Open Wire Reactance and Resistance Calculation

[W4AMV]

Steve in his prior post is correct and identification of the antenna terminal impedance vs. frequency, for example, is key. With that accomplished, there are a number of interactive Smith Chart programs which are easy to learn to solve the original post. See the site shown below.
 
http://sss-mag.com/smith.html

EZNEC DEMO will handle the impedance problem, or try any of the NEC freeware programs like 4NEC2. However, EZNEC in its DEMO form is really easy to learn and quite FUN and addictive! The DEMO version will readily handle most wire arrays.

Then after finding the antenna Z (from a WIRE MODEL) use the Smith Chart utilities to calculate the Z looking into the feed line or any other matching system. As Walt highlighted, this can be accomplished via math calculation. However, the REAL BEAUTY of the INTERACTIVE Smith Chart utilities is you obtain a quick intuition and feel for what reactive elements will accomplish and how the antenna impedance gets modified. I wrote one of these routines in MathCAD in 2001 and it appeared in Applied Microwaves. It is located at the site mentioned above. However, there are far more powerful and intuitive Smith Chart utilities available as shareware and I will try to post one or more of them here.

Alan W4AMV

[Steve - K4HX]

If you use feet for the cable length, the graph will be in feet. And yes, multiply the numbers by 100 (at least for this example).

See the image below. Notice this image is displaying ONLY current. You'll see a current peak at around 0.16. This means the current peak is 16 feet back towards the antenna from the tuner end of your 113 foot long feedline. So, if you cut off 16 feet or made the feedline 97 feet long from the start, you'd be at a current peak (or close enough).

W4AMV mentioned some modeling programs. 4Nec2 will model the feedlines too and do stub and matching section calculations.

Steve:
I see the horizontal axis current peaks are at .16, .82, .146.  Do I multiply by 100 to arrive at 16, 82 and 146?  Are these numbers in feet i.e. 16 feet, 82 feet and 146 feet for the current loops?  At first I thought these numbers were in wavelengths.

Thank you.
Chuck

[aa5wg]

Alan, Steve and all:

Thank you for the information regarding Smith Charts.  I will look for one of these programs and give it a go.

Steve, the calculated input impedance at the antenna coupler and feed line is found to be 83.48 ohms +j371.24.  This +j371.24 inductive reactance translates to a 8.3 uH coil.  This is for the 113 foot feed line example.

Question:  Can I use this 8.3 uH coil as a single shunt inductor at the input of the line at the antenna coupler?
               And/or, could I divide 8.3 uH by 2 and place a 4.15 uH coil in series with each leg of the ladder line at the line input to antenna coupler?

Thank you.
Chuck

[W4AMV]

Hi Chuck. Glad to help, what FUN! I need clarification on your question. The calculated input Z at the antenna coupler (which is at the end of the feed line??) is 83.48 ohms + j 371.24 ohms. Is that correct ? If that is the case, then the problem is to match this to 50 ohms ? If that is the case,  then you calculated the SERIES impedance at a given frequency and found that the equivalent L is +j371.25 ohms. Is that correct ? If so, then you only need to add a series CAPACITIVE reactance at THAT calculated frequency. That reactance is -j 371. Now I would have a real value remaining of 83 ohms. Not a bad match to 50. So... you can see, I hope, why I have a problem with your QUESTION. Let me know where I might be amiss.

[W2DU]

Hi Chuck,

Glad you found the stub-matching material of useful value.

The 1606A and B are identical except for cosmetics--the A is black and the B is gray. Oh yeah, I forgot--the knobs on two are of different style.

On my Z-matching material in Reflections, as you know, I couldn't attach those files in BAS or EXE. Don't know why they're not allowed as attachments. So here's what I'm gonna do--I'm gonna email them to you. In the form you'll receive them you can use them directly on receiving them. Since you have an edition of Reflections the explanation of how to use the programs is explained in Chapter 15, along with the print-out of the programs. You'll find it interesting that when using the hyperbolic program on the PC vs the hand calculator with reverse-polish notation, the answers come out identically to at least 10 significant figures. They sorta validate each other, hey?

Chuck, you didn't say whether you're the same Chuck Pool I corresponded with several years ago.

Walt

[aa5wg]

Hi Walt:
Thank you for the information on the 1606A and 1601B.
Yes sir, I am the same guy who corresponded with you several years ago.
I enjoy reading your books.  I have three of them.
I look forward to receive your email and giving the software a go. 
Thanking you.
Chuck

[aa5wg]

Alan:
The calculated input Z at the antenna coupler is at the end of the feed line and it is 83.48 ohms +j371.24.  Yes this is correct.  The challenge is to match this to 50 resistive ohms, yes.  I did not calculate the SERIES impedance at the given frequency of 7.15 MHz.  At least I don't think so.  I have not had any good sleep for a couple of days and I think I goofed.  The calculated impedance was found to be 83.24 ohms +j371.24 (inductive) thus I should add -J371.24 of capacitive reactance to cancel the found inductive value of +j371.24.  This translates to an approximate capacitor of 60 pf.

Question:  Can I shunt this 60pf capacitor at the input end of the line at the tuner?  And/or could I also divide this 60 into two 30 pf capacitors and place one capacitor in series with each side of the line?  This would take place at the line input at the tuner.

Did I get it right?  I hope so.
Chuck

[W4AMV]

Hi Chuck. Yes, you almost on the track. The impedance between the terminals is SERIES in form. That is to say, IMPEDANCE is by definition a SERIES network. Therefore, to accomplish what you desire, you need to add a SERIES element. If you wish, add twice the required C in each arm of the feed line. Or, of course you could add a 1:1 balun. However, recognize a balun is not perfect and the impedance that you initially had will be slightly modified by the reactance of the balun. In any case, to your question, 120 pF added in series with each arm is desired. If you wanted to add a parallel element, you are going to have to find a PARALLEL network which has the same frequency response as this SERIES IMPEDANCE network.  And it exists! However, that is a topic for another thread! Hope this helps.

[aa5wg]

Alan:
The link antenna coupler I use can switch between series or parallel configuration.  Series for low Z line input and parallel for high Z line input.
I calculated 60 pf worth of shunt capacitance is needed to cancel the inductive reactance.  Or, I could use 120 pf worth of capacitance in each leg of the input line for series tune.  Is this correct?
Chuck

[k4kyv]

Alan:
The link antenna coupler I use can switch between series or parallel configuration.  Series for low Z line input and parallel for high Z line input.
I calculated 60 pf worth of shunt capacitance is needed to cancel the inductive reactance.  Or, I could use 120 pf worth of capacitance in each leg of the input line for series tune.  Is this correct?

The impedance is 83.48 ohms +j371.24.  That is a low Z line input, so the link antenna coupler will need to be in series configuration. Adding 120 pf in series with each leg would be equivalent to reducing the total capacitance in the main tuned circuit, since you are effectively placing the series tuning capacitor(s) in the ATU in series with the 120 pf capacitors you inserted into each leg of the balanced feed line to cancel out the +j371.24  .  You should be able tune out the reactance with nothing more than the main tuning capacitor, without the need for an additional set of 120 pf capacitors.  The main tuning capacitor would simply resonate at a lower capacitance setting than it would if the 83.48 ohms were purely resistive.

If the transmitter is picky about working into something close to a 50Ω load, you can transform the 83.48Ω to 50Ω, either by physically adjusting the link if it is set up for variable coupling by swinging the link in and out of the coil or else by rotating it variometer style, or by placing a variable capacitor in series with the link.  See a late 50s or early 60s ARRL handbook for figuring out how to determine the size of the series variable capacitor.

[W4AMV]

Sure, yes Don and Chuck. You're matcher is far more flexible than I had in mind!

[aa5wg]

Don, Alan , Walt and all:
Give me a couple of days please before I ask a follow up question.  I do appreciate all of your help!
Please check back because I value your advice very much!
Chuck

[aa5wg]

Hi to all:
I am still have a couple of questions.  But, I need to finish some reading.  I will check back as soon as I can.  Thank you for your help.
Chuck