EE281-Electric Circuits

class: center, middle

# EE-281
# OPAMPs

## Ozan Keysan

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

Office: C-113 <span class="meta">•</span> Tel: 210 7586
---
#A Typical Audio System

<img src="http://www.r3vlimited.com/Media/e30theproject/Pictures/Mods/Layout.jpg" alt="Drawing" style="width: 400px;"/>
---
#Operational Amplifiers (OPAMPs)
![](http://www.tandyonline.co.uk/media/catalog/product/cache/1/image/9df78eab33525d08d6e5fb8d27136e95/7/4/741-op-amp.png)

---
#Operational Amplifiers (OPAMPs)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/e/e0/OpAmpTransistorLevel_Colored_Labeled.svg/750px-OpAmpTransistorLevel_Colored_Labeled.svg.png)

[Inside OPAMPS](http://www.righto.com/2015/10/inside-ubiquitous-741-op-amp-circuits.html?m=1)

---
#Operational Amplifiers (OPAMPs)

![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Op-Amp_Internal.svg/600px-Op-Amp_Internal.svg.png)

---
#Typical OPAMP values

|  | Typical Values| Ideal Values |
| -- | -- | -- |
| G (Open-loop gain) | \$10^5-10^8\; \Omega\$ | \$\infty\$ |
| Rin (Input Resistance) | \$10^5-10^{13}\; \Omega\$ | \$\infty\$ |
| Rout (Output Resistance) | \$10-100\; \Omega\$ | \$0\$ |

---
# Assumptions

--
- ## Infinite Open-Loop Gain (\$G=\infty\$)

--
- ## Infinite Input Resistance (\$R\_{in}=\infty\$)

--
- ## Zero Output Resistance (\$R\_{out}=0\$)

--
## Therefore,
- ## Zero Input Currents (\$i_1 =0, \; i_2 = 0 \$)

--
- ### \$V_1 = V_2\$
---
#Example

---
#Inverting Amplifier

![](http://evalidate.freehostia.com/op-amp/invertingAmplifier/images/image%28inv_theory%29/equation1.PNG)
---
#Inverting Amplifier

## \$V\_0 =-\dfrac{R\_2}{R\_1}V\_{in}\$
---
#Example

## Find vo

![](https://raw.githubusercontent.com/ozank/ee281/master/images/opamp_ex1.png)

---
#Example

#### Find vo

![](https://raw.githubusercontent.com/ozank/ee281/master/images/opamp_ex1.png)

---
# Identify the Circuit
![](https://raw.githubusercontent.com/ozank/ee281/master/images/opamp_noninverting.png)

---
# Identify the Circuit

## $$V_o = (1 + \frac{R_f}{R_1}) V_i$$

---
# Non-inverting Amplifier
![](https://raw.githubusercontent.com/ozank/ee281/master/images/opamp_noninverting.png)

---
# Example:
###Find Vo
![](https://raw.githubusercontent.com/ozank/ee281/master/images/opamp_noninverting_ex.png)
--

Vo=7V
---
# Identify the Circuit
![](https://raw.githubusercontent.com/ozank/ee281/master/images/opamp_summing.png)

---
# Identify the Circuit
## $$V_o = - R_f(\frac{V_1}{R_1} + \frac{V_2}{R_2} +  \frac{V_3}{R_3})$$
---
#Summing Amplifier
![](https://raw.githubusercontent.com/ozank/ee281/master/images/opamp_summing.png)
---
#Example:
![](https://raw.githubusercontent.com/ozank/ee281/master/images/opamp_summing_ex.png)
--

Vo=-8V io=-4.8mA
---
#Identify the Circuit
<img src="https://raw.githubusercontent.com/ozank/ee281/master/images/opamp_difference.png" alt="Drawing" style="width: 700px;"/>

---
#Identify the Circuit

### $$V_o = (\frac{R_2}{R_1} + 1)\frac{R_4}{R_3+R_4}V_2 - \frac{R_2}{R_1}V_1$$
--

## If \$R_1=R_2\$ and \$R_3=R_4\$
--

## $$V_o = V_2 - V_1$$
---
#Difference Amplifier
<img src="https://raw.githubusercontent.com/ozank/ee281/master/images/opamp_difference.png" alt="Drawing" style="width: 700px;"/>

---
#Example:
### Design an opamp circuit with inputs \$v_1\$ and \$v_2\$ such that:

## $$V_o = 3V_2 - 5V_1$$

---
# Cascaded OPAMPS

---
#Example:
![](https://raw.githubusercontent.com/ozank/ee281/master/images/opamp_cascaded_ex.png)
--

V0=3.5 V
---
#Example: \$V_1\$= 7 V, \$V_2\$= 3.1 V
![](https://raw.githubusercontent.com/ozank/ee281/master/images/opamp_cascaded_ex2.png)

--
Vo=10V

---
# Any questions?

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