Effects of complex impedance thru a current transformer

I guess this is a "Oldztimerz" brain cramp question.

What should happen to complex impedance "Z" when it gets passed through a multi-filar toroidal current or voltage transformer/balun -- whether it is 1:1, 4:1, 9:1. etc, and both ports have self-resonance well above the test frequency?

I've spent a bunch of time this afternoon scouring sources like Jasik, Cebik et al., ARRL Antenna Handbook 21, and searching the Internet, with no real answers. (I realize my books may be dated -- like my Jasik is 1961, my ARRL Antenna Handbook is 2007 ...)

I 'm using home brew test equipment while doing measurements on a few more of my odd ball "HOA Stealth Antennas" (HOASAs??) for use in any number of single/multiple band configurations for 7-30 MHz. I don't really believe some of my measurements, and I really don't want to jump to conclusions just because I can get good matching at multiple lengths of feedline, good A/B results against a pretty reliable 135' doublet up 40 feet, and good results on 20/40 meter JT-65/JT-9 from a particular configuration.

Unless I'm really reading things all wrong, almost all the background information I've found is for using nearly non-reactive impedances on one or both sides of the transformer/choke. I can't seem to find anything that allows me to predict what might happen when relatively high or low reactance-to-resistance passes through an RF transformer/balun/choke.

I hope this makes sense.

What am I missing?



Thanks,
Crazed Ken/K8KJG

 

You are trying to understand a math model of a circuit that would require a year and a half in EE school. Nobody is just going to solve this specific problem and publish it. People who know how to make the model and solve for variables don't need a solution to appear somewhere. They can do it them self and they expect others wanting to also do it..

The problem you are trying to solve is more complex than you realize.

There is no such thing as reactance. That's why "imaginary" numbers are used to solve a function that can't be solved, ie. sqrt(-1) Reactance is created and used in mathematical models to represent RF or AC current flow from a voltage source but the phase of the current either leads or lags the applied voltage across a source or load. That out of phase current changes the solution in the model.

The model used to solve your problem depends upon whether the transformer is a transmission line type or if it is an auto transformer type. The math model will we different.

Although not an accurate statement at all, some explain an RF transformers effect on a complex wave represented by RF current as a step up or down in IMPEDANCE as a tranformer would transform a resistive source. This is totally different when a complex source feeds an LC circuit like an antenna tuner which transforms only resistance but absorbs, cancels reactance. Reactance is not transformed in an LC circuit.

Advice to all, if you want to solve engineering problems then go to engineering school. People are always trying to find shortcuts.

 

Mr. REASTON,

I don't disagree with some of what you said. However, your condescending and arrogant answer is of little value to anyone.

I do have just few years beyond a high school education when it comes EE/RF/Math/Physics, and from some pretty good schools. I also have more than just a couple of days in the RF/microwave research and design industry.

Identify yourself on a QRZ page so we know who you might be, where you might be, and what your credentials might be.

Ken
An Uneducated and Inexperienced Curmudgeon
K8KJG

 

Update:

Mr. REASTON,

After my post above, I must apologize to the forum for my post. I should have just ignored Mr. REASTON.

I looked at all twelve of Mr. REASTONS's posts over about the last year. If he holds an FCC or other government granted license to be part of the amateur radio community -- great. He remains totally anonymous.

All of his posts have been insulting, condescending, and inappropriate.

If I were a moderator, I'd ban him, and erase his negative and demoralizing posts that keep others from asking valid questions.

Ken

P.S. In my original post here, I must have double-thumbed a key or two. The post includes a screen capture of an on-line wavelength calculator I was looking at this morning when doing some measurements.

 

I'm gonna write that down.

 

The quick and dirty answer is that Re and Im are scaled by the Z ratio of the transformer, whatever it's type. I.e. 200+j400 transforms to 50+100 through a 1:4 xfmr.

The closer your transformer is to ideal, the better. That's the simple version of the answer that you may already know When impedances get extreme or freqs get near resonances or leakage inductances become significant, then naturally things get more complex! I don't often run into cases where xfmr imperfections make much of a difference (YMMV), but seam to recall that ABCD matrices were the way to solve.

 

I especially want to thank the many who contacted me outside of this forum thread, and for those who posted in this thread, like KD6RF.

I got the answer I was looking for, thanks to several kind individuals who contacted me privately.

It is way past my bedtime. Tomorrow I'll individually thank those of you who chose to provide backup to my questionable findings.

Again, thanks to all who assisted.

In the not too distant future I hope to put out a compilation of simple and inexpensive, but very effective stealth MF/HF antennas for those living in antenna-restricted communities.

Regards,
Ken
K8KJG

 

Keep up the good work Ken - hands-on antenna and circuit work is my fav part of Ham Radio.

Don't let REASTON bug you - Ol' Yeasty O.D.'s on his morning Grumpy-O's on occasion. We've learned to ignore him

 

Good answer! At HF, the transmission line in a TLT wrapped around the core is likely a small fraction of a wave length and will not rotate the impedance around the Smith Chart much.
"Reaston" is probably not an amateur radio operator.
73,
Pete

 

I think there's value to both ignoring and confronting nitwits