ + M +^
N −τ − M −
where q is the charge of the electrical carriers, N is the number density of free carriers, τ is the average time between collisions, or the mean free time, and M is the effective mass of the free carriers.
Law of mass action says that at thermal equilibrium, the concentrations of electrons and holes satisfy the following equality
np = n^2 i
The mobility is defined as the proportionality constant between an applied external electric field and the drift velocity of carriers
vdr = μEext
The electrical conductivity is related to the mobility by the following equation
σ = qnμn + qpμp
where n and p are the density of free carriers.
