[Antennas] Xms Line Zo,Formerly Hairpin monopoles
James Duffer
[email protected]
2003年5月09日 08:10:28 -0500
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)
> > >
> > >
> > >
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