PHYS225 Lecture 9 Electronic Circuits
Last lecture Field Effect Transistors Voltage controlled resistor Various FET circuits Switch Source follower Current source Similar to BJT Draws no input current Very high input impedance
The Operational Amplifier The operational amplifier ( op amp ) is a basic building block used in analog circuits. Its behavior is modeled using a dependent source. When combined with resistors, capacitors, and inductors, it can perform many useful functions: amplification/scaling of an input signal sign changing (inversion) of an input signal addition of multiple input signals subtraction of one input signal from another integration (over time) of an input signal differentiation (with respect to time) of an input signal analog filtering nonlinear functions like exponential, log, sqrt, etc.
Op Amp Circuit Symbol and Terminals V + positive power supply non-inverting input inverting input + output V negative power supply The output voltage can range from V to V + ( rails ) The positive and negative power supply voltages do not have to be equal in magnitude (example: 0V and +3V DC supplies)
Op-Amp Voltage Transfer Characteristic The op-amp is basically a differentiating amplifier: V cc v o slope = A >>1 v id = v p v n -V cc Regions of operation: In the linear region, v o = A (v p v n ) = A v id where A is the open-loop gain negative saturation linear positive saturation Typically, V cc 20 V and A > 10 4 linear range: -2 mv v id = (v p v n) 2 mv Thus, for an op-amp to operate in the linear region, v p v n (i.e., there is a virtual short between the input terminals.)
Achieving a Virtual Short Recall the voltage transfer characteristic of an op-amp: Plotted using different scales for v o and v p v n v o Plotted using similar scales for v o and v p v n v o ~10 V V cc slope = A >>1 v p v n ~10 V V cc slope = A >>1 v p v n -V cc -V cc ~1 mv ~10 V Q: How does a circuit maintain a virtual short at the input of an op-amp, to ensure operation in the linear region?
Achieving a Virtual Short Recall the voltage transfer characteristic of an op-amp: Plotted using different scales for v o and v p v n v o Plotted using similar scales for v o and v p v n v o ~10 V V cc slope = A >>1 v p v n ~10 V V cc slope = A >>1 v p v n -V cc -V cc ~1 mv ~10 V Q: How does a circuit maintain a virtual short at the input of an op-amp, to ensure operation in the linear region? A: By using negative feedback. A signal is fed back from the output to the inverting input terminal, effecting a stable circuit connection. Operation in the linear region enforces the virtual short circuit.
Op Amp Operation without Negative Feedback 1. Simple comparator with 1 Volt threshold: V is set to 0 Volts (logic 0 ) V + is set to 2 Volts (logic 1 ) A = 100 V IN 1V + + V 0 2 1 0 V 0 1 2 If V IN < 0.99 V, V 0 = 0V = Logic 0 If V IN > 1.01 V, V 0 = 2V = Logic 1 V IN 2. Simple inverter with 1 Volt threshold: V is set to 0 Volts (logic 0 ) V + is set to 2 Volts (logic 1 ) A = 100 1V + + V 0 2 1 0 V 0 1 2 If V IN < 0.99 V, V 0 = 2V = Logic 1 V IN If V IN > 1.01 V, V 0 = 0V = Logic 0 V IN
Feedback Feedback: Taking a portion of the output and feeding it back to the input Positive feedback: Feedback signal is in phase with the input signal Oscillations (good and bad) Increase circuit gain Negative feedback: Feedback signal is out of phase with the input signal Used in almost all practical amplifiers Pros: Increased circuit stability against fluctuations (including temp. changes), increased Z in, decreased Z out, decreased signal distortion, higher frequency range for constant gain Cons: Decreased circuit gain (feedback reduces input)
Negative vs. Positive Feedback Familiar examples of negative feedback: Thermostat controlling room temperature Driver controlling direction of automobile Pupil diameter adjustment to light intensity Fundamentally pushes toward stability Familiar examples of positive feedback: Microphone squawk in sound system Mechanical bi-stability in light switches Fundamentally pushes toward instability or bi-stability
Op Amp Golden Rules I. The output attempts to do whatever is necessary to make the voltage difference between the two inputs zero (consequence of very high voltage gain). II. The inputs draw no current (consequence of very high input impedance). (Note that these rules hold only if there is external negative feedback.)
Operational Amplifiers (Op Amps) Basic prototype: Very high-gain DC-coupled differential amplifier non-inverting (+) inverting ( ) Circuit symbol: input 1 input 2 output (The Art of Electronics, Horowitz and Hill, 2 nd Ed.)
LF411 Op Amp (The Art of Electronics, Horowitz and Hill, 2 nd Ed.) (Student Manual for The Art of Electronics, Hayes and Horowitz, 2 nd Ed.)
LF411 Op Amp (Student Manual for The Art of Electronics, Hayes and Horowitz, 2 nd Ed.)
What s Inside an Op-Amp?
Unity-Gain Voltage-Follower Circuit V IN v n v p + V 0 2 1 V 0 (V) v p = v n V 0 = V IN 1 2 V IN (V) ( valid as long as V V 0 V + ) Note that the analysis of this simple (but important) circuit required only one of the ideal op-amp rules. Q: Why is this circuit important (i.e., what is it good for)?
Unity-Gain Voltage-Follower Circuit V IN v n v p + V 0 2 1 V 0 (V) v p = v n V 0 = V IN 1 2 V IN (V) ( valid as long as V V 0 V + ) Note that the analysis of this simple (but important) circuit required only one of the ideal op-amp rules. Q: Why is this circuit important (i.e., what is it good for)? A: A weak source can drive a heavy load; in other words, the source V IN only needs to supply a little power (since I IN = 0), whereas the output can drive a power-hungry load (with the op-amp providing the power).