1. LECTURE 11 - THE OP-AMP Op-Amp: “Operational Amplifier” Circuit Symbol: Reality:

2. THE DIFFERENTIAL AMPLIFIER +  +  V0V0 AV 1 +  V1V1 RiRi Circuit Model in linear region +  A V+V+ VV V0V0 Differential Amplifier “Differential”  V 0 depends only on difference (V +  V - ) “Very high gain”  But if A ~, is the output infinite? The output cannot be larger than the supply voltages. It will limit or “clip” if we attempt to go too far. We call the limits of the output the “rails”.

3. WHAT ARE I-V CHARACTERISTICS OF AN ACTUAL HIGH-GAIN DIFFERENTIAL AMPLIFIER ? Example: Amplifier with gain of 10 5, with max V 0 of 3V and min V 0 of  3V. V IN (  V) 12 3 V 0 (V) 0.1 0.2 33 22 11 .2 (a) I-V near origin 33 (b) I-V over wider range V IN (  V) 1020 30 V 0 (V) 1  30  20  10 22 11 2 3 upper “rail” lower “rail” +  V0V0 +  V IN Circuit model gives the essential linear part But V 0 cannot rise above some physical voltage related to the positive power supply V CC (“ upper rail”) V 0 < V +RAIL And V 0 cannot go below most negative power supply, V EE i.e., limited by lower “rail” V 0 > V -RAIL

4. THE VOLTAGE FOLLOWER Negative feedback  Stabilizes the output NEGATIVE FEEDBACK V0V0 +  V IN

5. NEGATIVE FEEDBACK Familiar examples of negative feedback: Thermostat controlling room temperature Driver controlling direction of automobile Photochromic lenses in eyeglasses Familiar examples of positive feedback: Microphone “squawk” in room sound system Mechanical bi-stability in light switches Thermonuclear reaction in H-bomb Fundamentally pushes toward stability Fundamentally pushes toward instability or bi-stability

6. EASY WAY TO GET ANSWER FOR OP-AMP CIRCUITS “Ideal Op-Amp Technique”: With ideal op-amp technique we can analyze all sorts of negative feedback   VV )1( Why? (a) R IN large by design (b) V +  V (  )  voltage difference across R IN  0 V0V0 +  i IN(-) A i IN(+) Why? V 0 CANNOT  , BUT A   V +  V (  ) in order that V 0 = A (V +  V  ) Finite infinite must be zero

7. EXAMPLES USING IDEAL OP-AMP TECHNIQUE The non-inverting amplifier

8. EXAMPLES USING IDEAL OP-AMP TECHNIQUE ???????????????????