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ECE 2100 Circuit Analysis Lesson 16 Chapter 5: Operational Amplifiers 1 Daniel M. Litynski, Ph.D. http://homepages.wmich.edu/~dlitynsk/ Circuit Theorems - Chapter 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 Motivation Linearity Property Superposition Source Transformation Thevenin’s Theorem Norton’s Theorem Maximum Power Transfer 2 ECE 2100 Circuit Analysis Lesson 15 Chapter 4: Circuit Theorems Norton’s Theorem Maximum Power Transfer Wheatstone Bridge Operational Amplifiers (Review and continue the following) 4.7 Maximum Power Transfer (1) If the entire circuit is replaced by its Thevenin equivalent except for the load, the power delivered to the load is: P i 2 RL 2 VTh RTh RL RL For maximum power dissipated in RL, Pmax, for a given RTH, and VTH, 2 RL RTH Pmax VTh 4 RL The power transfer profile with different RL 4 4.7 Maximum Power Transfer (2) Example 8 Determine the value of RL that will draw the maximum power from the rest of the circuit shown below. Calculate the maximum power. + vx 4 v0 + i 2 vx 4 Fig. a 2 1 1 + 1V + 9V io + => To determine RTH Fig. b + 3vx + VTh 3vx => To determine VTH (a) (b) *Refer to in-class illustration, textbook, RL = 4.22 , Pm = 2.901W 9 ECE 2100 Circuit Analysis Chapter 1-4 Basic Concepts Basic Laws Methods of Analysis Circuit Theorems Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 20 EE2100 Circuit Analysis Chapter 5 Operational Amplifier Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 21 Operational Amplifier - Chapter 5 5.1 What is an Op Amp? 5.2 Ideal Op Amp 5.3 Configuration of Op Amp 5.4 Cascaded Op Amp 5.5 Application – Digital-to Analog Converter 22 5.1 What is an Op Amp (1) • It is an electronic unit that behaves like a voltage-controlled voltage source. • It is an active circuit element designed to perform mathematical operations of addition, subtraction, multiplication, division, differentiation and integration. 23 5.1 What is an Op Amp (2) A typical op amp: (a) pin configuration, (b) circuit symbol 24 5.1 What is an Op Amp (3) The equivalent circuit Of the non-ideal op amp Op Amp output: vo as a function of Vd vd = v2 – v1; vo = Avd = A(v2 –v1) 25 5.1 What is an Op Amp (4) Typical ranges for op amp parameters Parameter Typical range Ideal values Open-loop gain, A 105 to 108 Input resistance, Ri 105 to 1013 ∞ Output resistance, Ro 10 to 100 0 Supply voltage, VCC ∞ 5 to 24 V 26 5.2 Ideal Op Amp (1) An ideal op amp has the following characteristics: 1. Infinite open-loop gain, A ≈ ∞ 2. Infinite input resistance, Ri ≈ ∞ 3. Zero output resistance, Ro ≈ 0 27 5.2 Ideal Op Amp (2) Example 1: Determine the value of io. *Refer to in-class illustration, textbook Ans: 0.65mA 28