EE-281 Superposition & Homogeneity

Ozan Keysan

ozan.keysan.me

Office: C-113 • Tel: 210 7586

1 / 19

Linear Circuits

A circuit is linear if it satifies:

2 / 19

Linear Circuits

A circuit is linear if it satifies:

Superposition (Additive) Property:

$f(a + b) = f(a) + f(b)$

2 / 19

Linear Circuits

A circuit is linear if it satifies:

Superposition (Additive) Property:

$f(a + b) = f(a) + f(b)$
Homogeneity (Scaling) Property:

$f(Ka) = K f(a)$

2 / 19

Superposition

Drawing

3 / 19

Homogeneity

Drawing

4 / 19

5 / 19

Superposition in Circuit AnalysisThe voltages and currents can be found as the corresponding values obtained by assuming only one source at a time, with all other sources turned off.6 / 19

Steps for Superposition Method1. Turn off all independent sources except one.7 / 19

Steps for Superposition Method1. Turn off all independent sources except one.2. Calculate the output (voltage or current) due to that source.7 / 19

Steps for Superposition Method1. Turn off all independent sources except one.2. Calculate the output (voltage or current) due to that source.3. Repeat Step 1 for each independent source.7 / 19

Steps for Superposition Method1. Turn off all independent sources except one.2. Calculate the output (voltage or current) due to that source.3. Repeat Step 1 for each independent source.4. Add the contribution of each source to find the total output.7 / 19

How to turn of Sources?

Voltage Source

Drawing

8 / 19

How to turn of Sources?

Current Source

Drawing

9 / 19

Example

Solve the following circuit using superposition method:

Drawing

10 / 19

Example

Drawing

11 / 19

Example

Drawing

12 / 19

Source TransformationsCurrent and Voltage Sources can be Transformed13 / 19

Source Transformations

Current and Voltage Sources can be Transformed

Plot V-I Characteristics of the following circuits

13 / 19

Source Transformations

Current and Voltage Sources can be Transformed

Plot V-I Characteristics of the following circuits

13 / 19

From Voltage Source to Current Source

14 / 19

From Current Source to Voltage Source

15 / 19

Simplify and Solve the Circuit

Drawing

16 / 19

Simplify and Solve the Circuit

Drawing

17 / 19

Simplify and Solve the Circuit

Drawing

18 / 19

Any questions?

You can download this presentation from: keysan.me/ee281

19 / 19

Help

Keyboard shortcuts

↑, ←, Pg Up, k

Go to previous slide

↓, →, Pg Dn, Space, j

Go to next slide

Home

Go to first slide

End

Go to last slide

Number + Return

Go to specific slide

b / m / f

Toggle blackout / mirrored / fullscreen mode

Clone slideshow

Toggle presenter mode

Restart the presentation timer

?, h

Toggle this help

EE-281 Superposition & Homogeneity

Ozan Keysan

Linear Circuits

Linear Circuits

Superposition (Additive) Property:

f(a+b)=f(a)+f(b)f(a + b) = f(a) + f(b)

Linear Circuits

Superposition (Additive) Property:

f(a+b)=f(a)+f(b)f(a + b) = f(a) + f(b)

Homogeneity (Scaling) Property:

f(Ka)=Kf(a)f(Ka) = K f(a)

Superposition

Homogeneity

Superposition in Circuit Analysis

The voltages and currents can be found as the corresponding values obtained by assuming only one source at a time, with all other sources turned off.

Steps for Superposition Method

1. Turn off all independent sources except one.

Steps for Superposition Method

1. Turn off all independent sources except one.

2. Calculate the output (voltage or current) due to that source.

Steps for Superposition Method

1. Turn off all independent sources except one.

2. Calculate the output (voltage or current) due to that source.

3. Repeat Step 1 for each independent source.

Steps for Superposition Method

1. Turn off all independent sources except one.

2. Calculate the output (voltage or current) due to that source.

3. Repeat Step 1 for each independent source.

4. Add the contribution of each source to find the total output.

How to turn of Sources?

Voltage Source

How to turn of Sources?

Current Source

Example

Solve the following circuit using superposition method:

Example

Example

Source Transformations

Current and Voltage Sources can be Transformed

Source Transformations

Current and Voltage Sources can be Transformed

Plot V-I Characteristics of the following circuits

Source Transformations

Current and Voltage Sources can be Transformed

Plot V-I Characteristics of the following circuits

From Voltage Source to Current Source

From Current Source to Voltage Source

Simplify and Solve the Circuit

Simplify and Solve the Circuit

Simplify and Solve the Circuit

Any questions?

You can download this presentation from: keysan.me/ee281

Linear Circuits

Help

$f(a + b) = f(a) + f(b)$

$f(a + b) = f(a) + f(b)$

$f(Ka) = K f(a)$