1. What is an Op Amp? Ideal Op Amps Applications Examples Lecture 9. Op Amps I 1

2. 2 What is an Op Amp? Op Amp is short for operational amplifier. An operational amplifier is modeled as a voltage controlled voltage source. An operational amplifier has a very high input impedance and a very high gain. It has usually differential inputs and a single output.

3. 3 Use of Op Amps Op amps can be configured in many different ways using resistors and other components. Amplifiers provide gains in voltage or current. Op amps can convert current to voltage. Op amps can provide a buffer between two circuits. Op amps can be used to implement integrators and differentiators. Lowpass and bandpass filters.

4. 4 Applications of Op Amps Amplifiers provide gains in voltage or current. Op amps can convert current to voltage. Op amps can provide a buffer between two circuits. Op amps can be used to implement integrators and differentiators.

5. 5 The Op Amp Symbol + - Non-inverting input Inverting input Ground High Supply Low Supply Output

6. 6 The Op Amp Model – Voltage Dependent Source + -Inverting input Non-inverting input R in v+v+ v-v- + - A(v + -v - ) vovo

7. 7 Typical Op Amp The input resistance R in is very large (practically infinite). The voltage gain A is very large (practically infinite). + -Inverting input Non-inverting input R in v+v+ v-v- + - A(v + -v - ) vovo

8. 8 “Ideal” Op Amp The input resistance is infinite. The gain is infinite. The op amp is in a negative feedback configuration. Infinite input resistance means the current into the inverting input is zero: i - = 0 Infinite gain means the difference between v + and v - is zero: v + - v - = 0

9. 9 The Basic Inverting Amplifier - + V in + - + - V out R1R1 R2R2

10. 10 Solving the Amplifier Circuit Nodal Analysis: i 1 + i 2 + i - =0 - R1R1 R2R2 i1i1 i-i- i2i2

11. 11 Solving the Amplifier Circuit i 1 + i 2 + i - =0

12. 12 Amplifier gain: Solve for v out Solving the Amplifier Circuit

13. 13 How to solve Op Amp Circuit? Nodal analysis or other methods to solve for the output voltage in terms of the input(s). Keep in mind that the ideal op amp model leads to the following conditions: i - = 0 v + = v -

14. 14 Where is the Feedback? - + V in + - + - V out R1R1 R2R2

15. 15 The Non-Inverting Amplifier + - v in + - + - v out R1R1 R2R2

16. 16 Nodal Analysis: Finding the nodes + - v in + - + - v out R1R1 R2R2 i-i- i1i1 i2i2

17. 17 Nodal Analysis: Apply KCL

18. 18 Nodal Analysis: Solve for V out

19. 19 A Mixer Circuit - + v2v2 + - + - v out R2R2 RfRf R1R1 v1v1 + -

20. 20 Nodal Analysis: Finding the nodes - + v2v2 + - + - v out R2R2 RfRf R1R1 v1v1 + - i1i1 i2i2 ifif i-i-

21. 21 Nodal Analysis: Apply KCL

22. 22 Nodal Analysis: Solve for V out

23. 23 Class Examples Seeing atoms with STM 1 nA

24. 24 Class Examples Solar cell 1 nA A circuit constructed for measuring current from the solar cell. The first Op Amp is the current-to-voltage converter and the second op Amp inverts the voltage.