第一章第一篇sectiong

Two variables u(t) and i(t) are the most basic concepts in an electric circuit, they characterize the various relationships in an electric circuit

u(t)和i(t)这两个变量是电路中最基本的两个变量，它们刻划了电路的各种关系。

Charge and Current

The concept of electric charge is the underlying principle for explaining all electrical phenomena. Also, the most basic quantity in an electric circuit is the electric charge. Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C).

电荷和电流

电荷的概念是用来解释所有电气现象的基本概念。也即，电路中最基本的量是电荷。电荷是构成物质的原子微粒的电气属性，它是以库仑为单位来度量的。

We know from elementary physics that all matter is made of fundamental building blocks known as atoms and that each atom consists of electrons, protons, and neutrons. We also know that the charge e on an electron is negative and equal in magnitude to 1.60210×1019C, while a proton carries a positive charge of the same magnitude as the electron. The presence of equal numbers of protons and electrons leaves an atom neutrally charged.

我们从基础物理得知一切物质是由被称为原子的基本构造部分组成的，并且每个原子是由电子，质子和中子组成的。我们还知道电子的电量是负的并且在数值上等于1.602100×10-12C，而质子所带的正电量在数值上与电子相等。质子和电子数量相同使得原子呈现电中性。

We consider the flow of electric charges. A unique feature 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 energy

让我们来考虑一下电荷的流动。电荷或电的特性是其运动的特性，也就是，它可以从一个地方被移送到另一个地方，在此它可以被转换成另外一种形式的能量。

When a conducting wire is connected to a battery (a source of electromotive force), the charges are compelled to move; positive charges move in one direction while negative charges move in the opposite direction. This motion of charges creates electric current. It is conventional to take the currentflow as the movement of positive charges, 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 inventor. Although we now know that current in metallic conductors is due to negatively charged electrons, we will follow the universally 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 relationship among current i, charge q, and time t is

当我们把一根导线连接到某一电池上时(一种电动势源)，电荷被外力驱使移动；正电荷朝一个方向移动而负电荷朝相反的方向移动。这种电荷的移动产生了电流。我们可以很方便地把电流看作是正电荷的移动，也即，与负电荷的流动方向相反，如图1－1所示。这一惯例是由美国科学家和发明家本杰明－富兰克林引入的。虽然我们现在知道金属导体中的电流是由负电荷引起的，但我们将遵循通用的惯例，即把电流看作是正电荷的单纯的流动。于是电流就是电荷的时率，它是以安培为单位来度量的。从数学上来说，电流i、电荷q以及时间t之间的关系是：

The charge transferred between time t0 and t is obtained by integrating both sides of Eq. (1-1). We obtain

从时间t0到时间t所移送的电荷可由方程（1－1）两边积分求得。我们算得：

The way we define current as i in Eq. (1-l) 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

我们通过方程（1－1）定义电流的方式表明电流不必是一个恒值函数，电荷可以不同的方式随时间而变化，这些不同的方式可用各种数学函数表达出来。

电压，能量和功率

To move the electron in a conductor in a particular direction requires some work or energy transfer. This work is performed by an external electromotive force (emf), typically represented by the battery in Fig.l-1. This emf is also known as voltage or potential difference. The voltage uab between two points a and b in an electric circuit is the energy (or work) needed to move a unit charge from a to b; mathematically

在导体中朝一个特定的方向移动电荷需要一些功或者能量的传递，这个功是由外部的电动势来完成的。图1－1所示的电池就是一个典型的例子。这种电动势也被称为电压或电位差。电路中a、b两点间的电压等于从a到b移动单位电荷所需的能量（或所需做的功）。数学表达式为：

where w is 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 physicist Alessandro Antonio Volta (l745～l827), who invented the first voltaic battery. Thus, Voltage (or potential difference) is the energy required to move a unit charge through an element, measured in volts (V).

式中w是单位为焦耳的能量而q是单位为库仑的电荷。电压Uab是以伏特为单位来度量的，它是为了纪念意大利物理学家Alessandro Antonio Volta而命名的，这位意大利物理学家发明了首个伏达电池。于是电压（或电压差）等于将单位电荷在元件中移动所需的能量，它是以伏特为单位来度量的。

Fig.l-2 shows the voltage across an element (represented by a rectangular block ) connected to points a and b. The plus (+) and minus (-) signs are used to define reference direction or voltage polarity. The uab can be interpreted in two ways: ①point a is at a potential of uab volts higher than point b; ②the potential at point a with respect to point b is uab. It follows logically that in general

图1－2显示了某个元件（用一个矩形框来表示）两端a、b之间的电压。正号（＋）和负号（－）被用来指明参考方向或电压的极性，Uab可以通过以下两种方法来解释。1）在Uab伏特的电位中a点电位高于b点，2）a点电位相对于b点而言是Uab，通常在逻辑上遵循

Although 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 and energy. To relate power and energy to voltage and current, we recall from physics that power is the time rate of expending or absorbing energy, measured in watts (W). We write this relationship as

虽然电流和电压是电路的两个基本变量，但仅有它们两个是不够的。从实际应用来说，我们需要知道功率和能量。为了把功率和能量同电压、电流联系起来，我们重温物理学中关于功率是消耗或吸收的能量的时率，它是以瓦特为单位来度量的。我们把这个关系式写成：

Where p is power in watts (W), w is energy in joules (J), and t is time in seconds (s). From Eq. (1-1), Eq. (1-3), and Eq. (1-5), it follows that

式中p是以瓦特为单位的功率，w是以焦耳为单位的能量，t是以秒为单位的时间，从方程（1－1）、（1－3）和（1－5）可以推出

Because u and i are generally function of time, the power p in Eq. (1-6) is a time-varying quantity and is called the instantaneous power. The power absorbed or supplied by an element is the product of the voltage across the element and the current through it. If the power has a plus sign, power is being delivered to or absorbed by the element. If, on the other hand, the power has a minus sign, power is being supplied by the element. But how do we know when the power has a negative or a positive sign？

由于u和i通常是时间的函数，方程（1－6）中的功率p是个时间变量于是被称为瞬时功率，某一元件吸收或提供的功率等于元件两端电压和通过它的电流的乘积。如果这个功率的符号是正的，那么功率向元件释放或被元件吸收。另一方面，如果功率的符号是负的，那么功率是由元件提供的。但我们如何得知何时功率为正或为负？

Current direction and voltage polarity play a major role in determining the sign of power. It is therefore important that we pay attention to the relationship between current i and voltage u in Fig.1-3(a). The voltage polarity and current i direction must conform with those shown in Fig.1-3(a) in order for the power to have a positive sign. This is known as the passive sign convention. By the passive sign convention, current enters 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 ﹤ 0, as in Fig.1-3(b), the element is releasing or supplying power.

在我们确定功率符号时，电流的方向和电压的极性起着主要的作用，这就是我们在分析图1－3（a）所显示的电流i和电压u的关系时特别谨慎的重要原因。为了使功率的符号为正，电压的极性和电流的方向必须与图1－3（a）所示的一致。

这种情况被称为无源符号惯例，对于无源符号惯例来说，电流流进电压的正极。在这种情况下，p＝ui或ui>0，表明元件是在吸收功率。而如果p＝－ui或ui<0，如图1－3（b）所示时，表明元件是在释放或提供功率。

In fact, the law of conservation of energy must be obeyed in any electric circuit. For this reason, the algebraic sum of power in a circuit, at any instant of time, must be zero

事实上，在任何电路中必须遵循能量守恒定律。由于这个原因，任一电路中在任何瞬间功率的代数和必须等于零

This again confirms the fact that the total power supplied to the circuit must balance the total power absorbed. From Eq. (l-7), the energy absorbed or supplied by an element from time t0 to time t is

这再一次证明了提供给电路的功率必须与吸收的功率相平衡这一事实。从方程（1－7）可知，从时间t0到时间t被元件吸收或由元件提供的功率等于

Section2

An electric circuit is simply an interconnection of the elements. There are two types of elements found in electric circuits: passive elements and active elements. An active element is capable of generating energy while a passive element is not. Examples of passive elements are resistors, capacitors, and inductors. The most important active elements are voltage or current sources that generally deliver power to the circuit connected to them.

电路仅仅是元件之间的相互结合。我们发现电路中存在有两种元件：无源元件和有源元件。有源元件能够产生能量而无源元件却不能，无源元件有电阻、电容和电感器等。最重要的有源元件是通常向与它们相连的电路释放能量的电压和电流源。

Independent sources

An ideal independent source is an active element that provides a specified voltage or current that is completely independent of other circuit variables.

An independent voltage source is a two-terminal element, such as a battery or a generator, which maintains a specified voltage between its terminals. The voltage is completely independent of the current through the element. The symbol for a voltage source having u volts across its terminals 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

一个理想的独立源是产生完全独立于其它电路变量的特定电压或电流的有源元件。一个独立电压源是一个二端口元件，如一个电池或一台发电机，它们在其端部维持某个特定的电压。该电压完全独立于流过元件的电流，在其端部具有u伏电压的电压源的符号如图1－4（a）所示，极性如图所示，它表明a端比b端高u伏。如果u>0，那么a端的电位高于b端，当然，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 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.

在图1－4（a）中，电压u可以是随时间而变化，或者可以是恒定的，在这种情况下我们可能把它标为U，对于恒定电压源我们通常使用另一种符号，例如在两端只有U伏电压的电池组，如图1－4（b）所示。在恒定源的情况下我们可以交替地使用于图1－4（a）或图1－4（b）

We might 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.

我们可能已经注意到这一点，即图1－4（b）中的极性标号，是多余的因为我们可以根据长天线的位置符，确定电池极性

An independent current source is a two-terminal 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

一个独立电流源是二端元件在两端之间特定的电流流过，该电流完全独立于元件两端的电压，一个独立电流源的符合如图1－5所示。图中i是特定电流，该电流的方向由箭头标明

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 power, given by p = ui, to the external circuit. Otherwise it is absorbing power. For example, in Fig.1-6 (a) the battery is delivering 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.

独立源通常指的是向外电路释放功率而非吸收功率，因此如果u是电源两端的电压而电流i直接从其正端流出，那么该电源正在向对电路释放功率，由式p＝ui算出。否则它就在吸收功率。例如图1－6（a）中电池正在向外电路释放功率24w，在图1－6（b）中，电池就在充电情况，吸收功率24w。

Dependent sources

An 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 diamond-shaped symbols, as shown in Fig.1-7Since the control of the dependent source is achieved by a voltage or current of some other 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 voltage-controlled current source (VCCS).

（4）A current-controlled current source (CCCS).

Dependent sources are useful in modeling elements such as transistors, operational amplifiers and integrated circuits.

一个理想的受控源是一个有源元件，它的电源量是由另外一个电压和电流所控制。

受控源通常用菱形符号表明，如图1－7所示。由于控制受控源的控制量来自于电路中其他元件的电压或电流，同时由于受控源可以是电压源或电流源。由此可以推出四种可能的受控源类型，即

电压控制电压源（VCVS）

电流控制电压源（CCVS）

电压控制电流源（VCCS）

电流控制电流源（CCCS）

受控源在模拟诸如晶体管、运算放大器以及集成电路这些元件时是很有用的

It should be noted that an ideal voltage source (dependent or independent) will produce any current required to ensure that the terminal voltage is as stated, whereas an ideal current source will produce the necessary voltage to ensure the stated current flow. Thus an ideal source could in theory supply an infinite amount of energy. It should also be noted that not only do sources supply power to a circuit, but they can absorb power from a circuit too. For a voltage source, we know the voltage but not the current supplied or drawn by it. By the same token, we know the current supplied by a current source but not the voltage across it.

应该注意的是：一个理想电压源（独立或受控）可向电路提供以保证其端电压为规定值所需的任意电流，而电流源可向电路提供以保证其电流为规定值所必须的电压。还应当注意的是电源不仅向电路提供功率，他们也可从电路吸收功率。对于一个电压源来说，我们知道的是由其提供或所获得的电压而非电流，同理，我们知道电流源所提供的电流而非电流源两端的电压。