Presented by Byoung-Kuk Lee, Ph. D., Senior IEEE

Presented by Byoung-Kuk Lee, Ph. D., Senior IEEE

Energy Mechatronics Lab.

College of Information and Communication Eng.

Sungkyunkwan University Tel: +82-31-299-4581 Fax: +82-31-299-4612 http://seml.skku.ac.kr EML: bkleeskku@skku.edu

Circuit Elements

2.1 Voltage and Current Sources

 Ideal voltage source: a circuit element to maintain a prescribed voltage regardless of the current through the terminals

 Ideal current source: a circuit element to maintain a prescribed current regardless of the voltage across the terminals

 Types of electrical sources

• Independent source

The value of voltage or current is not influenced by any other current or voltage elsewhere in the circuit.

• Dependent source

The value of voltage or current is determined by the value of current or voltage elsewhere in the circuit.

Circuit Elements

Independent Sources

An ideal independent voltage source

An ideal independent current source

# Current through the terminals is not known

# Voltage across the terminals is not known Fig. 2.1

Circuit Elements

Dependent Sources

a. An ideal dependent voltage -controlled voltage source b. An ideal dependent current -controlled voltage source c. An ideal dependent voltage -controlled current source d. An ideal dependent current -controlled current source Fig. 2.2

 Active element: a device that can generate electric energy

(e.g., electric sources)

 Passive element: a device that cannot generate electric energy (e.g., R, L, C)

Circuit Elements

2.2 Electrical Resistance (1)

 Resistance: the capacity of materials to impede the flow of current

 A resistor constrains its voltage and current to be proportional to each other. (Ohm's law)

If the current flow in the resistor is in the direction of

the voltage drop across it

If the current flow in the resistor is in the direction of

the voltage rise across it

iR v 

R i  v

iR v  

R i   v

[Passive sign convention]

Circuit Elements

2.2 Electrical Resistance (2)

 Conductance: the reciprocal of resistance

G R 1



• Power in a resistor in terms of current

• Power in a resistor in terms of current:

 

R i

i iR vi p





  

R i

i iR vi p













R p v



Circuit Elements

2.3 Construction of Circuit Model

Ex. 2.5

4

v  iR  i

Circuit Elements

2.4 Kirchhoff's Laws

 Circuits are described by nodes and closed paths.

 Node: a point where two or more circuit elements meet

 Closed path (loop): a loop traced through connecting elements, starting and ending at the same node and encountering

intermediate nodes only once each.

 When just two elements connect at a single node, they are said to be in series. (all nodes are in series.)

Node Closed

loop

Fig. 2.15

Circuit Elements

KCL and KVL

 Kirchhoff’s current law (KCL)

The algebraic sum of all the currents at any node in a circuit equals zero.

# positive sign: a current leaving a node negative sign: a current entering a node

 Kirchhoff’s voltage law (KVL)

The algebraic sum of all the voltages around any closed path in a circuit equals zero.

# positive sign: a voltage drop between two nodes negative sign: a voltage rise between two nodes

Circuit Elements

Application of KCL and KVL

1 1

1

i R

v 

c c

c

i R

v 

l l

l

i R

v 

1

  0





l

v v v

v

[Ohm's law] [KCL]

1

 0

 i

i

1

 i

 0

i

 0



 i

i

 0



l

i

i

[KVL]

7 unknown parameters

Only three are independent

All nodes are in series l c

s

i i i

i 

  

Circuit Elements

Ex 2.8

Circuit Elements

AP 2.7(a) & AP 2.8(a)

Circuit Elements

2.5 Analysis of Circuit with Dependent Sources

 Two independent unknown variables are

0 20

5

500   

 i

i

0

5  



 i

i

i

KVL

KCL at node b

i

i

• Choosing a good node in KCL or an appropriate closed loop in KVL will reduce the number and complexity of equations to be solved.

Circuit Elements

AP 2.10

Circuit Elements

Homework #1

• Problems: 1.24, 1.26, 2.18, 2.28

• Due Date: next week class

• Where: 21502