[Antennas] Xms Line Zo,Formerly Hairpin monopoles
George, W5YR
[email protected]
Fri, 9 May 2003 14:27:19 -0500
Jim, you seem to prefer keeping this discussion on the reflector when your
objections properly belong in a private forum. However, that is your choice
. . .
Let me be as brief as I can.
You have chosen to view a very complex subject through the convenient
knothole of "typical amateur radio HF" practices. Consequently, you have
reached conclusions which while they work well enough in that area, are NOT
generally true, and neither Wes nor I are in error for pointing this out to
you.
Consult any undergraduate level text on transmission line theory and you
will find from the earliest discussion of first principles that
characteristic impedance is a frequency-dependent property of a line, any
line, any frequency, any termination, any construction, etc.
Now, you will also find that given certain fortuitous relationships between
certain line parameters you obtain the famous Heaviside line which amounts
to an all-pass filter. However, such a line has little if any practical
application due to the constraints placed upon it to meet these conditions.
So, in the real world, we proceed further and find that certain terms
involved in the basic equations that define Zo = Ro +jXo take on small but
not necessarily negligible values within certain frequency ranges. Not zero
values, note, just small possibly negligible values.
As amateurs, we take advantage of this and just ignore the Xo component of
Zo although it is not zero and is stated clearly for you in the TLDetails
program for each line in its list. You can choose in the program to either
ignore Xo or to use it.
Once we elect to regard Zo as a purely real quantity, we then are free to
make all sorts of convenient assumptions and approximations, including
calculating Zo of a given line structure from its geometrical format, etc.
So, that is where you are coming from: the world of approximations and the
elimination of complicating matters like complex Zo. The information I gave
you, and which Wes confirmed, was from the formal world of actual
definition, etc. which applies to *all* line applications regardless of
frequency, etc.
You choose to claim that what I say is incorrect because it disagrees with
your understanding of the matter. You are certainly free to reach that
conclusion and even to state it publicly as you insist upon doing.
Nonetheless, your conclusions are not correct in the general case nor am I
incorrect in stating the points that I did.
I hope that this will clarify at least my position in this tiresome matter.
I have said all that I intend to say since you feel compelled to doubt it
all in the first place, based upon your limited outlook.
And, yes, I am the unfortunate who posted an error concerning the
driving-point impedance of a folded dipole. Now, for the benefit of the
audience, how many other errors have you found?
Enough! Go forth and hold good thoughts and stay well.
73/72, George
Amateur Radio W5YR - the Yellow Rose of Texas
Fairview, TX 30 mi NE of Dallas in Collin county EM13QE
"In the 57th year and it just keeps getting better!"
<mailto:[email protected]>
----- Original Message -----
From: "James Duffer" <[email protected]>
To: <[email protected]>; <[email protected]>; <[email protected]>
Sent: Friday, May 09, 2003 8:10 AM
Subject: [Antennas] Xms Line Zo,Formerly Hairpin monopoles
> I am not questioning your desire for accuracy, and I know you would not
> deliberately mislead, but there may be some questionable content....I
recall
> that you erred previously on the impedance of a folded dipole...at least I
> think it was you....
>
> snip
>
> >I am sure that Wes and I would interested in knowing what you find out in
> >your investigation. I don't know about Wes, but I feel that my
contribution
> >is to provide accurate information about topics with which I am familiar.
> >Whether or not you choose to accept it is your choice - not my job! <:}
>
> I really haven't went to extremes in researching this....just reviewing
> Chapter 19 of the "ARRL Handbook for Radio Amateurs" and the "Antenna
> Engineering Handbook" Third edition by Richard Johnson, Chapter 42
> "Transmission Lines and Waveguides by Roderic V. Lowman. I also visited
the
> URL furnished by Wes which was more appropriate forfinding impedance
> resultingb from mismatched transmission lines rather than the
charateristic
> impedance Zo sometimes referred to as the "surge impedance".
>
>
> >For the record, however,
> >
> >1. the characteristic impedance of any transmission line is a complex
> >quantity of the form Zo = Ro+jXo
>
> With the jXo being insignificant for most applications. Zo equals the
> square root (L/C) where L and C is equal to the distributed linear
> capacitance and inductance and is determined primarily by the geometry of
> the transmission line.
> >
> >2. depending upon the frequency range involved, the reactive component Xo
> >of
> >Zo may or may not be of importance
>
> *****DEFINITELY******** Especially when the frequency range is within the
> normal range for the particular transmission lines application (where line
> losses are tolerable)
>
> >3. coax cable manufacturers *do* provide the complex Zo values for their
> >cables; the TLDetails program Wes referenced will show you what it is for
> >each of many commercial cables, and the calculations within the program
use
> >the complex Zo values;
>
>
> Not typically available or indicated on coaxial cable see charts provided
> with above mentioned reference material. Refer to the chart on Table 19.1
> Characteristics of Commonly Used Transmission Lines, Page 19.3 of the 1997
> ARRL Handbook for Radio Amateurs. I hope you are not getting the pf per
> foot column confused. The Zo is listed in the first column and it is not
a
> "complex" value.
>
>
> >4. your geometric interpretation is a useful approximation, within
certain
> >frequency ranges, but is not universally applicable nor is it a formal
> >definition of Zo
>
> Agree that it is not the "formal definition of Zo", however it is the most
> common method of determining it if you do not have the means to measure
the
> linear distributed capacitance and inductance. Again refer to most text
on
> transmission lines especially two wire and coax. If you want to "pick at
> knits", it could become more complicated.....but that isn't necessary. If
> you were to construct your on two wire transmission you coluld get a good
> approximation by the formula Zo=276Log2S/d. Agreed that proximity of a
> ground plane does actually influence the Zo, but why convolute the process
> with frequency?
>
> >5. characteristic impedance is a complex quantity.
>
> If you desire to make it so, by bringing in a bunch of insignifacnt
factors
> other than geomety of the line.
> >
> >73/72, George
> >Amateur Radio W5YR - the Yellow Rose of Texas
> >Fairview, TX 30 mi NE of Dallas in Collin county EM13QE
> >"In the 57th year and it just keeps getting better!"
> ><mailto:[email protected]>
> >
>
> If you desire to compare radiation resistance with Zo in and analogy
manner,
> its all right. The world will not be any worse for it. However I see a
big
> difference and little relationship between them.
>
> 73, Jim, wd4air\\
>
>
>
> @hotmail.com>
> >To: <[email protected]>; <[email protected]>
> >Sent: Thursday, May 08, 2003 10:09 AM
> >Subject: Re: [Antennas] Re: Hairpin monopoles
> >
> >
> > >
> > >
> > >
> > > >From: Wes Stewart <[email protected]>
> > > >To: James Duffer <[email protected]>, [email protected]
> > > >Subject: Re: [Antennas] Re: Hairpin monopoles
> > > >Date: Wed, 7 May 2003 17:10:50 -0700 (PDT)
> > > >
> > > >
> > > >--- James Duffer <[email protected]> wrote:
> > > >[snip]
> > > >
> > > >George's explanation is of course right on.
> > > >
> > > > >
> > > > > An interesting analogy but leaves some questions.
> > > > > If the transmission line
> > > > > is terminated in a load that is equal to the
> > > > > transmission lines
> > > > > characteristic impedance, then what has frequency
> > > > > got to do with
> > > > > characteristic impedance???? The charateristic
> > > > > impedance is dependent on
> > > > > the physcial construction
> > > > > conductor diameter and distance of the conductors.
> > > >
> > > >Characteristic impedance is dependent on R, L and C
> > > >per unit length. R, L and sometimes C are frequency
> > > >dependent.
> > >
> > > Which is dependent on the physical construction of the transmission
> >line.
> > > Refer to the formulas for Zo of parallel or coaxial lines (Zo= 276 Log
> >2S/d
> > > where S is center to center distance between the conducior and d is
> >diameter
> > > of conductor[same units], Zo= 138 log (b/a) where b is inside diameter
> >of
> > > outer conductor and a is outside diameter of inner conductor.
> > >
> > > Wouldn't manufacturers of coaxial cable state that the characteristic
> > > impedance Zo is for example 50 Ohms at 100 Mhz if it was indeed
> >dependent
> >on
> > > operating frequency. Sorry but I am from Missouri and you have to
"show
> > > me".
> > >
> > > In that line, I am going to visit the URL you referenced and ponder
this
> > > some more, cause if I am wrong I want to know why and I will change my
> > > thinking when convinced.
> > >
> > > 73, Jim, wd4air
> > >
> > >
> > >
> > >
> > >
> > >
> > > >As George told you, the characteristic impedance is
> > > >reactive, especially at audio frequencies.
> > > >Terminating a reactive line with a real resistance
> > > >causes the line to be mismatched. The mismatch is
> > > >frequency dependent.
> > > >
> > > >If you want a simple way to explore this, I suggest
> > > >that you go to:
> > > >
> > > >http://www.qsl.net/ac6la/tldetails.html
> > > >
> > > >and download the program.
> > > >
> > > >Once you install it, select Belden 9913 line and set
> > > >the frequency to 0.001 MHz. Make the load R=50, X=0
> > > >and then look at the SWR. You should see that it is
> > > >1.77:1.
> > > >
> > > >If you terminate the line in its characteristic
> > > >impedance; 50 -j28.8, then the line is matched, but
> > > >you have a 1.77:1 mismatch at the input. (Assuming
> > > >realitively short lengths)
> > > >