# Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Chapter 6 The Operational Amplifier.

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Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Chapter 6 The Operational Amplifier

Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.2  The operational amplifier or op amp for short, finds daily usage in a large variety of electronic applications.

Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.3  op amps have three principal terminals: the output the non-inverting input the inverting input

Ideal Op Amp Rules  No current ever flows into either input terminal.  There is no voltage difference between the two input terminals. The op amp acts to make this happen! Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.4

 Apply KVL, Ohm’s law, and the ideal op amp rules to find Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.5

Example: v in (t)=5 sin 3t mV, R f =47 kΩ, R 1 =4.7 kΩ Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.6 v out (t) = -50 sin 3t mV

Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.7 To solve, use KVL, KCL, and op amp rules. Suggested circuit variables to perform the circuit analysis

Example: v in (t)=5 sin 3t mV, R f =47 kΩ, R 1 =4.7 kΩ Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.8 v out (t) = 55 sin 3t mV

 v out (t) =v in (t)  this design allows connection of a practical voltage source to a load without experiencing voltage droop! Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.9

10 This amplifier performs the operation of adding. It also introduces a gain of –R f /R

Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.11 This voltage is not affected by the circuit on the right. Op amps can be combined in stages to create the desired relationship between the outputs and the inputs.

Zener diode: i=0 if v<4.7 volts Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.12 This circuit will produce an accurate voltage regardless of the age of the battery V bat.

With a reference voltage source V ref, we can drive a constant current I s =V ref / R ref through any load R L. Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.13

The op amp can be modeled as a dependent voltage source, with the following components as shown:  input resistance R i  output resistance R o  open loop gain A Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.14

Example: v in (t)=5 sin 3t mV, R f =47 kΩ, R 1 =4.7 kΩ Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.15 For a 741op amp (A=200,000, R i =2MΩ, R o =75Ω v out (t) = -49.997 sin 3t mV. An ideal op amp produces v out (t) = -50 sin 3t mV. [Analyze the detailed op amp model using nodal analysis.]

When A=∞, R o =0 Ω, and R i =∞ Ω, the op amp behaves according to the ideal op amp rules. (v d =0 and i in =0) Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.16

When v 1 = v 2 = v CM, the output should be zero, but real op amps produce a small “common mode” voltage v oCM. A CM =| v oCM / v CM | Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.17

 The enormous but unpredictable gain of the op amp is made usable through negative feedback.  When v in goes up, v d goes down, and the op amp reacts by lowering v out until the “unwanted” non-zero v d is pushed back to zero. Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.18 this “feedback” resistor allows the output to affect the input terminal.

 An op amp requires power supplies.  Usually, equal and opposite voltages are connect to the V + and V - terminals.  Typical values are 5 to 24 volts.  The power supply ground must be the same as the signal ground. Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.19 in this example +18V is connected to V + and -18 V is connected to V -

v out =10v in, but only up to the ±18 V supplies Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.20

Non-zero output “offsets” can be removed: Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.21

Slew rate is the maximum V/μs for output.  examples: input (green) and output (red) Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.22

 Op amps in open loop can be used to make decisions. In this case, is v in >2.5 V? Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.23

Design a circuit that provides a “logic 1” 5 V output if a certain voltage signal drops below 3 V, and zero volts otherwise. Answer: Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.24

This device allows precise amplification of small voltage differences: v out =K(v + -v - ) Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.25