Circuit Network Analysis - [Chapter1] Basic Circuit Laws

Network Analysis

Chapter 1 Basic Circuit Laws

Chien-Jung Li

Department of Electronic Engineering

National Taipei University of Technology

In This Chapter

• Fast reviews of some basic circuit laws

• Historical points of view

• Reviews of circuit analysis methods

Department of Electronic Engineering, NTUT

(such as mesh-current and node-voltage methods,

Thevenin’s and Norton’s theorem, and superposition

principles)

2/32

Circuit Quantities & Prefixes

QuantityQuantityQuantityQuantity SymbolsSymbolsSymbolsSymbols UnitUnitUnitUnit Abbr.Abbr.Abbr.Abbr.

Time (時間) t second (秒) s (sec)

Energy (能量) w, W joule (焦耳) J

Power (功率) p, P watt (瓦特) W

Charge (電荷) q, Q coulomb (庫倫) C

Current (電流) i, I ampere (安培) A

Voltage (電壓) v, V volt (伏特) V

Resistance (電阻) R ohm (歐姆) Ω

Conductance (電導) G siemens (姆歐) S

Inductance (電感) L henry (亨利) H

Capacitance (電容) C farad (法拉) F

Impedance (阻抗) Z (Z) ohm (歐姆) Ω

Reactance (電抗) X ohm (歐姆) Ω

Admittance (導納) Y (Y) siemens (姆歐) S

Susceptance (電受) B siemens (姆歐) S

Frequency (cyclic) (頻率) f hertz (赫茲) Hz

Frequency (radian) (頻率) ω radians/second rad/s

ValueValueValueValue PrefixPrefixPrefixPrefix Abbr.Abbr.Abbr.Abbr.

10-18 atto a

10-15 femto f

10-12 pico p

10-9 nano n

10-6 micro µ

10-3 milli m

103 kilo k

106 mega M

109 giga G

1012 tera T

Department of Electronic Engineering, NTUT3/32

Functional Notations (I)

• V , I : 電壓, 電流

• VDC , IDC : 直流電壓, 直流電流

• VAC , IAC : 交流電壓, 交流電流

• V (t), I (t) : 時變電壓, 時變電流

• v (t), i (t) : 時變電壓, 時變電流


Functional Notations (II)

di

Di

DI : 表示直流: 表示交流, 小訊號分析: 表示(直流+交流), 大訊號分析


• 電路分析時的慣用表示法::::

0 1s 2s 3s 4st

DI 直流

0 1s 2s 3s 4st

di 交流(小訊號分析)

0 1s 2s 3s 4st

DI = +D D di I i

直流+交流(大訊號分析)

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Energy and Power (I)

• Energy: capacity for, or the actual performance of work

JamesJamesJamesJames PrescottPrescottPrescottPrescott JouleJouleJouleJoule (1818–

1889) was an English physicist,

born in Salford, Lancashire.

Joule studied the nature of

heat, and discovered its

relationship to mechanical

work. This led to the theory of

conservation of energy, which

led to the development of the

first law of thermodynamics.

The SI derived unit of energy,

the joule, is named after him.(from Wikipedia)

United Kingdom (UK)

1焦耳=施加1牛頓作用力於物體使之經過1米距離所需的能量=移動1庫侖電荷通過1伏特電壓差所需做的功=產生(釋放)1瓦特功率1秒所需做的功


Energy and Power (II)

• Power: rate of performing work or the rate of energy change

JamesJamesJamesJames WattWattWattWatt (1736–1819)

was a Scottish inventor

and mechanical engineer

whose improvements to

the Newcomen steam

engine were fundamental

to the changes brought by

the Industrial Revolution in

both the Kingdom of Great

Britain and the world. The

SI unit of power, the watt,

was named after him.(from Wikipedia)

Scotland

( ) ( )=

dw tp t

dt( ) ( )= ∫

2

1

t

tw t p t dt

1瓦特 = 1焦耳/1秒


Current and Voltage

• Current is a measure of the rate of charge through acircuit. A flow of 1 coulomb/sec. past a certain point in acircuit constitutes a current of 1 ampere, or equivalently,1A = 1 C/s.

( ) ( )=

dq ti t

dt( )= ∫

2

112

t

tQ i t dt

Q12 is the total charge passing over interval from t1 to t2

• Voltage is the electrical pressure between two points inan electrical circuit. It is always measured between twopoints. The SI unit of voltage, the volt, was named afterthe Italian physicist Alessandro Volta.


Coulomb, Ampere, and Volta

CharlesCharlesCharlesCharles----AugustinAugustinAugustinAugustin dededede CoulombCoulombCoulombCoulomb

(1736–1806) was a French

physicist. He is best known for

developing Coulomb's law, the

definition of the electrostatic

force of attraction and

repulsion. The SI unit of charge,

the coulomb, was named after

him. (from Wikipedia)

AndréAndréAndréAndré----MarieMarieMarieMarie AmpèreAmpèreAmpèreAmpère (1775–

1836) was a French physicist

and mathematician who is

generally regarded as one of

the main discoverers of

electromagnetism. The SI unit

of measurement of electric

current, the ampere, is named

after him. (from Wikipedia)

CountCountCountCount AlessandroAlessandroAlessandroAlessandro GiuseppeGiuseppeGiuseppeGiuseppe AntonioAntonioAntonioAntonio

AnastasioAnastasioAnastasioAnastasio VoltaVoltaVoltaVolta (1745–1827) was an

Italian physicist known especially for

the development of the first electric

cell in 1800. (from Wikipedia)


Resistance and Conductance

• Resistance is the opposition to current flow present in allconducting material. A lump package of resistance iscalled a resistor. The symbol for resistance is R, and theunit is ohm (Ω). An alternate way to characterizeresistance is through the concept of conductance, G,and unit is the siemens.

= 1G

R= 1

RG


Ohm’s Law and Resistive Power

GeorgGeorgGeorgGeorg SimonSimonSimonSimon OhmOhmOhmOhm (1789–1854) was

born at Erlangen, Bavaria. He has

exerted an important influence on the

development of the theory and

applications of electric current. Ohm's

name has been incorporated in the

terminology of electrical science in

Ohm's Law (which he first published

in Die galvanische Kette...), the

proportionality of current and voltage

in a resistor, and adopted as the SI

unit of resistance, the ohm (symbol

Ω). (from Wikipedia)

( ) ( )v t R i t= ⋅ ( ) ( ) ( )v ti t G v t

R= = ⋅

( )i t

R( )v t( ) ( ) ( ) ( ) ( )22 v t

p t i t v t R i tR

= ⋅ = ⋅ =


Circuit Models – Active Components

• Independent Sources:

( )sv t ( )si t

1v 1A v⋅ 1i 1mR i⋅

1v 1mg v⋅ 1i 1iβ ⋅

• Dependent Sources:

VCVS ICVS (CCVS)

VCIS

(VCCS)ICIS (CCCS)


Circuit Models – Passive Components

• Resistor (R), Inductor (L), and Capacitor (C)

RRRR LLLL CCCC


Equivalent Resistance

• Resistors in Series

• Resistors in Parallel


= + + +⋯1 2eq nR R R R

= + + +⋯1 2

1 1 1 1

eq nR R R R

= + + +⋯1 2eq nG G G G

eqR

1R2R

nR

1R2RnReqR

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Voltage Divider


( ) ( )=+

00

0 1s

Rv t v t

R R

0R

1R

( )sv t ( )0v t

( )1v t

( ) ( )=+

11

0 1s

Rv t v t

R R

15/32

Current Divider


( ) ( )=+

10

1 0s

Ri t i t

R R

0R1R( )si t( )0i t( )1i t

( ) ( )=+

01

1 0s

Ri t i t

R R

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Kirchoff’s Voltage and Current Laws

• KVL: The algebraic sum of the voltages around a closedloop is zero.

GustavGustavGustavGustav RobertRobertRobertRobert KirchhoffKirchhoffKirchhoffKirchhoff (1824–1887) was a German

physicist who contributed to the fundamental understanding

of electrical circuits, spectroscopy, and the emission of black-

body radiation by heated objects. He coined the term "black

body" radiation in 1862, and two sets of independent

concepts in both circuit theory and thermal emission are

named "Kirchhoff's laws" after him, as well as a law of

thermochemistry. The Bunsen–Kirchhoff Award for

spectroscopy is named after him and his colleague, Robert

Bunsen.

0nn

v =∑

• KCL: The algebraic sum of the currents at a node zero.

=∑ 0nn

i


Kirchoff’s Voltage Law (KVL)

1v

2v 3v

4v

5v

x

1 2 3 4 5 0v v v v v− + + − + =


Kirchoff’s Current Law (KCL)

1i

2i

3i

4i5i

1 2 3 4 5 0i i i i i− + − − + =


Historical Points of View (I)

Watt 1736-1819Coulomb 1736–1806

Ampere 1775 –1836Volta 1745 –1827

Ohm 1789 –1854

Kirchhoff 1824 –1887

1700 19001800

Joule 1818-1889

1709

鋼琴1752

避雷針1783

降落傘熱氣球

1769

蒸汽機

1767

汽水 1791

輪船

1800

電池

1804

鐵路機車

1807

蒸汽船

1816

聽診器

1821

電動機

1826

內燃機

1831

電報發電機

1834

冰箱

1835

左輪手槍

1836

縫紉機

1843

冰淇淋

1801

紡織機

1860

自走魚雷

1852

載人電梯

1865

鐵絲網

1869

吸塵器

1870

汽油引擎

1876

擴音器

1877

留聲機麥克風

1882

電風扇

1889

汽車

1893

無線電

1898

遙控器


1859 達爾文物種起源出版

Historical Points of View (II)

1700 19001800

1774-1783

美國獨立戰爭

1774

大陸會議

1776

傑佛遜獨立宣言,

美國成立1789

美國憲法生效華盛頓第一任總統

1861

南北戰爭爆發

1865

林肯遇刺身亡

-1722 康熙末期 1735-95 乾隆 1795-1820嘉慶

1820-50道光

1850-61咸豐

1856-75同治

1871-1908光緒1722-35 雍正

1754 吳敬梓歿

1763 曹雪芹歿

1796-1804

白蓮教起義

1805 紀曉嵐歿

1840-42 第一次鴉片戰爭

1851 洪秀全成立太平天國

1852 曾國藩成立湘軍

1856-60 第二次鴉片戰爭, 英法

聯軍

1861 慈禧垂簾聽政

1865 李鴻章成立江南製造局

1866左宗棠成立福州造船廠

1885劉銘傳任台灣巡撫

1894中日甲午戰爭

1898譚嗣同,

康有為戌戊變法

1900義和團起義

1784 鹿港開港

1810清廷設噶瑪蘭廳(宜蘭)

1863 雞籠開港

1864 打狗開港

1874 牡丹社事件

1884 中法戰爭, 砲轟基隆

1885 台灣脫離福建省, 為台灣省

1887 台灣鐵路

1760 英國工業革命開始

1789-1794 法國大革命

1795 法王路易十六上斷頭台

1799-1814 拿破崙王朝

1871 德意志帝國成立 1889 巴黎艾菲爾鐵塔

1895馬關條約


Mesh Current Method (I)

1i 2i 3i

4i 5i 6i

1i 2ibbi


• Loop current assumed in every mesh. (apply KVL)

• A given mesh current may not equal to the actual current.

= −1 2bbi i i

22/32

Mesh Current Method (II)


1I 2I 3I

( )− + + − − =1 1 220 6 5 25 0I I I

( ) ( )+ − + − + − + =2 1 2 2 325 5 3 32 2 6 0I I I I I

( )− + − + + + =3 2 3 36 2 4 7 49 0I I I I

• 3 meshes, 3 loop currents, 3 KVL equations:

• The currents are determined:

= = = −1 2 35A, 2A, 3AI I I23/32

Node Voltage Method (I)

1v 2v 3v

4v 5v 6v

7v 8v


• Firstly define a common or ground node. Such a node may not

correspond to the actual ground.

• (n+1) nodes are reduced to n nodes when one ground node is

designated. (then, apply KCL)

24/32

Node Voltage Method (II)


1V 2V 3V

( )−− + + + + + =1 21 110 32

5 03 6 5 3 3

V VV V

• 3 nodes, 3 node voltages, 3 KCL equations:

= − = =1 2 310V, 16V, 28VV V V

( ) ( )− −− + − + + =2 1 2 3232

3 03 3 2 4

V V V VV

( )−+ − =3 2 3 7 0

4 7

V V V

such that

25/32

Thevenin’s Theorem

( )tv t

eqR


• Thevenin’s theorem states that:

All effects of any linear circuit external to two reference terminals can be

completely predicted from a model consisting of a single ideal voltage in

series with a single resistor.

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Norton’s Theorem


• Norton’s theorem states that:

All effects of any linear circuit external to two reference terminals can be

completely predicted from a model consisting of a single ideal current

source in parallel with a single resistor.

( ) ( )= t

neq

v ti t

R

( )ni teqR

( ) ( )=t eq nv t R i t

• If the Thevenin’s model is known, the Norton current is

• If the Norton’s model is known, the Thevenin voltage is

27/32

“Equivalent” Model

• When a complex circuit is replaced by a Thevenin or aNorton model, the model predicts correct resultsexternal to the reference terminals only.

• The internal action of original circuit has been “lost,” andany internal calculations in the Thevenin or Nortonmodel are generally meaningless.

• The models are useful when there is a portion of acircuit that remains fixed for which there is little interestin the internal behavior nut in which the effect on anexternal circuit is to be studied under varying conditions.

• Equivalent does not mean Identical.


Example of Thevenin’s Model


Resistive

linear circuit

(energized)

• Determine open-circuit voltage

• De-energize all internal sources and determined

Resistive

linear circuit

(de-energized)

= =+6

12 8 V6 3ocV

= + = Ω +

15 7

1 13 6

eqR

=t ocv v

ocv

eqR

eqR

• Equivalent model:

29/32

Example of Norton’s Model


sci

• Determine short-circuit current

• De-energize all internal sources and determined

• Equivalent model:

=n sci i

( )= ⋅ =+ +

12 6 8 A

3 6 || 5 6 5 7sci

eqR

= + = Ω +

15 7

1 13 6

eqR

30/32

De-energize Sources

• Voltage source short-circuit

Since an ideal voltage source does not care how much current flows through it.

• Current source open-circuit

Since an ideal current source does not care how much voltage across it’s terminals.


de-energizing

de-energizing

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Principle of Superposition


= + +1 2 3oc oc oc ocv v v v1ocv

2ocv

3ocv

ocv

• Any voltage or current response

in a linearlinearlinearlinear circuit resulting from

several voltage and/or current

sources may be determined by

the combinationcombinationcombinationcombination ofofofof thethethethe effecteffecteffecteffect ofofofof

eacheacheacheach sourcesourcesourcesource.

32/32

Circuit Network Analysis - [Chapter1] Basic Circuit Laws

Engineering

Transcript of Circuit Network Analysis - [Chapter1] Basic Circuit Laws