CHAPTERS 6 & 7 CHAPTERS 6 & 7 NETWORKS 1: NETWORKS 1: October 2002 – Lecture 6b ROWAN UNIVERSITY College of Engineering Professor Peter Mark Jansson, PP PE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING Autumn Semester 2002

test II no adjustment mean = Fs, 1 A- w/ 10 points mean = 76 7-Fs, 5 As

networks I Today’s learning objectives – build understanding of the operational amplifier introduce capacitance introduce inductance

homework 6 Chapter 6 Pages Problems 6.4-3, 6.4-5, Chapter 7 Pages Problems 7.4-3, 7.5-3, 7.6-1, 7.8-3

new concepts from ch. 6 operational amplifier the ideal operational amplifier nodal analysis of circuits containing ideal op amps design using op amps characteristics of practical op amps

new concepts from ch. 7 energy storage in a circuit capacitors series and parallel inductors series and parallel using op amps in RC circuits

definition of an OP-AMP The Op-Amp is an “active” element with a high gain that is designed to be used with other circuit elements to perform a signal processing operation. It requires power supplies, sometimes a single supply, sometimes positive and negative supplies. It has two inputs and a single output.

OP-AMP symbol and connections _+_+ +–+– +–+– INVERTING INPUT NODE NON-INVERTING INPUT NODE OUTPUT NODE i1i1 i2i2 ioio vovo v2v2 v1v1 NEGATIVE POWER SUPPLY POSITIVE POWER SUPPLY

THE OP-AMP FUNDAMENTAL CHARACTERISTICS _+_+ INVERTING INPUT NODE NON-INVERTING INPUT NODE OUTPUT NODE i1i1 i2i2 ioio vovo v2v2 v1v1 RoRo RiRi

THE IDEAL OP-AMP FUNDAMENTAL CHARACTERISTICS _+_+ INVERTING INPUT NODE NON-INVERTING INPUT NODE OUTPUT NODE i1i1 i2i2 ioio vovo v2v2 v1v1

THE INVERTING OP-AMP _+_+ i1i1 i2i2 ioio vovo v2v2 v1v1 RfRf RiRi +–+– vsvs Node a 1. Write Ideal OpAmp equations. 2. Write KCL at Node a. 3. Solve for v o /v s

THE INVERTING OP-AMP _+_+ i1i1 i2i2 ioio vovo v2v2 v1v1 RfRf RiRi +–+– vsvs Node a At node a:

THE NON-INVERTING OP-AMP _+_+ i1i1 i2i2 ioio vovo v2v2 v1v1 RfRf RiRi +–+– vsvs Node a At node a:

HW example see HW problems 6.4-1, 6.4-2, 6.4-6

Op Amp circuit types for K < 0 for K > 1 for K = 1 special case 0 < K < 1

What you need to know Parameters of an Ideal Op Amp Types of Amplification Gain (K) vs. Which nodes and Amps circuits are needed to achieve same How to identify which type of circuit is in use (effect) How to solve simple Op Amp problems

DEFINITION OF CAPACITANCE Measure of the ability of a device to store energy in the form of an electric field. CAPACITOR: IMPORTANT RELATIONSHIPS: +–+– i + + _ _

CALCULATING i c FOR A GIVEN v(t) Let v(t) across a capacitor be a ramp function. t v vv tt As Moral: You can’t change the voltage across a capacitor instantaneously.

VOLTAGE ACROSS A CAPACITOR

ENERGY STORED IN A CAPACITOR

CAPACITORS IN SERIES +–+– C1C1 C2C2 C3C3 + v 1 -+ v 2 -+ v 3 - i v KVL

Capacitors in series combine like resistors in parallel. CAPACITORS IN SERIES

CAPACITORS IN PARALLEL C1C1 C2C2 C3C3 i i1i1 i2i2 i3i3 KCL Capacitors in parallel combine like resistors in series.

HANDY CHART ELEMENT CURRENTVOLTAGE

DEFINITION OF INDUCTANCE Measure of the ability of a device to store energy in the form of a magnetic field. INDUCTOR: IMPORTANT RELATIONSHIPS: i + _ v

CALCULATING v L FOR A GIVEN i(t) Let i(t) through an inductor be a ramp function. t i ii tt As Moral: You can’t change the current through an inductor instantaneously.

CURRENT THROUGH AN INDUCTOR

ENERGY STORED IN AN INDUCTOR

INDUCTORS IN SERIES L1L1 L2L2 L3L3 + v 1 -+ v 2 -+ v 3 - i KVL Inductors in series combine like resistors in series.

INDUCTORS IN PARALLEL L1L1 L2L2 L3L3 v i1i1 i2i2 i3i3 KCL +–+–

INDUCTORS IN PARALLEL Inductors in parallel combine like resistors in parallel.

HANDY CHART ELEMENT CURRENTVOLTAGE

OP-AMP CIRCUITS WITH C & L _+_+ i1i1 i2i2 ioio vovo v2v2 v1v1 CfCf RiRi +–+– vsvs Node a

QUIZ: Find v o = f(v s ) _+_+ i1i1 i2i2 ioio vovo v2v2 v1v1 RfRf +–+– vsvs Node a LiLi

ANSWER TO QUIZ

IMPORTANT CONCEPTS FROM CH. 7 I/V Characteristics of C & L. Energy storage in C & L. Writing KCL & KVL for circuits with C & L. Solving op-amp circuits with C or L in feedback loop. Solving op-amp circuits with C or L at the input.

1st ORDER CIRCUITS WITH CONSTANT INPUT +–+– t = 0 R1R1 R2R2 R3R3 Cvsvs + v(t) -

Thevenin Equivalent at t=0 + RtRt C +–+– V oc + v(t) - KVL i(t) + -

SOLUTION OF 1st ORDER EQUATION

SOLUTION CONTINUED

WITH AN INDUCTOR +–+– t = 0 R1R1 R2R2 R3R3 Lvsvs i(t)

Norton equivalent at t=0 + RtRt I sc + v(t) - L i(t) KCL

SOLUTION

HANDY CHART ELEMENT CURRENTVOLTAGE

IMPORTANT CONCEPTS FROM CHAPTER 8 Determining Initial Conditions Setting up differential equations Solving for v(t) or i(t)