use these measurements in the transmission-line equations to determine the actual antenna impedance at each frequency.
Fig 1 above is Table 6 from the handbook, and it lists the direct measurements, and Xu corrected to the measurement frequency. So, taking the measurement at 27MHz indicating Xu=85, corrected it is 85*10/27=31.5Ω.
The right hand two columns are their calculated impedance at the far end of 74' of Columbia 1188 (now known as Carol C.1188) 50Ω coaxial cable.
Fig 2 above is Fig 33 from the handbook. It shows the data in Fig 1 (Table 6) graphically. The lower graph looks sensible, it is typical of what we would expect from a half wave dipole, R increases relatively slowly with increasing frequency, magnitude of R somewhere between about 40Ω and 100Ω depending on height above ground etc, and X increasing relatively quickly from negative values, through zero at resonance, to positive values.
But, on closer examination of Fig 1 (Table 6), something isn't quite right.
Firstly, the data row for 29.0MHz looks wrong. If the impedance looking into the 50Ω line is 50+j0, then VSWR=1 and the impedance at the other end must also be 50+j0 and VSWR=1. The reported 52+j8Ω (VSWR=1.18) would seem to have significant error, and gives cause to look further at the table.
Fig 3 is a plot of calculated VSWR from the ARRL's data in Fig1 (Table 6). Not only is the anomaly at 29.0MHz apparent, but the relationship between VSWR at the source end and load end seem to be quite bizarre. VSWR at the source end should not be greater than at the load end in this type of scenario.
The ARRL does report some measurements that suggest the
characteristic impedance of the coax as 56.58-j7.96Ω. Whilst cables are
not perfect, and foam cables are more susceptible to problems than
solid dielectric cables, the reactance component here is much more
negative than would be expected from such a line at around 30MHz, TLLC
reports 50.00-j0.57 Ω. A possible explanation is that the line is not
uniform, that it is defective, something that should have been
investigated at the time.
If we take the measured data reported in cols 1, 2 and 4 of Fig 1 (Table 6) as correct and use TLLC to calculate the load impedances expected with 74' of C.1188 cable (as used by ARRL), we obtain different results.
Fig 4 shows the reworked load end impedance RL and XL using TLLC .
Fig 5 is a plot of calculated VSWR from the reworked data in Fig 4. The relationship between VSWR at the source and load ends passes a reasonableness test, as VSWR a load increases, so does VSWR at the source, but at a slower rate, and VSWR at the load is always greater than at the source.
Fig 6 is a plot of calculated feed point impedance from Fig 4 based on the reported measurement data and impedance transformation using TLLC.
This looks ok, except that this is not the way a typical dipole behaves.
Fig 7 is a plot of feed point impedance from an NEC model of a half wave dipole similar to that described in the article.
As mentioned earlier, normally R increases relatively slowly with increasing frequency, magnitude of R somewhere between about 40Ω and 100Ω depending on height above ground etc, and X increasing relatively quickly from negative values, through zero at resonance, to positive values.
The behavior of X in Fig 6 is not what you would expect from a dipole. The ARRL have not mentioned whether they have effectively prevented common mode current, there may be more to this antenna than a simple isolated dipole... the reworked impedance plots certainly suggest so.
Fig 8 is a plot of feed point VSWR(50) from the NEC model, it is
more like the load end VSWR line in FIg 5 than Fig 3.
The ARRL worked solution contains errors in the final solution, and although the graphs of calculated feed point impedance look reasonable, they are not supported by a more accurate model of transmission line impedance transformation if the reported Noise Bridge measurements are taken as correct.
The line section measured and then projected has been characterised
with Zo inconsistent with its claimed performance, hinting that it is
not uniform, and therefore defective. This would have been revealed by
testing a different type of cable and reconciling the results. If the
cable was faulty, it may have contributed to the bizarre results.
This case highlights the importance of reviewing measurement and calculation results, and following up apparent inconsistency. In this case, following the obvious inconsistency of the data at 29.0MHz showed widespread error, and unanswered questions about the behavior of X on the actual measured antenna which this author cannot follow up.
All in all, it is just a really bad example that leaves too many questions about results that do not reconcile with expectations. It appears to be based on an article in QST in August 1989, and after more than fifteen years is still published in the ARRL Antenna Handbook with the same issues.
Use at your own risk, not warranted for any purpose. Do not depend on any results without independent verification.
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© Copyright: Owen Duffy 1995, 2012. All rights reserved. Disclaimer.