=== Begin LPDA.DOC ===
LPDA.BAS 03/13/87
This program is used to design log-periodic dipole arrays. The design
procedure used is a combination of that presented in the ARRL Antenna
Book, Fourteenth Edition, pp 6-24 through 6-26, and the corrections
discussed in the Technical Correspondence column of QST for October,
1986, p 51. Reference to the Antenna Book is required in order to get
the full benefit of the program. However, simply selecting a
frequency range and allowing all other values to default to their
initial values will produce a workable LPDA design with about 8.5 dB
gain (according to Fig. 59 in the Antenna Book).
SELECTION OF PARAMETERS
It is usually wise to select a frequency range slightly wider than the
desired one. Reducing the lowest frequency by about 5% from the
actual lowest frequency of operation and increasing the highest
frequency by about 5% should do the trick. This is done because the
SWR of the array tends to increase at the ends of the design range.
The tau and sigma parameters affect the gain, boom length and number
of elements of the array. The usual procedure is to use the default
tau and sigma to start with, then adjust them for the desired boom
length and number of elements, accepting whatever gain you get.
(Mechanical construction considerations seem to take precedence over
getting that last half dB of gain!) Tau and sigma are used to
calculate alpha, the array half-angle. The program lets you adjust
alpha as an alternative to adjusting sigma. I find it easier to
visualize the effect on the array size of adjusting alpha than of
adjusting sigma. There are no hard and fast rules here. The program
specifies minimum and maximum values, and as long as you stay within
these you'll be OK. The gain you'll get can be determined using the
final tau and sigma values on the chart in Fig. 59 of the Antenna
Book.
All feeder calculations are made assuming round conductors (wire or
tubing). Spacing is center-to-center. Note that the default R0
(feed-point impedance) is 200. This is based on the assumption that a
4:1 balun will be used to feed the array from 50-ohm coax. Direct 50-
ohm feed is often not possible. (Sometimes it will result in a
conductor spacing smaller than the conductor diameter, a physical
impossibility in this universe.) If the design bandwidth of the array
is fairly small (single band), another possible approach is to design
the array for a 104-ohm R0 and use a 1/4-wave matching section of 72-
ohm coax between the feedpoint and the 50-ohm feedline. In any case,
select the element feeder diameters based on mechanical
considerations. The required feeder spacing is then calculated by the
program. You can then specify the actual spacing you will use, and
the program will calculate how the difference between the actual
spacing and the calculated will affect the input impedance of the
array.
The Antenna Book shows a terminating stub at the back of the array.
It is not clear that this performs any useful function, although
experimentation may be in order. At least one 2-meter array
constructed in the ARRL lab by K1TD exhibited the expected
characteristics with the end of the feeder left unterminated (open).
I'd like to hear from anyone who develops further information,
experimental or theoretical, on this point.
GL de KE3Z
SAMPLE RUN:
Log-periodic dipole array calculations
Enter lowest frequency: 13
Enter highest frequency: 32
Enter TAU, 0.8 <= TAU < 1.0 (default .9 ):
Enter SIGMA, 0.05 <= SIGMA < .1662 (default .05 ):
Frequency: 13 to 32
Operating BW: 2.461538
Array BW: 1.254
Structure BW: 3.086769
TAU: .9
SIGMA: .05
ALPHA: 26.56505
Boom length: 25 ft 7.02 in (307.02 in)
Number of elements: 11.69781
Longest element: 37 ft 10.15 in (454.15 in)
Max. stub length: 9 ft 5.53 in (113.53 in)
Change T)au, S)igma, A)lpha or F)requency
calculate X)msn line or for element data?
Frequency: 13 to 32
Operating BW: 2.461538
Array BW: 1.254
Structure BW: 3.086769
TAU: .9
SIGMA: .05
ALPHA: 26.56505
Boom length: 25 ft 7.02 in (307.02 in)
Number of elements: 11.69781
Longest element: 37 ft 10.15 in (454.15 in)
Max. stub length: 9 ft 5.53 in (113.53 in)
El. Length Spacing
1 37 ft 10.15 in (454.15 in) ---
2 34 ft .73 in (408.73 in) 3 ft 9.41 in (45.41 in)
3 30 ft 7.86 in (367.86 in) 3 ft 4.87 in (40.87 in)
4 27 ft 7.07 in (331.07 in) 3 ft .78 in (36.78 in)
5 24 ft 9.97 in (297.97 in) 2 ft 9.1 in (33.1 in)
6 22 ft 4.17 in (268.17 in) 2 ft 5.79 in (29.79 in)
7 20 ft 1.35 in (241.35 in) 2 ft 2.81 in (26.81 in)
8 18 ft 1.22 in (217.22 in) 2 ft .13 in (24.13 in)
9 16 ft 3.49 in (195.49 in) 1 ft 9.72 in (21.72 in)
10 14 ft 7.94 in (175.94 in) 1 ft 7.54 in (19.54 in)
11 13 ft 2.35 in (158.35 in) 1 ft 5.59 in (17.59 in)
12 11 ft 10.51 in (142.51 in) 1 ft 3.83 in (15.83 in)
Change T)au, S)igma, A)lpha or F)requency
calculate X)msn line or for element data?x
Enter desired R0 (default 200 ):
Enter element dia. in inches (default .125 ):
Enter feeder wire dia. in inches (default .125 ):
Enter actual feeder spacing in inches (default = 2.140283 ): 2
Required feeder spacing: 2.140283 in. Actual: 2 in.
Required feeder Z0: 423.5471 Actual: 415.4214
Desired R0: 200 Actual: 197.6417
SWR: 1.011932
Frequency: 13 to 32
Operating BW: 2.461538
Array BW: 1.254
Structure BW: 3.086769
TAU: .9
SIGMA: .05
ALPHA: 26.56505
Boom length: 25 ft 7.02 in (307.02 in)
Number of elements: 11.69781
Longest element: 37 ft 10.15 in (454.15 in)
Max. stub length: 9 ft 5.53 in (113.53 in)
Change T)au, S)igma, A)lpha or F)requency
calculate X)msn line or for element data?
=== End LPDA.DOC ===
Roy
... 2,000,000 Extra Class Lemmings can't be wrong.
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* Origin: KB6PI's Antenna Farm * San Diego, CA (1:202/909.10)
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