32-RF/Microwave Circuit Analysis Overview

In this post, we will shift gears from creating a circuit diagram to circuit analysis. The circuit analysis method is based on methods described in Chapter 6 of "Computer-Aided Analysis of Linear Circuits" by M. L. Edwards published in September 2001 online.  The paper describes general N-port linear RF/microwave circuit analysis in Matlab circa 2001. A modern Matlab version is available in this GitHub repository.

The circuit analysis method is:

// *********************** Circuit analysis process ***********************
// 1) Define default units
// 2) Deine the frequency range
// 3) Define the circuit as a netlist
// 4) Add each component admittance Y-matrix to circuit Y-matrix
// 5) Reduce circuit Y-matrix to 2-port Y-matrix
// 6) Convert Y-matrix to S-matrix
// 7) Repeat steps 4-6 for each frequency
// 8) Display the results on plot or/and data table
// ***********************************************************************

The key equations used in the admittance matrix method are:

From "Computer-Aided Analysis of Linear Circuits", M.L. Edwards, pg. 6-6.

Note that the matrices are created using the complex admittance of the circuit components. Because of this, we need a complex matrix library for C#. For this project, we will use a Nuget library called MathNet.Numerics. The library supports complex numbers, complex math operations, complex vector operations and complex matrix math. The reader can find documentation and tutorials on the library here.