measuring characteristic impedance

If we tell you that for AWG 24 stranded twisted-pair cable, the characteristic impedance is around 120 ohms, would you accept it, or would you still like to know how to measure this value?

For low frequency Zo, it is easy. First, take a short length of line, leave the far end open and measure the capacitance. Then short the two wires at the far end together and measure the inductance. The characteristic impedance is the square root of L/C. Make sure you know what frequency is being used to measure L and C and be sure that your length of line is < about 0.05 wavelengths at that frequency.

Measuring high frequency (dispersive) Zo is much more difficult. I will give you references for that if you want. The techniques are related to micronwave network analyzer calibration. Lots of math.

Dr. Rautio,

I am a self-starter in EM simulations for MW/Antenna/RF structures. I want to develop a strong understanding of EM fudamentals used in the simulation of these structures, could you please advice me regarding how to start ?....could you please be kind enough to suggest me few books or references....I would greatly appreciate your kind help.....

Thank you

There are probably a zillion ways to measure it.

One crude way: unroll a good length of line (say 50 feet or more), solder a 120 ohm resistor to the far end, at the close end hook up a pulse generator and and oscilloscope. See if there is any reflection of the pulse rising edge that is observed on the scope after a round trip time delay. If you can see any voltage spike, solder a different value, 110, 130, etc ohm resistor at the far end. When you have soldered the resistor that results in the smallest reflection back to the source, read that resistor value and that IS your characteristic impedance.

Make sure that you use "low inductance" resistors. Chips are best!

Hi maverick09 -- I needed about 3 years of grad school at Syracuse University to get started doing numerical EM. This was after about 8 years doing microwave design. This one is hard to self-teach.

First you need to get a good understanding of basic EM theory. I used Harrington, "Time Harmonic Fields" and two semesters of graduate level EM courses. There are several more recent books (by Pozar, Jackson, Balanis, and others) that also do a good job in this area.

Then, to solve numerical EM problems, the classic book is again by Harrington, "Field Computation by Moment Methods". I was really lucky on this one, Harrington himself taught the course. The book is very intense in linear algebra and field theory. If you have a solid understanding of field theory (for example, you know how to use infinite sums of Hankel functions and spherical Bessel functions, etc.), then the Moment Method book might be something you can learn on your own. I know of no more modern book on the topic. Harrington pretty much said it all. There are also books on FEM and FDTD and TLM, but I do not work in those areas.

If you decide to go for a Ph. D. in numerical electromagnetics, be careful. At least for linear problems, there are very few areas that have not been almost completely researched, you may have difficulty finding a dissertation topic. However, there are a lot of non-linear problems left to work, but Method of Moments works only for linear problems, so you will have to find some other kind of approach. FDTD has seen a lot of work in this area recently. Non-linear TLM, as far as I know, would also be good.

If what you want to do is to learn how to use existing EM tools, I'm sure there are a number of good books. The best is probably one by Dan Swanson and Wolfgang Hoefer, but that is about filters. If you do filters, Dan's book is an absolute must have. Your specific problem is known as a 2-D problem. I think there are a lot of public domain tools for solving that, a google search should turn up all kinds of possibilities, but I don't work in that area myself. Perhaps others can make some good suggestions.

biff44 -- An advantage of your measurement approach is that it takes an average of Zo over the bandwidth of the input signal, which might be more useful than just the low frequency Zo. Also, it would be real easy to watch the TDR and introduce discontinuities (like walls, people, pieces of metal, etc.) near the line and see how much affect they have on the reflection.

Dr. Rautio,

Thank you for your valuable suggestion. I am doing my Ph.D in Microsensors/MEMS. I am greatly interested in RFMEMS structures and their EM simulations. I am currently working on the design of antenna, our group has a license for a popular FEM based software, so I have to work on it.......

However I dont have a background of MW simulations, so I was wondering how could I start in understanding the theory behind any general EM simulations and hopefully learn finer points of the simulation........ and produce better results......

Thank you.

Hi Maverick09 -- I think you would do well to grab one, or perhaps two semesters of course work at the graduate level on EM theory using Harrington's book, or one of the more recent equivalents. You will learn the tools you need to understand numerical EM theory. It will be hard, but work away at it until you understand it completely. The numerical EM you can then probably pick up on your own. There are books out there about FEM and FDTD and TLM, all good volume meshing techniques. Those are not my areas so I don't have good references available at my finger tips. The most rewarding part is when you start seeing how everything all fits together so beautifully, and all that complicated stuff we all used to be so afraid of...is really very simple. Trying to describe how beautiful the mathematics is to those who have not yet realized this simplicity is like trying to describe the beauty of music to someone who can not hear. You will understand when you arrive. Good luck!

Hi,
Can anyone tell me why 50 ohm is always considered as the characteristic impedance. Is there any history behind it.

Thanku

In coaxial cables 50 ohms can be conveniently made. It is difficult (because of the log radius ratio) to get below 30 and above 90 ohms. Many of the parameters of maximum power and minimum attenuation were for air dielectric cable and do not apply to plastic dielectric cable as commonly made today.

In the early days of HF and below it was common to use parallel conductor transmission lines with mostly air insulation. Common impedances were 75, 300, and 600 ohms. The phased array antennas used the 300 and 600 line because it was close to the antenna impedance. 75 was close to dipole impedances.