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基础模拟和数字电路习题解答 英文原版Anant Agarwal& Jeffrey H.Lang
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本书通过介绍如何从麦克斯韦方程利用一系列简化假设直接得到集总电路抽象,在电气工程和物理间建立了清晰的联系。本书中始终使用抽象的概念,以统一在模拟和数字设计中所进行的工程简化。本书更为强调数字领域。第1章 电路抽象 第2章 电阻网络 第3章 网络定理 第4章 非线性电路分析 第5章 数字抽象 第6章 MOSFET开关 第7章 MOSFET放大器 第8章 小信号模型 第9章 储能元件 第10章 线性电气网络的一阶暂态过程 第11章 数字电路的能量和功率 第12章 二阶电路的暂态过程 第13章 正弦稳态:阻抗和频率响应 第14章 正弦稳态:谐振 第15章 运算放大器抽象 第16章 二极管 附录A 麦克斯韦方程和集总事物原则 附录B 三角函数及其恒等式 附录C 复数 附录D 解联立线性方程组
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Foundations of Analog and Digital
Electronic Circuits
Solutions to Exercises and Problems
Anant Agarwal and Jeffrey H. Lang
Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology
c
1998 Anant Agarwal and Jeffrey H. Lang
July 3, 2005
Chapter 1
The Circuit Abstraction
Exercises
Exercise 1.1 Quartz heaters are rated according to the average power drawn from a 120
volt AC 60 Hz voltage source. Estimate the resistance (when operating) a 1200 watt
quartz heater.
NOTE: The voltage waveform for a 120 volt AC 60 Hz waveform is
The factor of
in the peak amplitude cancels when the average power is computed.
One result is that the peak amplitude of the voltage from a 120 volt wall outlet is about
170 volts.
Solution:
Power
watts
"!#$&%'!( *)+
,
*)
+
,
; where
is average value of sinusoidal voltage,
- .!/0123
Average value of a sinusoidally oscillating signal is the peak value divided by
.
Therefore
4
(5
%
Therefore
( 6
1
2
CHAPTER 1. THE CIRCUIT ABSTRACTION
ANS::
(5-6
Exercise 1.2
a) The battery on your car has a rating stated in ampere-hours which permits you to es-
timate the length of time a fully charged battery could deliver any particular current
before discharge. Approximately how much energy is stored by a 50 ampere-hour
12 volt battery?
b) Assuming 100% efficient energy conversion, how much water stored behind a 30
meter high hydroelectric dam would be required to charge the battery?
Solution:
a)
. "!4
'! !
#
!
#"$&%'(*)
+,
02
.-
4
/"0&%,12(
)
+34(
1-
5"0&%,'6(7)
.+,4(
.-
!
8
/
9
0
;:
<5)
.+,
/
=
?>
'@BA
"
+3-
b) Potential Energy
(DC
Electrical Energy; assume
0E
efficiency
*!
!
)
5
=
F>
'@GA
3
.+3-H
=
?>JIKML
ON P
FQ
IK
R
+
)
*8
'
, height of water, assuming that there is enough water in the dam such that
the height does not change as some of the water is taken out
"
GSUTVS
XW$
4
1YZ["
\
ANS:: (a)
=
F>
@
Joules, (b) 7200 kg, or about 8 tons.
Exercise 1.3 In the circuit in Figure 1.1, R is a linear resistor and
^];_a`
a constant
(DC) voltage. What is the power dissipated in the resistor, in terms of
(
and
];_a`
?
Solution:
. !
But
<
(
(Ohm’s Law), so
.[
.
(
!4
],_a`
%
(
ANS::
b
+
ced
,
3
R
+
v
-
Figure 1.1:
Exercise 1.4 In the circuit of the previous exercise (Figure 1.1),
]
`
0
, a sinu-
soidal (AC) voltage with peak amplitude
]
`
and frequency
, in radians/sec.
a) What is the average power dissipated in R?
b) What is the relationship between
]D_a`
and
]
`
in Figure 1.1 when the average
power in
(
is the same for both waveforms?
Solution:
t
v
V
DC
V
AC
2V
DC
peak= =
Figure 1.2:
a) If peak voltage is
]
`
, then
]
`
X],_a`
where
]3_a`
is the average amplitude of the voltage signal.
e'"5
]
)
\
%
(
],_a`
%
(
]
`a<
%
(
]
`
%
(
b) If peak voltage is
]
`
, then
]
`
X],_a`
where
]3_a`
is the average amplitude of the voltage signal.
4
CHAPTER 1. THE CIRCUIT ABSTRACTION
ANS:: (a)
]
%
`
<
(
(b)
]
`
X],_a`
Problems
Problem 1.1 Determine the resistance of a cube with sides of length
-
cms and resistivity
Ohm-cms, when a pair of opposite surfaces are chosen as the terminals.
Problem 1.2 Sketch the
Z(
characteristic of a battery rated at 10V with an internal
resistance of 10 Ohms.
Problem 1.3 A battery rated at 7.2V and 10000 joules is connected across a lightbulb.
Assume that the internal resistance of the battery is zero. Further assume that the resis-
tance of the lightbulb is
6
.
1. Draw the circuit containing the battery and the lightbulb and label the terminal
variables for the battery and the lightbulb according to the associated variables dis-
cipline.
2. What is the power into the lightbulb?
3. Determine the power into the battery.
4. Show that the sum of the power into the battery and the power into the bulb is zero.
5. How long will the battery last in the circuit?
Problem 1.4 A sinusoidal voltage source
4
is connected across a 1k resistor.
1. Make a sketch of
%
, the instantaneous power supplied by the source.
2. Determine the average power supplied by the source.
3. Now, suppose that a square wave generator is used as the source. If the square wave
signal has a peak-to-peak of 20V and a zero average value, determine the average
power supplied by the source.
4. Next, if the square wave signal has a peak-to-peak of 20V and a 10V average value,
determine the average power supplied by the source.
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