*After a few more revisions, and if there is positive feedback I might work on getting a print edition made.*

**This is a work in progress, and this is currently in the form of a PDF download.**This lesson plan is not meant to cover the study of electromagnetics in general. Rather, this lesson plan is meant to augment a study in electromagnetics with several labs, mostly computational. These lesson plans use a circuit simulation tool called Circuit Mason, which is a simple way to explore complicated concepts without the need for expensive test equipment.

These lessons are divided into three sections: Theory, Simulation, and Advanced Concepts. The Theory section does not take the place of an actual text book on the materials, this is a supplement. The Simulation section explains the basic mechanics for running Circuit Mason, and begins to intertwine the theory with modeling. The Advanced Concepts section provides a greater understanding of advanced RF concepts and how to apply Circuit Mason to them.

It is hoped these labs might become adapted to a college or
advanced high school class, or perhaps the motivated amateur or ham.
It is assumed the reader is familiar with basic electronics concepts
such as Ohms law, voltage dividers, and complex numbers. This lab is
most useful if the reader is familiar with basic electromagnetic
propagation theory and transmission line theory.

**If you are a teacher who:**

**would like to incorporate this into a class (true educational purpose), and****the work book cost is too high for your class, and/or****the work book needs some revisions to fit into a curriculum...**

**Then contact me and we can probably work something out. I have a long history of volunteer tutoring high school and GED students, and I would love to continue to help inspire future engineers.**

**Table
of Contents**

Special Request: 1

Introduction 2

Circuit Mason 2

Installation 3

Theory 4

Lesson 1: Voltage waves 5

Motivation 5

Section 1: Voltage waves 5

Section 2: Wave Bounce Diagram for DC voltages 7

Section 3: Wave Bounce Diagrams for Digital signals 9

Section 4: Wave Bounce Diagrams for RF signals 10

Lesson 2: Reflections and Transmissions 13

Motivation 13

Section 1: Reflection and transmission in log scale 13

Section 2: S-Parameters 13

Section 3: Voltage versus Power Gain 16

Section 4: S-Parameters and multiple driven ports 17

Section 5: Smith Charts 19

Section 6: S-Parameters equations 22

Simulation 23

Lesson 3: Introduction to Simulation 24

Motivation 24

Section 1: Using Mason to Solve Circuits 25

Step 1: How to place a control element 25

Step 2: Place the control elements 27

Step 3: Add a simple transmission line 28

Step 4: Fix the Width of the Value Field (if needed) 29

Step 5: Modify the Parameters 30

Step 6: Connect the transmission line to the Ports 31

Step 7: Generate the symbol references 32

Step 8: Run Mason and Plot 33

Section 2: Mason Plot 34

Section 3: Observations 37

Lesson 4: Optimization with variables 38

Motivation 38

Section 1: First Attempt at Improving the Quarter-Wave Transformer 38

Section 2: Second Attempt at Improving the Quarter-Wave Transformer 40

Section 3: Using the optimizer 43

Lesson 5: Power Dividers and Advanced Optimization Techniques 50

Motivation 50

Section 1: Dividers 50

T-Junction divider 51

Wilkinson divider 52

Lossy divider 53

Section 2: Sets with a Wilkinson with Extra Line Length 53

Lesson 6: Statistical Design 57

Motivation 57

Section 1: Statistical Analysis 57

Section 2: Statistical Optimization 60

Supplemental Materials 61

PrimCalc 61

Designing from Physical Properties to Electrical Properties 61

Designing from Electrical Properties to Physical Properties 62

PADS-ASCII output 63

MATLAB/ Primitive File Output 64

Motivation 64

Details 65

Subcircuits 66

Advanced Concepts 68

Lesson 7: Lossless Taper Design 69

Motivation 69

Section 1: Circuit Analysis 69

Lesson 8: Broadband Wilkinson Design 74

Motivation 74

Section 1: Even and odd mode analysis 74

Even Mode: 75

Odd Mode: 75

Optimization technique 78

Resistor choices 79

Circuit Design 80

Lesson 9: Broadband matching with Constant Q Lines 81

Section 1: Constant Q Lines (heavy on the theory) 81

Neat Smith Chart Fact 81

Constant Q Lines 81

Section 2: Designing a Simple Matching Network 83

Section 3: Designing a Matching Network with Constant Q Lines 87

Appendix A: Using the Math Parser 90

muParser 90

Built-in variables 90

Built-in functions 91

Built-in binary operators 92

Appendix B: Flags 93

Special File Outputs 93

Output File Data Formats 94

Random Number Generation Controls 95

Appendix C: Complete Optimization and Statistics Options 96

Goals 96

Optimization sets for parameters and Figures of Merit 97

Optimizers 98

Statistical Analysis Tools 100

Appendix D: Select Mason Models 101

Lumped Elements 101

Simple Transmission Lines 102

Connectors 102

Microstrip structures 103

Appendix E: Making Dynamic Components 107

Basic attributes 107

Arguments 108

Assumptions 108

Calculations 108

Synthesis (optional) 109

PCB (optional) 109

Example primitive file: a lossless transmission line 112

Additional Constraints 112