SOME THOUGHTS ON
Perhaps a more suitable name (or description) would be a
selective multiple dipole array; or an "Isbell" antenna, in honour of one of its
main conceptors; much in accordance with the well known "Yagi-Uda" or "Yagi"
antenna i.e. "Isbell" antenna (conceived at the University of Illinois in
The advantage of the "Isbell" is that it can operate over a range of
frequencies where only one dipole is active at the operating frequency, the other
elements being essentially dormant or; perhaps operating in a parasitic fashion
much like that of the Yagi antenna?
The radiation pattern is somewhat broad,
and the power gain somewhat modest, for the size of the structure.
because only a limited portion of the array is active at a given
"Isbell" (L-P) antenna's are nevertheless useful for applications
where it is necessary to cover a wide frequency band without resorting to an
antenna switching system. e.g. Television reception.
Adjacent half wave
dipoles are traspose mounted on the feeder-boom.
Feedpoint impedance is
reckoned to be approx' 100 ohm.
According to Ref 2 :- A 1/8 λ short-circuited
matching stub; cut for the lowest operating frequency will provide a match to
300 ohm ribbon at the vertex/feedpoint of the array.
performance is supposedly PERIODIC with the LOGarithm of the
frequency of the lowest "cell"
Despite all the nomograms and formulae usually
associated with this antenna the physical design reduces to simple "plane"
Essentially the criterium for design of an isbell (L-P) is
1) Upper and lower operating frequencies
2) Number of
3) Apex angle of antennae
4) The requirement that each sucessive
element is a scaled-down length of its immediate predecessor, and so on, down
through the array.
This scaling factor is called τ
Derivation of this factor is shown later.
τ is also used to calculate the sucessive inter-element
5) Boom length is usually (but not mandatory) equal to one
wavelength (1λ ) at the lowest design frequency.
This gives a reasonable
with an apex angle of approx' 15° to 30°
To design an "Isbell" (L-P) antennae to the following
Freq (low) 150 MHz
Freq (high) 300 MHz
where L L is
a length = to ¼ λ of lower design freq'
...and L H is a length = to ¼
λ of higher design freq'
and of course frequency and wavelength are related
as C = λ x F
where C = velocity of electromagnetic radiation reckoned at 3 x
10 8 m/s
LET THE FUN BEGIN ! . . . . .
By definition L 2
= L L x τ
AND L 3 = L 2
Therefore L 3 = L L x τ 2
So logically we can see that for an array of N
elements LN = L L x τ (n-1)
LH = L L x τ (n-1)
as element length is inversley proportional
to frequency we can say :-
our example : -
τ 9 = 0.5 .........(take log of both sides)
log τ = log 0.5
(perhaps this is where
the LOGarithm comes from?)
..........(antilog of both sides)
therefore τ = 0.92587
from this calculate the lengths of each successive element.
relationship of the antenna's elements lengths from longest to smallest is in
fact a "Geometric progression".
Perhaps this is where the
PERIODICity comes from ?
We can also use the same factor to calculate
the element spacing upon the boom i.e.
To calculate inter-element spacing:
is shown below.
(more trigonometry and algebra I'm afraid !)
By similar triangles
we can say ;
the ratio ....(transposing)
........but L 2 = τ L L
........taking out the
common factor of L L
where LL = ¼ λ of lower design
and L H = ¼ λ of higher design freq'
Boom length usually
1 λ at lowest design frequency
X 1 = first inter-element
The next inter-element spacing
(X 2 ) is then = X 1
and so on following the design requirement
that each successive spacing is a scaled down dimension of its immediate
Now consider this :
If we were to design an L-P antenna
using a boom of 1 λ at the lowest operating frequency and we wished to cover a
frequency ratio of 2:1 (as in our example of 150 MHz to 300 MHz) we can
substitute values of wavelength in the above formula and simplify and reduce the
equation further viz :
therefore Boom would be equal to λ
would be equal to 1/4 λ
L H would be equal to 1/8 λ (of 150
substituting in the above formula we get:
therefore X 1 =
2 λ (1- τ ) ....(2:1 freq ratio).....EQUATION 3
and by similar reasoning we obtain:
1 = 1.5 λ (1- τ ) ....(3:1 freq ratio)
1 = 1.3 λ (1- τ ) ....(4:1 freq ratio)
would wonder if the antenna would function the same should the spacing and
element length not be logarithmically aperiodic, and dipoles be equally spaced?
Compare the operation of a multiple dipole for 20/15/10 metre ham bands all
terminated at the feed point where the only active dipole is the one resonant at
the feed frequency, the others remaining dormant.
Some published designs
show the Log Periodic antenna with either boom/feeder half seperated at an
angle; so called Pyramidal or trapezoid style.
This is supposed to produce a
slight increase in gain over the conventional "flat" design ( all other
parameters remaining equal).
Figs 1 & 2 show the authors construction in
Antenna design: 16 elements, frequency coverage 50 - 590
I could not discern any difference when used as a receiving antennae,
except to say the "pyramidal" form is visually more striking
Fig 3 (photo-scan)
shows this style in use by German broadcaster Deutsche Welle.
(5.85 - 26.1 MHz
400 Kw power handling capability)
Provided you know the upper and lower limit frequencies for your
antenna and number of elements required, using formula 1 and formula 2 and
perhaps formula 3 you can calculate all the various dimensions needed to
construct an "LPA" (Log periodic array)
||Log periodic antennas.
||QST magazine Nov 59 pg 11|
||Log periodic antenna's
||Electronics Australia Dec65/Jan66|
||"Pyramidal " TV/FM antenna
||Popular Electronics July 69 pg 27|
Response from noted Antenna academic; L B Cebik (W4RNL) SK
Frank Hughes VK6FH Mar
2001, (update Oct 2009)