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CHAPTER 9

CHAPTER 9. Basics of Operational Amplifiers. OBJECTIVES. Describe and Analyze: Op-Amp Basics Feedback Inverting Amplifiers Non-Inverting Amplifiers Comparators Troubleshooting. Introduction. Op-Amps have: Differential Inputs: (+) & (-) High “Open Loop” Gain: A OL > 100,000

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CHAPTER 9

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  1. CHAPTER 9 Basics of Operational Amplifiers

  2. OBJECTIVES Describe and Analyze: • Op-Amp Basics • Feedback • Inverting Amplifiers • Non-Inverting Amplifiers • Comparators • Troubleshooting

  3. Introduction Op-Amps have: • Differential Inputs: (+) & (-) • High “Open Loop” Gain: AOL > 100,000 (Open-loop means without feedback. More on that later.) • High Input Impedance: Zin > 1 Meg • Low Output Impedance: Zout  0

  4. Introduction Some Facts about Op-Amps: • Op-amps are the most commonly used linear ICs. • An IC package can have 1, 2, 4, or more op-amps. • Op-amps come in many varieties based on parameters such as bandwidth, cost, and transistor type (BJT, JFET, MOSFET).

  5. Op-Amp Basics Analysis can be based on two approximations: • No current flows into or out of the input pins • The voltage across the input pins is zero

  6. Op-Amp Basics The front-end of an Op-Amp is a differential amplifier

  7. Voltage Follower Simplest circuit, illustrates use of negative feedback

  8. Non-Inverting Amplifier Av = 1 + (Rf / Ri)

  9. Non-Inverting Amp Gain equation derived as follows: • Vin applied to (+) input means V(+) = Vin • zero difference across inputs implies V(-) = V(+) • V(-) = V(+) implies V(-) = Vin • Iin = 0 implies V(-) = Vin = [Ri / (Ri + Rf)]  Vout • which leads to Vin / Vout = Ri / (Ri + Rf) • which leads to Vout / Vin = Av = (Ri + Rf) / Ri • which is the same as Av = 1 + Rf / Ri

  10. Non-Inverting Amp An example calculation: • Find Vout if Vin = 1 Volt DC, Rf = 10k, Ri = 5k • Find voltage at (-) input • Av = 1 + Rf / Ri = 1 + 10k / 5k = 1 + 2 = 3 • Vout = Av  Vin = 3  1V = 3 Volts DC • V(-) = V(+) = 1 Volt DC

  11. Negative Feedback Negative feedback reduces gain to a useable value

  12. Negative Feedback Besides setting the gain, negative feedback provides performance improvements such as: • Makes Zin higher • Makes Zout lower • Increases the usable bandwidth • Reduces distortion in the op-amp

  13. Negative Feedback It looks complicated, but actually it’s not

  14. Negative Feedback We can analyze negative feedback as follows: • Some of the output is fed back to the input: Vfb = B  Vout where 0 < B < 1 • The signal that gets to the op-amp is the applied input plus the feedback: Vx = Vin + Vfb = Vin + B  Vout • But the output is the open-loop gain of the op-amp times the signal that gets to the input: Vout = AOL Vx = AOL (Vin + B  Vout) • Now we can find closed-loop gain: ACL = Vout / Vin as we will see on the next slide.

  15. Negative Feedback Start with Vout = AOL (Vin + B  Vout) Then Vout = AOL Vin+AOL B  Vout Then Vout – B  AOL Vout = AOL Vin Then (1 - B  AOL ) Vout = AOL Vin Then Vout = [AOL / (1 - B  AOL ) ]  Vin Then Vout / Vin = ACL = AOL / (1 - B  AOL ) Where ACL is the closed-loop gain Now, if B  AOL >>1 (which is usually the case) then ACL 1 / B where B is set by a resistor ratio.

  16. The Inverting Amplifier Av = - (Rf / Ri) where minus means 180O phase shift

  17. The Inverting Amp Gain equation derived as follows: • Vin applied to (-) input through Ri • zero difference across inputs implies V(-) = V(+) • (+) input grounded implies V(-)  0 (-) input is a “virtual ground” • which leads to Iin = Vin / Ri and If = Vout / Rf • no current into (-) input implies If = Iin • so Vout / Rf = Vin / Rin and Vout / Vin = Rf / Rin • If Vin makes Iin flow in, Vout must make If flow out. So Vout has opposite polarity of Vin: Av = -Rf / Ri

  18. The Inverting Amp An example calculation: Find Vout if Vin = 1 Volt DC, Rf = 10k, Ri = 5k • Av = - Rf / Ri = - (10k / 5k) = - 2 • Vout = Av  Vin = -2  1V = -2 Volts DC

  19. Comparators Very small V between inputs gives a binary output

  20. Comparators Some Facts about Comparators: • Comparator output is high or low depending on which input has the higher voltage applied to it. • An open-loop op-amp can be used as a comparator. • Open-loop op-amps go into saturation, and they take a relatively long time to get out of saturation. • The output can “chatter” (oscillate high / low) when inputs are equal. Chatter can be cured with hysteresis. • There are ICs designed to be comparators. They are better at the job than op-amps.

  21. Troubleshooting • Check the power rails: +VCC and –VCC • Check if the output is in saturation (usually, saturation is not a good thing). • Check the input voltages, knowing that voltage across inputs is supposed to be virtually zero. • Check that polarity (phase) of output is the same as input for a non-inverting amplifier. • Check that polarity (phase) of output is the opposite input for an inverting amplifier. • Check signal levels based on gains (look at the resistor ratios of the feedback loops).

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