## Description

ECE 831: Analog Circuit Theory was a 3-credit course taught at Michigan State University for Electrical and Computer Engineering majors. * The catalog description for this course is: Positive real functions. Filter approximations. Passive and active network synthesis. Nullor network analysis and synthesis. Active filters. Stability. Research Project. *The prerequisite for this course is an undergraduate course in electric circuits.

The reference textbooks used in this course are :

W-K. Chen, Passive and Active Filters: Theory and Implementations, Wiley, 1986

L. T. Bruton, RC-Active Circuits Theory and Design, Prentice-Hall, 1980

**Table of Contents**

Chapter 1: Fundamentals of Passive Circuit Theory

A) Passive Network Nodal Analysis

Nodal Analysis Algorithm

B) Source Transformations

Pushing a Voltage Source Through a Node

C) Passive Network Mesh Analysis

Mesh Analysis Algorithm

D) Source Transformations (revisted)

Moving a Current Source Around a Loop

E) Duality

Inspection Transformation

F) Linearity and Superposition

Proof using Node Equations, Proportionality

G) Substitution Theorem

Voltage Substitution, Current Substitution

H) Two Ports

Y-parameters, Z-parameters, Conversion, Transfer Functions, Reciprocity

I) Interconnection of Two Ports

Series Combination, Parallel Combination

J) Scaling Network Functions

Magnitude Scaling, Frequency Scaling

K) Tellegen’s Theorem

Application to the Conservation of Power

Chapter 1: Supplemental Problems and Solutions

S1.1, S1.2, S1.3, S1.4, S1.5, S1.6, S1.7, S1.8, S1.9, S1.10

Chapter 2: Fundamentals of Active Circuit Theory

A) Nullator and Norators

Independent Sources, Norator, Short Circuit, Open Circuit, Nullator, Ideal Op-Amp, Ideal BJT

B) Nullator-Norator Nodal Analysis

Nodal Analysis Algorithm, Treble Tone Control, Simulated Impedance

C) Equivalence Relationships

Nullator Series Equivalence, Norator Series Equivalence, Nullator Parallel Equivalence, Norator Parallel Equivalence, Open Circuit Equivalence, Short Circuit Equivalence,

D) Controlled Source Models

VCCS, VCVS, CCCS, CCVS

E) Symbolic SPICE

Simulated Voltage Source, Simulated Inductance, Software

Chapter 2: Supplemental Problems and Solutions

S2.1, S2.2, S2.3

Chapter 3: Op-Amp Circuit Synthesis

A) Op-Amp Relocation

Pairing Property, Nullator Trees, Tree Generation Property, Relocation Theorem

B) Ground Relocation

Norator Trees, Indefinite Admittance Matrix, Singular Property, Characteristic Equations, Ground Relocation Theorem, Interchange Theorem

C) Transfer Function Synthesis

Source Insertion, Generating Active Filters

D) Gain-Bandwidth-Product Errors

fO – QO Errors, Error Approximation using Sspice, High Frequency Stability

E) Numeric Op-Amp Relocation Software

Case Study – Tow-Thomas Active Filter

Chapter 3: Supplemental Problems and Solutions

S3.1, S3.2, S3.3

Chapter 4: Passive Circuit Synthesis

A) LC One Port Synthesis

Even and Odd Polynomials in s, Imaginary Axis Roots, Partial Fraction Expansion form of Z(s), Reactance vs ω, First Foster Canonical Form, Duality, Second Foster Canonical Form, First Cauer Canonical Form, Continued Fraction Expansion, Second Cauer Canonical Form, Third Cauer Canonical Form

B) RC One Port Synthesis

LC – RC Transformation, Properties of RC Input Impedance, First and Second Foster Form Synthesis, First and Second Cauer Form Synthesis, Number of Elements, Internal Critical Frequencies, Third Cauer Form Synthesis

C) Two Port Synthesis by Ladder Development

Zeros of Transmission, LC Ladder Networks, Zero Shifting, Pole Removal

D) RC Ladder Two Port Synthesis

Zero Shifting, Case Study, Interpretation of Poles and Zeros

Chapter 4 Supplemental Problems and Solutions

S4.1, S4.2, S4.3, S4.4, S4.5, S4.6, S4.7

Chapter 5: Approximation Theory

A) Butterworth Low-Pass Approximation

Ideal Normalized Low-Pass Filter, Butterworth Approximation, Roots on a Unit Circle

B) Butterworth Filter Sections

Second Order Block, Normalized, Scaling, Third Order Block, Nth Order Block, Normalized Element Table

C) Butterworth High-Pass Approximation

Ideal Normalized High-Pass Filter, Low-Pass to High-Pass Transformation

D) Butterworth Band-Pass Approximation

Ideal Normalized Band-Pass Filter, Low-Pass and High-Pass Configuration

E) Butterworth Band-Stop Approximation

Ideal Normalized Notch Filter, Low-Pass and High-Pass Configuration

F) Chebyshev Low-Pass Approximation

Chebyshev Approximation,

G) Chebyshev Polynomials

Chebyshev Polynomials, Roots on an Ellipse

H) Normalized Chebyshev Low-Pass Table

Normalized Element Table for -1dB and-3dB Ripple

I) Design Example

Fifth Order Design

J) Bessel-Thomson Low-Pass Approximation

Delay Approximation,Bessel-Thomson Polynomials,

K) Normalized Bessel-Thomson Low-Pass Table

Normalized Element Table

L) Step Response

Approximating Delay Based on Bandwidth

M) Delay Scaling

N) Passive Butterworth Low-Pass Filters

O) Passive Butterworth High-Pass Filters