1. Introduction to Electrical & Computer Engineering Operational Amplifiers (Op Amps) 1 Dr. Cynthia Furse University of Utah

2. Electrical Engineering: What Can You Do To a Voltage?? V DC I

3. Electrical Engineering: What Can You Do To a Voltage?? VoltageCurrent Voltage R I V= I R A Resistor CONVERTS Voltage to Current (and Current to Voltage)

4. Electrical Engineering: What Can You Do To a Voltage?? Voltage (V) Voltage V/x A Voltage Divider DIVIDES Voltage. A Current Divider DIVIDES Current.

5. Electrical Engineering: What Can You Do To a Voltage?? Voltage (V) Voltage V/x A Voltage Divider DIVIDES Voltage. A Current Divider DIVIDES Current.

6. Why Do We Need an Op Amp? An Op Amp circuit can AMPLIFY (X) De-AMPLIFY (divide), ADD (+) SUBTRACT (-) COMPARE ( >=< ) SWITCH a voltage(s) And more…

7. What is an Op Amp?  CIRCUITS by Ulaby, Maharbiz & Furse All rights reserved. Included by permission. © 2016 National Technology and Science Press Voltage Inputs Vn Vp Voltage Output Negative Voltage Supply Positive Voltage Supply An Op Amp is an ACTIVE device (needs an outside Power Supply)

8. Inside The Op-Amp (741) Vp All rights reserved. Included by permission. © 2016 National Technology and Science Press Vp Vn Vo Vcc and –Vcc power the transistors.

9. Operational Amplifier “Op Amp” Op Amp showing power supply (which is how we connect it up) Op Amp with power supply not shown (which is how we usually display op amp circuits) All rights reserved. Reprinted with permission. © 2016 National Technology and Science Press

10. Op Amp Gain (A)  A = Op Amp Gain / Open Loop Gain  Op Amps have high voltage gain (A)  Linear response All rights reserved. Reprinted with permission. © 2016 National Technology and Science Press Slope = A

11. Op Amp Saturation – Acts Like a Switch  CIRCUITS by Ulaby, Maharbiz & Furse All rights reserved. Included by permission. © 2016 National Technology and Science Press

12. Op Amp Gain (A) vs. Circuit Gain (G) Op Amp Gain (A) A is HIGH (>10,000) Also called open-loop gain or voltage gain. All rights reserved. Reprinted with permission. © 2016 National Technology and Science Press Circuit Gain (G) G is large or small, >1 (Amp X), < 1 (DeAmp) Inverting (-) Non-Invert. (+)

13. Non-Ideal Op Amp Equivalent Circuit All rights reserved. Reprinted with Permission. © 2016 National Technology and Science Press

14. Ideal Op Amp Equivalent Circuit All rights reserved. Reprinted with Permission. © 2016 National Technology and Science Press  v p =v n  i p =i n =0 Non-Ideal Op Amp Ideal Op Amp

15. Circuit Gain Depends on … Circuit! (max) = V cc All rights reserved. Do not reproduce or distribute. © 2016 National Technology and Science Press Non-Inverting Amplifier Remember Saturation:

16. Op Amps All rights reserved. Reprinted with Permission. © 2016 National Technology and Science Press  v p =v n  i p =i n =0  Vo max = +/-Vcc Non-Ideal Op Amp Ideal Op Amp

17. Introduction to Electrical & Computer Engineering Wild Horse Corral, Antelope Island 17 Dr. Cynthia Furse University of Utah

18. Introduction to Electrical & Computer Engineering Operational Amplifiers (Op Amps) Non-Inverting Op Amp Calculation Example 18 Dr. Cynthia Furse University of Utah

19. Non-Ideal Op Amp Equivalent Circuit All rights reserved. Reprinted with Permission. © 2016 National Technology and Science Press

20. Example 4-1: Op Amp Amplifier Node a Node b All rights reserved. Reproduced with permission. © 2016 National Technology and Science Press Example: Non-Inverting Amplifier Want: v o = G v s Find Circuit Gain G = v o / v s

21. Example 4-1: Op Amp Amplifier Solve Using Node-Voltage Method KCL at Node a: KCL at Node b: Node a Node b All rights reserved. Reproduced with permission. © 2016 National Technology and Science Press

22. Example 4-1: Op Amp Amplifier = 4.999975 Node a Node b All rights reserved. Reproduced with permission. © 2016 National Technology and Science Press See Details of applying Cramer’s Rule, attached

23. All rights reserved. Do not reproduce or distribute. © 2016 National Technology and Science Press  Apply Cramer’s Rule

24. Example 4-1: Ideal Op Amp Amplifier Solve Using Node-Voltage Method KCL at Node a: KCL at Node b: Node a Node b All rights reserved. Reproduced with permission. © 2016 National Technology and Science Press  Ideal Op Amp:  v p =v n =v s  i p =i n =0  Also Ro=0

25. Circuit Gain Depends on … Circuit! (max) = V cc All rights reserved. Do not reproduce or distribute. © 2016 National Technology and Science Press Non-Inverting Amplifier Remember Saturation:

26. Introduction to Electrical & Computer Engineering Operational Amplifiers (Op Amps) 26 Dr. Cynthia Furse University of Utah