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Electrical and Electronic Engineering Basics

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2021-02-10 03:43
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2021年2月10日发(作者:民族包)


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







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

-


-


-


-


-


-


-


-



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