Using Matrices to Calculate Transmsmisison through 1D Layered Media

• Multiply 2x2 matrices, one for each layer to get an overall matrix connecting intial and final amplitudes
• Applies to optical filters where two field componenent are conserved across a boundary
• Applies to acoustical filters where one has area changes, holes, or side branches
• Applies to a series of abrupt quantum wells (continuous wave function and derivative)
• Text discussing the theory of an acoustical wave guide. A lot of this devotes itself to details of particular situations, but several pages go through showing how to compute the transmission coefficient from matrices.
• Spreadsheet for an acoustical waveguide with up to six boundaries.
• The matrices are complex, so this resorts to computing real and imaginary parts at each stage and going on to the next stage. After the first or 2nd stage, most of the later stages can be done by copying and pasting for the next stage.
• This sheet is poorly documented, but one can see the general outlines of how it behaves.
• The transmission coefficient varies with frequency, and this sheet uses VBA to loop over frequency and then display the results in a graph.
• The user has control of starting frequency, frequency step and final frequency. Feel free to change these and then do a fresh plot of transmission vs. frequency.