ECE 1270 Introduction to Electric Circuits Suketu Naik

0ECE 1270: Introduction to Electric Circuits

Lecture 6:

Advanced Nodal

Analysis

Chapter 4

Techniques of Circuit

Analysis: Sections 4.3,4.4

ECE 1270 Introduction to Electric Circuits Suketu Naik

1

____ Controlled

Voltage Source

____ Controlled

Voltage Source____ Controlled

Current Source____ Controlled

Current Source

Dependent Sources and Their Applications

Example:

MOSFET Switch

Example:

Voltage Amplifier

Example:

Transimpedance

Amplifier

Example:

Bipolar Junction

Transistor

ECE 1270 Introduction to Electric Circuits Suketu Naik

2Node Voltage Method: Dependent Sources

Find unknown voltages by summing the currents leaving each node

Step2: Define Node

Voltages

Step1: Label Nodes

Example 4.3

ECE 1270 Introduction to Electric Circuits Suketu Naik

3Node Voltage Method: Independent Sources

Step3: Write

Current Leaving

Each Branch

Step4: Solve

Simultaneous

Equations in

Standard Form

Passive Sign

Convention

02

8

10

0

5

020

0

52

20

2212

1211

ivvvv

vvvvSubstitute iϕ with

5

21 vvi

010

13

10

1

5

1

10

8

5

1

105

1

20

1

5

1

2

1

21

21

vv

vv Find the

unknown

voltage or

current

ECE 1270 Introduction to Electric Circuits Suketu Naik

4AP4.3a: Find power associated with each source

Simultaneous Equations:

Passive Sign

Convention

Solution

p50V=

p5A=

p3 i1=

ECE 1270 Introduction to Electric Circuits Suketu Naik

5

Super Node

ECE 1270 Introduction to Electric Circuits Suketu Naik

6Supernode

Combine nodes to form a

supernode

Circuit with voltage

source between two

nodes

ECE 1270 Introduction to Electric Circuits Suketu Naik

7Fig. 4.13: Voltage Source Between Nodes

Step2: Define Node

Voltages

Step1: Label Nodes

ECE 1270 Introduction to Electric Circuits Suketu Naik

8Fig. 4.13: Voltage Source Between Nodes

Step3: Write

Current Leaving

Each Branch

Passive Sign

Convention

At Node 2

At Node 3

Now add them together (or isolate i and

equate them) to get Eq.1: Step4: Solve

Simultaneous

Equations in

Standard FormWhat about Eq. 2?

ECE 1270 Introduction to Electric Circuits Suketu Naik

9Alternative: Create a Supernode

- Now we can write Eq.1 directly as …

- What about Eq. 2?

ECE 1270 Introduction to Electric Circuits Suketu Naik

10AP4.5 (create super node): Find v

Simultaneous Equations:

Passive Sign

Convention

Solution

v=

ECE 1270 Introduction to Electric Circuits Suketu Naik

11AP4.6: Find v1

Simultaneous Equations:

Passive Sign

Convention

Solution

v1=

ECE 1270 Introduction to Electric Circuits Suketu Naik

12AP4.4: Find vo

Simultaneous Equations:

Passive Sign

Convention

Solution

vo=

ECE 1270 Introduction to Electric Circuits Suketu Naik

13Example: Transistor Circuit* *=if time permits

Note: When a signal level is low, it can be passed through an amplifier to increase its level.

An amplifier can be built from BJT transistor. The following schematic represents a part of the amplifier.

See page 98-99 for equations

Find Vo if Vcc=15 V, R1=100 kΩ, R2=50 kΩ, Rc=10 kΩ, RE=4.25 kΩ, β=300