I'm trying to work out how to solve an engineering problem. I'm hoping Sage can help me, but I can't work out the maths of it. I'm hoping someone here might be able to.
A vector network analyzer (VNA) is a bit of electronic test equipment which measures complex impedance values as a function of frequency. Let's assume at 500 differenct frequencies. The VNA should be calibrated prior to making a measurement. It's calibrated using some standard devices. * A 50 Ohm resistor. Assumed to be perfect. * A short circuit, which is not perfect, and so it is characterised by 4 parameters called Ts, L0, L1 and L2. * A open circuit, which is not perfect, and so it is characterised by 4 parameters called To, C0, C1 and C2. These standards are expensive (several thousand $'s). Knowing the true values of these 8 paramters, which are pre-programmed into the firmware of the VNA, the computer in the VNA can calculate a set of correction coefficients which can remove most of its systematic errors. The values of these 8 parameters are all known. But how they affect the measurements is not known. But the point is, that using these high quality standards, on a good VNA, the results are accurate. Now comes the tricky bit. I have a second VNA, which is differnet from the first. It too uses the 50 Ohm resistor, short circuit and open circuit. But it uses a different set of open and short circuits. These are cheap or home-made ones, for which we don't know the values of the 8 parameters Ts, L0, L1, L2, To, C0, C1 and C2. So if I program in 8 random values for these paramters into the second VNA, and take a mesurement at 500 frequencies, I can be 99.9999% sure the resuts will be wrong. Is there any way, by comparing * True values, measured on a VNA with good calibration standards * Incorrect values, measured on a VNA with standards which have unknown coefficents I can work out what the value of these 8 coefficients should be? It is tediuous to change the coefficents in the VNA, so comparting results at 500 frequencies with lots of different values for the 8 paramters is not practical. Would programming in 8 differents sets of coefficients be sufficient to work out the correct values? (That would be 64 coefficents in total). That would be very tedious to do, but it might be possible. It *may* be possible to program them by computer, but I am not sure of that. They might need to be entered manually with keys on the VNA, which will be tedious. Can anyone help me with the maths, and give me an idea what functions in Sage might help. I'm guessing this is some non-linear fitting problem, but I'm not sure. Dave -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
