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...
Circuit Mason Labs (as E-book, PDF format)
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