A good Smith Chart program

What are you trying to do? I have gotten much use of the Smith chart primarily for use with optical thin films. I use the chart as a conceptual tool, but when I get down to serious work I use two by two matrices with complex components. I think that there use was pioneered by Ernst Guillemin and others in the 1930;s and 1940's. Sometimes they are called ABCD matrices.

Bill

-- Fermez le Bush--about two years to go.

Do you know of any program using ABCD matrices with complex elements? I've used APL in the past, but it's pretty complicated for use on a PC.

I wrote a paper back in 1953, on transistor analysis using ABCD matrices. I never found an easy way to do the calculations required.

With programs like SPICE, other methods are probably not very useful.

try "Smith" at

"Tony" wrote in news:eqm8it$3o1$ snipped-for-privacy@aioe.org:

Doesn't look like a bad program. I'm currently taking a course called: Distributive Systems.

We are learning about transmission lines and the inital part of the course was interesting, now we got into all this Smith Chart stuff and it's slightly confusing as to what I'm trying to accomplish.

Thanks for the help.

I am not all that much into programming since I retired. I have written programs in BASIC and Pascal for optical thin-films (very similar to electrical four-terminal applications). I have also adapted the technique for analyzing optical resonators to an HP-67. I have used the same concepts for Excel spread sheets.

Once you get started, it is pretty straight forward. As in all programming, you have to kill any bugs or prevent them from hatching in the first place. As for programming hints, I offer the following.

1. For vectors that matrices work upon, only the ratio counts. The impedance is Z=V/I corresponding to matrix vector [V,I]. Thus, you can use vectors with components [Z,1] to track impedance through a series of four terminal networks using ABCD vectors. For optics, the local index is n=H/E where E represents the electric field and H represents the magnetic field.
2. What happens in the network or thin-films can be represented in several ways. For example, you can track the impedance, or alternatively, the forward and backward waves (in terms of a complex reflection coefficient). These are related by similarity transformations. Similarity transformations are part of a study of linear algebra and well worth understanding.
3. A short summary of ABCD matrices is given by Louis Pipes in the Condon Handbook of Physics.
4. Way back, John Slater in the book Microwave Electronics discussed the bilinear transformation as a conformal transformation of complex quantities. Every EE should understand that backwards and forwards.

Bill

-- Fermez le Bush--about two years to go.

Think of the Smith chart as a plot in the complex reflection coefficient plane. The same information provided by the Smith chart can be presented in many other ways. That is why, in another post, I suggested learning linear algebra including similarity transformations. Also consider bilinear transformations as espoused by John Slater.

These concepts will be useful in many branches of technology. Some examples are crystallography, cartography, optical thin-films, electron spin, and many other scientific inquiry. The point to remember is that the same mathematics describe many apparently diverse phenomena.

Bill

-- Fermez le Bush--about two years to go.

I have pipe's book "Matrix Methods for Engineering". What I was looking for was a PC program for doing simple calculations with ABCD matrices with complex elements. Such programs exist in APL, and there is a PC version of APL, but this is too cumbersome.

I use the "slide rule" equivalent of the Smith Chart for RF calculations. For thin film optics, my usage has been limited to di-chroic reflectors. For these, ray tracing works.

I don't know what you mean by ray tracing in this context. If it is a way of adding up partial reflections at each surface, the result can be treated as a similarity transformation between impedance (or index) and reflection coefficient.

bill

-- Fermez le Bush--about two years to go.