EE281-Electric Circuits

class: center, middle

# EE-281
# Thevenin-Norton Theorems
# Maximum Power Transfer

## Ozan Keysan

[ozan.keysan.me](http://ozan.keysan.me)

Office: C-113 <span class="meta">•</span> Tel: 210 7586

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# Thevenin's Theorem

### Any linear two-terminal circuit can be replaced by a voltage source and a series resistance.

<img src="./images/thevenin_equivalent.png" alt="Drawing" style="width: 400px;"/>
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# Thevenin's Theorem

### Procedure for finding thevenin equivalent

## 1- Find open circuit voltage (\\(V\_{th}=V\_{oc}\\))

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# Thevenin's Theorem

### Procedure for finding thevenin equivalent

## 1- Turn off independen sources and find equivalent circuit (\\(R\_{th}=R\_{eq}\\))

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# Example

### Find the thevenin equivalent of the circuit between a and b.

<img src="./images/thevenin_ex.png" alt="Drawing" style="width: 700px;"/>
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# Example-2

### Find the thevenin equivalent of the circuit between a and b.

<img src="./images/thevenin_ex2.png" alt="Drawing" style="width: 700px;"/>
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# Norton's Theorem

### Any linear two-terminal circuit can be replaced by a current source and a parallel resistance.

<img src="./images/norton_equivalent.png" alt="Drawing" style="width: 400px;"/>
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# Norton's Equivalent

#### Norton equivalent is the source transformed version of thevenin equivalent.

## \\(I\_N = \dfrac{V\_{TH}}{R\_{TH}}\\)

## \\(R\_N = R\_{TH}\\)
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### Short circuit current gives the norton current

## \\(I\_{SC} = I\_{N}\\)
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# Example

### Find the norton equivalent of the circuit between a and b.

<img src="./images/norton_ex.png" alt="Drawing" style="width: 700px;"/>
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# More exercise on Monday!

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# Why do they specifiy resistance of a speaker?

![](http://i01.i.aliimg.com/photo/v25/916996245/50mm_2inch_8_ohm_0_5W_dynamic.jpg)

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# Plot the Power in \\(R_L\\) as a function of resistance?

![](http://raise.spd.louisville.edu/EE220/images/L6-3.gif)

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#Maximum Power Transfer

![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Maximum_Power_Transfer_Graph.svg/800px-Maximum_Power_Transfer_Graph.svg.png)

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#Maximum Power Transfer

## \\(P\_{load}\\) is maximum when:

## \\(R\_{load}=R\_{thevenin}\\)

####[Proof](http://en.wikipedia.org/wiki/Maximum_power_transfer_theorem)
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# Any questions?

## You can download this presentation from: [keysan.me/ee281](http://keysan.me/ee281)