-
Electrical and Electronic Engineering
Basics
UNIT 1
A
Electrical
Networks
An
electrical circuit or
network
（网络，电路）
is
composed of elements such as resistors
（
电阻器）
，
inductors
（
电感器）
，
and
capacitors
（
电容器）
connected together in some
manner
．
If
the
network
contains
no
energy
sources,
such
as
batteries
or
electrical
generators, it is known as a passive
network
（无源网络）
. On the other
hand, if one or
more energy sources are
present, the resultant combination is an active ne
twork
（
有源网
络）
. In studying the behavior of an electrical
network, we are interested in determining
the voltages and currents that exist
within the circuit. Since a network is composed of
passive circuit elements, we must first
define the electrical
characteristics
（特性曲线）
of these elements.
In the case of a resistor,
the voltage-current relationship is given by Ohm
’
s
（欧姆）
law, which states that the voltage
across the resistor is equal to the current
through the
resistor multiplied by the
value of the resistance. Mathematically, this is
expressed as
U=IR
(1-1A-1)
Where u=voltage, V; i=current, A;
R=resistance,
The voltage across a pure inductor is
defined by Faraday
’
s
（法拉第）
law , which
states
that the voltage
across the inductor is
proportional
to
the rate of change with
time of the current through the
inductor.
Thus we have
u=L
di/dt
(1-1A-2)
Where
di/dt=rate of change of current, A/s;
L=inductance, H.
The voltage developed across a
capacitor is proportional to the electric charge
（电
荷）
q
accumulating on the plates of the capacitor. Since
the accumulation of charge
may be
expressed as the summation, or
integral
（
积分）
, of
the charge
increments
（增
量）
dq, we have the equation
U= 1/c
∫
dq
(1-1A-3)
+
+
+
R
L
C
i
i
i
??
??
??
Where the capacitance C is the proportionality
constant relating voltage and charge.
By
definition,
current
equals
the
rate
of
change
of
the
charge
with
time
and
is
u
R
?
iR
u
L
?
L
d
i
/
d
t
u
C
?
(1/
C
)
i
d
t
expressed as i=dq/dt, Thus an increment of
charge dq is equal to the current multiplied
by the corresponding time increment, or
dq=i dt. Eq.(1-1A-3)may then be written as
t
?
(1/
L
)
idt
u
L
d
i
?
u
R
/
R
i
U= 1/c
∫
t
i
?
C
d
u
/
d
(1-1A-4)
Where C
=capacitance, F.
a)
b)
c)
A summary of Eqs.
(1-1A-1) (1-1A-2) and (1-1A-4) for the three forms
of passive
circuit element
is
given
in
Fig. that
conventional
current
flow is
used;
?
?
1
hence the
current in each element is shown in the direction
of deceasing voltage.
Active
electric
devices
involve
the
conversion
of
energy
to
electrical
form.
For
example, the electric
energy in a battery is derived from its stored
chemical energy.
The
electric
energy
of
a
generator
is
a
result
of
chemical
energy
of
the
rotating
armature.
（电枢，衔铁，加固）
Active
electrical
elements
occur
in
two
basic
forms:
voltage
sources
and
current
sources. In their ideal form, voltage
sources generate a constant voltage independence
of the current drawn from the source.
The
aforementioned
（上述的，前面提到的）
battery and generator are regarded as
voltage sources since their voltage is essentially
constant
with
load.
On
the
other
hand,
current
sources
produce
a
current
whose
magnitude
is
independent
of
the
load
connected
to
the
source.
Although
current
sources are not as
familiar in practice, the concept dose find wide
use in
representing
（代表，表示，阐明）
an amplifying
(
放大
)device, such as the
transistor, by means
of an equivalent
electrical circuit.
Symbolic
（符号的，记号的）
representations of
voltage
and current sources are shown in Fig.1-1A-2.
A common method of
analyzing an electrical network is
mesh
（网孔）
or loop
analysis. The fundamental law that is
applied in this method is
Kirchhoff
’
s fist
law
（基
尔霍夫第一定律）
,
which
states
that
the
algebraic
sum
of
the
voltages
around
a
closed
loop is 0, or, in any closed loop, the sum of the
voltage rises must equal
the
sum of the voltage
drops. Mesh analysis consists of assuming that
currents
—
termed
loop
currents
—
flow
in
each
loop
of
a
network,
algebraically
summing
the
voltage
drops
（电压降）
around each loop, and setting each sun
equal to 0.
Consider
the
circuit
shown
in
Fig.
1-1A-3a
which
consists
of
an
inductor
and
resistor connected in
series
（串联）
to a
voltage source e. Assuming a loop current I,
the voltage drops summed around the
loop are
-e+u
R
+u
L
=0
(1-1A-5)
The input
voltage is
summed negatively since,
in
the direction assumed
current,
it
represents an
increase in voltage. The drop across each passive
element is positive
since the current
is in the current is in the direction of the
developed voltage.
+
u
R
??
+
u
R
??
+
+
+
+
R
R
+
+
+
u
e
e
L
u
i
L
i
L
u
L
E
i
i
??
??
Using the equation or the
voltage drops in a resistor and inductor, we have
C
??
??
??
L
di/dt+Ri=e
(1-1A-6)
??
??
??
u
C
+
Eq.(1-1A-6) is the
differential equation for the current in the
circuit.
a)
b)
a)
b)
It
may be that the inductor voltage rather than the
current is variable of interest in
the
circuit, As noted in Fig. 1-1A-1,
i=
L
-1
∫
u
L
dt.
Substituting this integral for I in Eq.(1-1A-6)
Gives
U
L
+R/
L
∫
u
L
dt=e (1-1A-7)
After
differentiation
（
微
分
）
with
respect
to
time,
Eq.(1-1A-7)
becomes
du
L
/d
t+R/
L u
L
= de/dt
( 1-1A-8)
which is the
differentiation equation for the inductor
voltage.
2
Fig. (1-1A- 3b shows a series circuit
containing a resistor, inductor, and capacitor.
Following the mesh-analysis method
outlined above, the circuit equation is
L
di/dt+Ri+1/c
∫
idt
=e (1-1A-9
Recalling
that
current
i=dq/dt,
a
substitution
of
this
variable
（变量）
may
be
made
to
eliminate
（消除，对消）
the
integral
from
the
equation.
The
result
is
second-
order differential equation
L d
2
q/d
2
t
+Rdq/dt+q/C=e
A
电路
电容器
等元件组成。如果网络不包含能源，如电池或发电机，
那么就被称作
么组合的结果为
是确定电路中的电压和电流。因为网络由无源电路元件组成，所以<
/p>
必须首先定义这些元件的电特性。
就电阻来说，
律指出：电阻两端的电
压等于电阻上流过的电流乘以电阻值。在数
学上表达为：
(1-1A-1)
式中
<
/p>
u
=
电压，伏特；
纯电感电压由法拉第定律定义，法
拉第定律指出：电感
两端的电压正比于流过电感的电流随时间的变化率。因此可得到：<
/p>
。换句
话说，如果存在一个或多个能源，那
有源网络
。在研究电网络的
特性时，我们感兴趣的
电压
-
电流的关系由欧姆定律给出，
u=iR
i
=
电流，安培；
R
=
电阻，欧姆。
?
L
d
i
d
t
3
电路或电网络由以某种方式连接的电阻器、电感器和
无源网络
欧姆定
u