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: AOL > 100,000 (Open-loop means without feedback. More on that later.) • High Input Impedance: Zin > 1 Meg • Low Output Impedance: Zout  0 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). 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 Op-Amp Basics The front-end of an Op-Amp is a differential amplifier Voltage Follower Simplest circuit, illustrates use of negative feedback Non-Inverting Amplifier Av = 1 + (Rf / Ri) 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 Non-Inverting Amp An example calculation: a) Find Vout if Vin = 1 Volt DC, Rf = 10k, Ri = 5k b) 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 [...]... 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) ... but actually it’s not 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)... 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... 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 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 Comparators . CHAPTER 9 Basics of Operational Amplifiers OBJECTIVES Describe and Analyze: • Op-Amp Basics • Feedback • Inverting Amplifiers • Non-Inverting Amplifiers • Comparators. MOSFET). 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 Op-Amp Basics . Op-Amp Basics The front-end of an Op-Amp is a differential amplifier Voltage Follower Simplest circuit, illustrates use of negative feedback Non-Inverting Amplifier