circuit->Chapter 1 Basic Concepts

Chapter 1 Basic Concepts

• 1.1Circuit and Circuit Model
• 1 Electric circuit
• 2 Circuit model
• 1.2 Systems of Units
• 1.3 Charge and Current
• Charge
• Electric Current
• Direction of Current Flow
• Current reference directions
• Voltage
• Polarity of Voltage(or Reference direction)
• Summary
• 1.5 Power and Energy
• Power
• Passive Sign Convention(关联参考方向,无源符号约束)
• Active Sign Convention
• Power Absorbed or Supplied (Load or Source)
• law of conservation of energy
• 1.6 Circuit Elements
• Independent Voltage Sources
• Independent Current Sources
• Dependent (controlled) Sources

1.1Circuit and Circuit Model

1 Electric circuit

An elcectric circuit is an interconnection of ecectrical elements.
1)To gather,store,process,transport,and present information.
2)To distribute(分配) and convert(交换) energy between various forms.

2 Circuit model

Ideal circuit component:a mathematical model of an actual electric component.

Circuit model:A commonly used mathematical model for electric system.

$Actual~electrical~compont\\ \downarrow\\ Emphasize~the~main~character \& Neglect~the~left\\ \downarrow\\ Ideal~circuit~component$Actual electrical compont↓Emphasize the main character&Neglect the left↓Ideal circuit component
注:此处left是剩余的意思

Lumped elements→Lumped circuit(集总)
Actual scale of the circuit is much smaller than wavelength(波长) relating to the running frequency of the circuit

d<<λ(Lumped circuit abtraction) Distributive circuit(l<<λ)

Distributive circuit(l≈λ)

1.2 Systems of Units

SI(International System of Units)(国际单位制)
An international measurement language.
Adoped by the General Conference on Weights and Measures(国际计量大会 in 1960.
The six basic SI units

Quantity	Basic Unit	Symbol
Length	meter	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Thermodynamic temperature	kelvin	K
Luminous intensity(光强)	candela	cd

1.3 Charge and Current

Charge

is an electrical property of the atomic particles of which matter consists, measured in coulombs ©

Electric Current

is the time rate of change of
charge, measured in amperes (A)
$i(t)\overset{def}{=} \lim_{\Delta\rightarrow0}\frac{\Delta q}{\Delta t}= \frac{dq}{dt}$i(t)=defΔ→0lim​ΔtΔq​=dtdq​
A direct current (dc) is a current that remains
constant with time
An alternating current (ac) is a current that varies
sinusoidally with time

Direction of Current Flow

The direction of current flow is conventionally
taken as the direction of positive charge movement
注意是正电荷移动方向

Current reference directions

To specify the current in a conductor, we need both a reference direction and numerical value, which can be positive or negative.

To specify the current reference direction:
i >0 means the real direction is same to the reference direction
i <0 means the real direction is opposite to the reference direction

Voltage

Voltage (or potential difference) is the energy required to move a unit charge through an element, measured in volts (V)
$U\overset{def}{=} \frac{dW}{dq}$U=defdqdW​
dc voltage (produced by a battery)
ac voltage (produced by an electric generator)

Polarity of Voltage(or Reference direction)

To specify the voltage reference direction:

A plus-minus pair of algebraic signs indicates that + terminal is U volts positive with respect to - terminal.
1.U > 0 means the potential of + terminal is higher than potential of - terminal.
2.U < 0 means the potential of + terminal is lower than potential of - terminal.

1.U_AB > 0 means the potential of A is higher
than potential of B.
2.U_AB < 0 means the potential of A is lower
than potential of B.

Summary

➢Current and voltage are the two basic variables
in electric circuits
➢ Electric current is always through an element
➢ Electric voltage is always across the element or between two points
A voltage can exist between a pair of electrical terminals whether a current is flowing or not.

1.5 Power and Energy

Power

is the time rate of expending or absorbing energy.(Measured in watts(W))

Instantaneous power: time-varying quantity
How to distinguish between energy supplied to an element,
and energy that is supplied by the element itself?

Passive Sign Convention(关联参考方向,无源符号约束)

Passive sign convention is satisfied when current enters through the positive polarity of the voltage.

Active Sign Convention

Current enters through the negative polarity of the voltage.

Power Absorbed or Supplied (Load or Source)

Passive Sign Convention
P=ui Power absorbed by an element
P>0 absorbing positive power (absorbing power)
P<0 absorbing negative power (supplying power)

Active Sign Convention
P = ui Power supplied by an element
P>0 supplying positive power (supplying power)
P<0 supplying negative power (absorbing power)

方向一致正值=方向不一致负值:吸收能量
方向一致负值=方向不一致正值:放出能量

law of conservation of energy

$\sum p=0$∑p=0
Power absorbed=Power supplied

Energy is the capacity to do work, measured in joules (J).

The energy w absorbed or supplied by an element from time t0 to time t is
$w=\int_{t_0}^tp$w=∫t0​t​p

1.6 Circuit Elements

● When we speak of Circuit Elements, it is important to differentiate between the physical device itself and the mathematical model which we will use to analyze its behavior in a circuit.

● We will use the expression circuit element to refer to the mathematical model.

● All the simple circuit elements that we will consider can be classified according to the relationship of current through the element to the voltage across the element(VCR).

Independent Voltage Sources

Symbols for independent voltage source

(a) used for constant or time-varying voltage,
(b) used for constant voltage (dc).
An independent voltage source is characterized by a terminal voltage which is completely independent of the current through it.

The independent voltage source is an ideal source and does not represent exactly any real physical device, because the ideal source could theoretically deliver an infinite amount of energy from its terminals.
This idealized voltage source does, however, furnish a reasonable approximation for several practical voltage sources.

Independent Current Sources

Symbols for independent current source

The current through the independentcurrent source is completely independent of the voltage across it.

● The independent current source is at best a reasonable approximation for a physical element.
● In theory it can deliver infinite power from its terminals, because it produces the same finite current for any voltage across it, no matter how large that voltage may be.
● It is, however, a good approximation for many practical sources, particularly in electronic circuits.

Dependent (controlled) Sources

An ideal dependent (or controlled) source is an active element in which the source quantity is controlled by another voltage or current.
There are four kind of Controlled Sources, that is,

● current-controlled current source, CCCS;

● voltage-controlled current source, VCCS;

● voltage-controlled voltage source, VCVS;

● current-controlled voltage source, CCVS.