Dr. Holbert Lecture 4

EEE 202 1

Laila Rosemaizura Binti Yaakop 1

Nodal Analysis

Laila Rosemaizura Binti Yaakop 2

Steps of Nodal Analysis

1. Choose a reference (ground) node.

2. Assign node voltages to the other nodes.

3. Apply KCL to each node other than the

reference node; express currents in terms

of node voltages.

4. Solve the resulting system of linear

equations for the nodal voltages.

Dr. Holbert Lecture 4

EEE 202 2

Laila Rosemaizura Binti Yaakop 3

Example: A Summing Circuit

The output voltage V of this circuit is proportional to the sum of the two input

currents I1 and I2

This circuit could be useful in audio applications or in instrumentation

The output of this circuit would probably be connected to an amplifier

Laila Rosemaizura Binti Yaakop 4

1. Reference Node

The reference node is called the ground node

where V = 0

+

V 500

500

1k

500

500I1 I2

Dr. Holbert Lecture 4

EEE 202 3

Laila Rosemaizura Binti Yaakop 5

Steps of Nodal Analysis

1. Choose a reference (ground) node.

2. Assign node voltages to the other

nodes.

3. Apply KCL to each node other than the

reference node; express currents in terms

of node voltages.

4. Solve the resulting system of linear

equations for the nodal voltages.

Laila Rosemaizura Binti Yaakop 6

2. Node Voltages

V1, V2, and V3 are unknowns for which we

solve using KCL

500

500

1k

500

500I1 I2

1 2 3

V1 V2 V3

Dr. Holbert Lecture 4

EEE 202 4

Laila Rosemaizura Binti Yaakop 7

Steps of Nodal Analysis

1. Choose a reference (ground) node.

2. Assign node voltages to the other nodes.

3. Apply KCL to each node other than the

reference node; express currents in

terms of node voltages.

4. Solve the resulting system of linear

equations for the nodal voltages.

Laila Rosemaizura Binti Yaakop 8

Currents and Node Voltages

500

V1500V1 V2

500

21 VV

500

1V

Dr. Holbert Lecture 4

EEE 202 5

Laila Rosemaizura Binti Yaakop 9

3. KCL at Node 1

500

500I1

V1 V2

500500

1211

VVVI

Laila Rosemaizura Binti Yaakop 10

3. KCL at Node 2

500

1k

500 V2 V3V1

0500k1500

32212 VVVVV

Dr. Holbert Lecture 4

EEE 202 6

Laila Rosemaizura Binti Yaakop 11

3. KCL at Node 3

2323

500500I

VVV500

500

I2

V2 V3

Laila Rosemaizura Binti Yaakop 12

Steps of Nodal Analysis

1. Choose a reference (ground) node.

2. Assign node voltages to the other nodes.

3. Apply KCL to each node other than the

reference node; express currents in terms

of node voltages.

4. Solve the resulting system of linear

equations for the nodal voltages.

Dr. Holbert Lecture 4

EEE 202 7

Laila Rosemaizura Binti Yaakop 13

+

V 500

500

1k

500

500I1 I2

4. Summing Circuit Solution

Solution: V = 167I1 + 167I2

Laila Rosemaizura Binti Yaakop 14

A Linear Large Signal

Equivalent to a Transistor

5V

100Ib

+

Vo

50

Ib

2k1k+

+

0.7V

Dr. Holbert Lecture 4

EEE 202 8

Laila Rosemaizura Binti Yaakop 15

Steps of Nodal Analysis

1. Choose a reference (ground) node.

2. Assign node voltages to the other nodes.

3. Apply KCL to each node other than the

reference node; express currents in terms

of node voltages.

4. Solve the resulting system of linear

equations for the nodal voltages.

Laila Rosemaizura Binti Yaakop 16

Linear Large Signal Equivalent

5V100Ib

+

Vo

50

Ib

2k

1k

0.7V

1

2 3 4

V1V2 V3 V4

+

+

Dr. Holbert Lecture 4

EEE 202 9

Laila Rosemaizura Binti Yaakop 17

Steps of Nodal Analysis

1. Choose a reference (ground) node.

2. Assign node voltages to the other nodes.

3. Apply KCL to each node other than the

reference node; express currents in terms

of node voltages.

4. Solve the resulting system of linear

equations for the nodal voltages.

Laila Rosemaizura Binti Yaakop 18

KCL @ Node 4

k2100

50

443 VIVV

b

100Ib

+

Vo

50

Ib

2k

1k+

0.7V

1

2 3 4

V1V2 V3 V4

5V

+

Dr. Holbert Lecture 4

EEE 202 10

Laila Rosemaizura Binti Yaakop 19

The Dependent Source

We must express Ib in terms of the node voltages:

Equation from Node 4 becomes

k1

21 VVIb

0k2k1

10050

42143 VVVVV

Laila Rosemaizura Binti Yaakop 20

How to Proceed?

The 0.7-V voltage supply makes it impossible to apply KCL to nodes 2 and 3,

since we dont know what current is passing through the supply

We do know that

V2 V3 = 0.7 V

The above is a needed constraint equation

Dr. Holbert Lecture 4

EEE 202 11

Laila Rosemaizura Binti Yaakop 21

100Ib

+

Vo

50Ib

2k

1k

0.7V

1

4

V1V2 V3 V4

+

+

050k1

4312 VVVV

KCL at

Supernode