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1、第一章第一篇sectiongTwo variables u(t) and i (t) are the most basic concepts in an electric circuit, they characterize the various relati on shipsin an electriccircuitu(t)和i(t)這兩個(gè)變量是電路中最基本的兩個(gè)變量,它們刻劃了電路的各種關(guān) 系。Charge and Curre ntTheconcept of electric charge is the underlyingprincipleforexplaining all elect
2、ricalphenomena. Also, the most basic quantity in anelectric circuit is the electric charge. Charge is an electrical property of the atomic particles of which matter con sists, measured in coulombs (C).電荷和電流電荷的概念是用來(lái)解釋所有電氣現(xiàn)象的基本概念。也即,電路中最基本 的量是電荷。電荷是構(gòu)成物質(zhì)的原子微粒的電氣屬性,它是以庫(kù)侖為單位來(lái)度量的。We know from eleme ntary
3、physics that all matter is made of fun dame ntal building blocks known as atoms and that each atom consists of electrons, prot ons, and n eutr ons. We also know that the chargee on an electr on isnegative and equal in magnitude to 1.60210 x 10-19C, while a proton carries a positive charge of the sam
4、e magnitude as the electron. The presenee of equal numbers of protons and electrons leaves an atom neutrallycharged.我們從基礎(chǔ)物理得知一切物質(zhì)是由被稱為原子的基本構(gòu)造部分組成的, 并且每個(gè)原子是由電子,質(zhì)子和中子組成的。我們還知道電子的電量是負(fù)的并且 在數(shù)值上等于1.602100 x 10-12C,而質(zhì)子所帶的正電量在數(shù)值上與電子相等。 質(zhì)子和電子數(shù)量相同使得原子呈現(xiàn)電中性。We con sider the flow of electric charges. A unique f
5、eature of electric charge or electricity is the fact that it is mobile; that is, it can be transferred from one place to another, where it can be converted to another form of en ergy 讓我們來(lái)考慮一下電荷的流動(dòng)。電荷或電的特性是其運(yùn)動(dòng)的特性,也就是,它可以從一個(gè)地方被移送到另一個(gè)地方,在此它可以被轉(zhuǎn)換成另外一種形式的能量。Whena con duct ing wire is conn ected to a batt
6、ery (a source of electromotive force), the charges are compelled to move; positive charges move in one directi on while n egative charges move in the opposite directio n. This motion of charges creates electric current. It is conventional to take the curre ntflow as the moveme nt of positive charges
7、, that is, opposite to the flow of negative charges, as Fig.l-1 illustrates. This convention was introduced by Benjamin Franklin (l706 l790), the American scientist and inven tor. Although we now know that curre nt in metallic con ductors is due to n egatively charged electr ons, we will follow the
8、uni versally accepted convention that current is the net flow of positive charges. Thus, Electric current is the time rate of charge, measured in amperes (A).Mathematically, the relati on ship among curre nti , charge q, and time tis當(dāng)我們把一根導(dǎo)線連接到某一電池上時(shí)(一種電動(dòng)勢(shì)源),電荷被外力驅(qū) 使移動(dòng);正電荷朝一個(gè)方向移動(dòng)而負(fù)電荷朝相反的方向移動(dòng)。這種電荷的移動(dòng)
9、產(chǎn) 生了電流。我們可以很方便地把電流看作是正電荷的移動(dòng), 也即,與負(fù)電荷的流 動(dòng)方向相反,如圖1 1所示。這一慣例是由美國(guó)科學(xué)家和發(fā)明家本杰明一富蘭 克林引入的。雖然我們現(xiàn)在知道金屬導(dǎo)體中的電流是由負(fù)電荷引起的,但我們將遵循通用的慣例,即把電流看作是正電荷的單純的流動(dòng)。 于是電流就是電荷的時(shí) 率,它是以安培為單位來(lái)度量的d。從數(shù)學(xué)上來(lái)說(shuō),電流 i、電荷q以及時(shí)間t之 間的關(guān)系是:i二竺二dti fThe charge transferredbetween time 10 and t is obtainedbyintegrating both sides of Eq. (1-1). We obt
10、ain從時(shí)間t0到時(shí)間t所移送的電荷可由方程(1 1)兩邊積分求得。我們算得:tqpidt(42)The way we define current as i in Eq. (1-1) suggests that current need not be a constant-valued function, charge can vary with time in several ways that may be represented by different kinds of mathematical functions 我們通過(guò)方程(1 1)定義電流的方式表明電流不必是一個(gè)恒值函數(shù),電荷
11、可以不同的方式隨時(shí)間而變化,這些不同的方式可用各種數(shù)學(xué)函數(shù)表達(dá)出來(lái)。電壓,能量和功率To move the electro n in a con ductor in a particular directi onrequires some work or energy transfer.This work is performed by anexternal electromotive force (emf), typicallyrepresented by the batteryin Fig .l-1. This emf is also known as voltage or potenti
12、al differe nee.The voltage uab between twdq points a and b in ' an electric circuit is the energy (or work) needed to move a unit charge from a to b; mathematically 在導(dǎo)體中朝一個(gè)特定的方向移動(dòng)電荷需要一些功或者能量的傳遞,這個(gè)功是由外部的電動(dòng)勢(shì)來(lái)完成的。圖1 1所示的電池就是一個(gè)典型的例子。這種電動(dòng)勢(shì)也 被稱為電壓或電位差。電路中a、b兩點(diǎn)間的電壓等于從a到b移動(dòng)單位電荷所 需的能量(或所需做的功)。數(shù)學(xué)表達(dá)式為:wher
13、e wis energy in joules (J) and q is charge in coulombs (C). The voltage uab is measured in volts (V), named in honor of the Italian physicistAlessa ndro Antonio Volta (1745l827), who inven ted the first voltaicbattery. Thus, Voltage (or potentialdifferenee) is the energy requiredto move a unit charg
14、e through an eleme nt, measured in volts (V).式中w是單位為焦耳的能量而q是單位為庫(kù)侖的電荷。電壓Uab是以伏特為單位 來(lái)度量的,它是為了紀(jì)念意大利物理學(xué)家 Alessandro Antonio Volta而命名的, 這位意大利物理學(xué)家發(fā)明了首個(gè)伏達(dá)電池。 于是電壓(或電壓差)等于將單位電 荷在元件中移動(dòng)所需的能量,它是以伏特為單位來(lái)度量的。Fig.1-2 shows the voltage across an element (represented by a rectangular block ) conn ected to points a a
15、n d b. The plus (+) and minus (-) sig ns are used to defi ne refere nee direct ion or voltage polarity. Theuab can beinterpreted in two ways: point a is at a potential of uab volts higher than point b;the potential at point a with respect to point b is uab. It follows logically that in gen eral圖1-2顯
16、示了某個(gè)元件(用一個(gè)矩形框來(lái)表示)兩端a、b之間的電壓。正號(hào)(+ ) 和負(fù)號(hào)(一)被用來(lái)指明參考方向或電壓的極性,Uab可以通過(guò)以下兩種方法來(lái)解釋。1)在Uab伏特的電位中a點(diǎn)電位高于b點(diǎn),2) a點(diǎn)電位相對(duì)于b點(diǎn)而言 是Uab,通常在邏輯上遵循Uab = - UbaAlthough current and voltage are the two basic variables in an electric circuit, they are not sufficient by themselves. For practical purposes, we need to know power
17、and energy. To relate power and energy to voltage and current,we recallfrom physics that power is the time rate ofexpending or absorbing energy, measured in watts (W). We write this relati on ship as雖然電流和電壓是電路的兩個(gè)基本變量,但僅有它們兩個(gè)是不夠的。從實(shí)際應(yīng)用來(lái)說(shuō),我們需要知道功率和能量。為了把功率和能量同電壓、電流聯(lián)系起來(lái),我 們重溫物理學(xué)中關(guān)于功率是消耗或吸收的能量的時(shí)率,它是以瓦特為
18、單位來(lái)度量的。我們把這個(gè)關(guān)系式寫(xiě)成:dwdtWhere p is power in watts (W),w is en ergy in joules (J), andt is timein seco nds (s). From Eq. (1-1), Eq. (1-3), and Eq. (1-5), it follows that 式中p是以瓦特為單位的功率,w是以焦耳為單位的能量,t是以秒為單位的時(shí) 間,從方程(1 1)、(1 3)和(1 5)可以推出p = ui館Because u and i are gen erally function of time, the power p in
19、Eq. (1-6) is a time-varying quantity and is called the instantaneous power. The power absorbed or supplied by an eleme nt is the product of the voltage across the eleme nt and the curre nt through it. If the power has a plus sign, power is being delivered to or absorbed by the element. If, on the ot
20、her hand, the power has a minus sig n, power is being supplied by the eleme nt. But how do we know whe n the power has a n egative or a positivesign ?由于u和i通常是時(shí)間的函數(shù),方程(1 6)中的功率p是個(gè)時(shí)間變量于是被稱 為瞬時(shí)功率,某一元件吸收或提供的功率等于元件兩端電壓和通過(guò)它的電流的乘 積。如果這個(gè)功率的符號(hào)是正的,那么功率向元件釋放或被元件吸收。另一方面, 如果功率的符號(hào)是負(fù)的,那么功率是由元件提供的。但我們?nèi)绾蔚弥螘r(shí)功率為 正或?yàn)樨?fù)
21、?Curre nt direct ion and voltage polarity play a major role in determ ining the sign of power. It is therefore important that we pay attentionto therelati on shipbetwee n curre nt i and voltage u in Fig.1-3(a). The voltagepolarityand curre nti direct ion must conform with those show n inFig.1-3(a)in
22、 order for the power to have a positive sign. This is knownas the passive sig n conven ti on. By the passive sig n conven ti on, curre nt en ters through the positive polarity of the voltage. In this case,p =ui or ui >0 implies that the element is absorbing power. However, if p = - ui or ui v 0,
23、as in Fig.1-3(b), the element is releasing or supplying power.在我們確定功率符號(hào)時(shí),電流的方向和電壓的極性起著主要的作用,這就是我們?cè)诜治鰣D1 3 (a)所顯示的電流i和電壓u的關(guān)系時(shí)特別謹(jǐn)慎的重要原因。為 了使功率的符號(hào)為正,電壓的極性和電流的方向必須與圖1 3 (a)所示的一致。 這種情況被稱為無(wú)源符號(hào)慣例,對(duì)于無(wú)源符號(hào)慣例來(lái)說(shuō),電流流進(jìn)電壓的正極。在這種情況下,p= ui或ui>0,表明元件是在吸收功率。而如果p= ui或ui<0, 如圖1 3 (b)所示時(shí),表明元件是在釋放或提供功率。In fact, the l
24、aw of conservation of energy must be obeyed in any electric circuit.For this reason, the algebraic sum of power in a circuit, at anyin sta nt of time, must be zero事實(shí)上,在任何電路中必須遵循能量守恒定律。由于這個(gè)原因,任一電路中在任何瞬間功率的代數(shù)和必須等于零.二 p 0This aga in con firms the fact that the total power supplied to the circuit must b
25、alanee the total power absorbed. From Eq. (l-7), the energy absorbed or supplied by an element from timet 0 to time t is這再一次證明了提供給電路的功率必須與吸收的功率相平衡這一事實(shí)。從方程(17)可知,從時(shí)間t0到時(shí)間t被元件吸收或由元件提供的功率等于tw = t pdt門Section2An electric circuit is simply an interconnection of the elements. There are two types of eleme
26、nts found in electric circuits: passive eleme nts and active eleme nts. An active eleme nt is capable of gen erati ng en ergy while a passive element is not. Examples of passive elements are resistors, capacitors, and in ductors.The most importa nt active eleme nts are voltageor curre nt sources tha
27、t gen erally deliver power to the circuitconn ectedto them.電路僅僅是元件之間的相互結(jié)合。我們發(fā)現(xiàn)電路中存在有兩種元件:無(wú)源元件和 有源元件。有源元件能夠產(chǎn)生能量而無(wú)源元件卻不能,無(wú)源元件有電阻、電容和 電感器等。最重要的有源元件是通常向與它們相連的電路釋放能量的電壓和電流 源。In depe ndent sourcesAn ideal independent source is an active element that provides a specified voltage or curre nt that is complet
28、ely in depe ndent of other circuit variables.An independent voltage source is a two-terminal element, such as a battery or a gen erator, which main tai ns a specified voltage betwee n its termi nals. The voltage is completely independent of the current through the element. The symbol for a voltage s
29、ource hav ingu volts across its termi nals is shown in Fig.1-4(a). The polarity is as shown, indicating that terminal a is u volts above terminal b. Thus if u > 0, then terminal a is at a higher potential than terminal b. The opposite is true, of course, if u < 0 一個(gè)理想的獨(dú)立源是產(chǎn)生完全獨(dú)立于其它電路變量的特定電壓或電流
30、的有源元 件。一個(gè)獨(dú)立電壓源是一個(gè)二端口元件, 如一個(gè)電池或一臺(tái)發(fā)電機(jī), 它們?cè)谄涠?部維持某個(gè)特定的電壓。該電壓完全獨(dú)立于流過(guò)元件的電流,在其端部具有 u 伏電壓的電壓源的符號(hào)如圖1 4 (a)所示,極性如圖所示,它表明a端比b端 高u伏。如果u>0,那么a端的電位高于b端,當(dāng)然,如果u<0,反之亦然。 In Fig.1-4(a), the voltage u may be time varying, or it may be constant, in which case we would probably label it U. Another symbol that is
31、often used for a constant voltage source, such as a battery with U volts across its terminals, is shown in Fig.1-4(b). In the case of constant sources we shall use Fig.1-4(a) and 1-4(b) interchangeably.在圖1 4(a)中,電壓u可以是隨時(shí)間而變化,或者可以是恒定的,在這種情 況下我們可能把它標(biāo)為U,對(duì)于恒定電壓源我們通常使用另一種符號(hào),例如在兩 端只有U伏電壓的電池組,如圖1 4 (b)所示。在
32、恒定源的情況下我們可以交 替地使用于圖1 4 (a)或圖1 4 (b)Wemight observe at this point that the polarity marks on Fig.1-4(b) are redundant since the polarity could be defined by the positions of the longer and shorter lines.我們可能已經(jīng)注意到這一點(diǎn),即圖1 4 (b)中的極性標(biāo)號(hào),是多余的因?yàn)槲覀?可以根據(jù)長(zhǎng)天線的位置符,確定電池極性An independent current source is a two-ter
33、minal element through which a specified current flows. The current is completely independent of the voltage across the element. The symbol for an independent current source is shown in Fig.1-5, where i is the specified current. The direction of the current is indicated by the arrow 一個(gè)獨(dú)立電流源是二端元件在兩端之間
34、特定的電流流過(guò), 該電流完全獨(dú)立于元件 兩端的電壓,一個(gè)獨(dú)立電流源的符合如圖 15所示。圖中 i 是特定電流,該電 流的方向由箭頭標(biāo)明Independent sources are usually meant to deliver power to the external circuit and not to absorb it. Thus if u is the voltage across the source and its current i is directed out of the positive terminal, then the source is delivering
35、 power, given by p = ui , to the external circuit. Otherwise it is absorbing power. For example, in Fig.1-6(a) the battery isdelivering 24 W to the external circuit. In Fig.1-6(b) the battery is absorbing 24 W, as would be the case when it is being charged.獨(dú)立源通常指的是向外電路釋放功率而非吸收功率,因此如果u是電源兩端的電壓而電流i直接從
36、其正端流出,那么該電源正在向?qū)﹄娐丰尫殴β?,由式p= ui算出。否則它就在吸收功率。例如圖1 6(a)中電池正在向外電路釋放功率 24w, 在圖1 6 (b)中,電池就在充電情況,吸收功率 24w。Dependent sourcesAn ideal dependent (or controlled) source is an active element in which the source quantity is controlled by another voltage or current.Dependent sources are usually designated by diam
37、ond-shaped symbols, as shown in Fig.1-7Since the control of the dependent source is achieved by a voltage or current of someother element in the circuit, and the source can be voltage or current, it follows that there are four possible types of dependent sources, namely:( 1) A voltage-controlled voltage source (VCVS).( 2) A current-controlled voltage source (CCVS). ( 3) A volta
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