1. Chapter 4 The Operational Amplifier

2. Ckts W/ Operational Amplifiers Why Study OpAmps At This Point? 1.OpAmps Are Very Useful Electronic Components 2.We Have Already Developed The Tools To Analyze Practical OpAmps Circuits 3.The Linear Models for OpAmps Include Dependent Sources A PRACTICAL Application of Dependent Srcs

4. OpAmp Symbol & Model The Circuit Symbol Is a Version of the Amplifier TRIANGLE  The Linear Model OUTPUT RESISTANCE INPUT RESISTANCE GAIN Typical Values

5. -Vcc, when A(Vp-Vn)<-Vcc A(Vp-Vn), when -Vcc< A(Vp-Vn)< +Vcc +Vcc, when A(Vp-Vn) >+Vcc Vo =

7. 2 Ways of Using Op-Amps “Open Loop”: very high gain amplifier –Useful for comparing 2 voltages –Fixed gain, always at MAX OUTPUT!! “Closed Loop” with negative feedback –Useful for amplifying, adding, subtracting, differentiation and integration (using capacitors) –Variable gain, controlled by resistor selection

8. “Open-Loop” examples Ideal Comparator and Transfer Characteristic  “Zero-Cross” Detector → Heart of Solid State Relay Cnrtl

9. “Closed Loop” Example: Unity Gain Buffer  Controlling Variable =  Solve For Buffer Gain  Thus The Amplification

10. Consequences for Vp-Vn Normally, A is 10,000 or more, so to avoid saturation, abs(Vp-Vn) must be < Vcc/10000, or, if Vcc = 20V, about 2 mV which is negligible for most circuits With an Ideal Op-amp, A = infinity, so Vp = Vn to avoid saturation Negative Feedback resistors “force” Vp = Vn i.e. if Vp-Vn gets large, A(Vp-Vn) pulls back toward zero (more on this later)

11. But…always remember Vcc/-Vcc limits… if Vo saturates Vp does not = Vn !!! Terminal Characteristics for an ideal op amp in it’s Linear Range: Ip = In = 0 (very high input resistance=1MOhm) Io can be very large (coming from Vcc/-Vcc)

12. Inverting Amplifier Vo = -RfVs Rs When in linear region

13. Inverting Amplifier with Feedback Path broken Vo= -AVs Saturation (unless Vs<2mv)

14. Summing Amplifier Vo = - Rf (Va + Vb + Vc) (in linear region) Rs

15. Non-Inverting Amplifier Vo=(Rs+Rf) Vg Rs In linear region

16. Difference Amplifier Vo= Rb (Vb – Va) in linear region AND Ra IFF Ra/Rb = Rc/Rd

17. Common Mode Rejection Ratio IF Ra/Rb =(1-e) Rc/Rc (e=very small) CMMR = abs(1 + Rb/Ra) e

18. Comparator, used in digital circuits

19. Application, the Flash Converter Comparators quantize

20. Encoder converts to binary