# Talk:Log-periodic antenna

## Typo?

Was " log-periodic antenna " in the first section a mistype? Is there anything generically called a periodic antenna? {Note that a the time of this edit, periodic antenna does not exist.}

According to the NTIA (http://www.its.bldrdoc.gov/fs-1037/dir-027/_3924.htm) it's "An antenna that has an approximately constant input impedance over a narrow range of frequencies. Note: An example of a periodic antenna is a dipole array antenna. Synonym resonant antenna." Colonies Chris 12:20, 9 June 2006 (UTC)

I´ll explain here WHY it is called a LOGARITHMIC PERIODIC ANTENNA

This antenna has a remarkable WIDE range of frequencies with approximately constant gain and impedance. The relation between upper and lower frequency can be 10:1 and even more. The antenna has a vertex, which is an imaginary point where converge the imaginary straight lines that join the extremes of all the irradiating elements or dipoles. Those converging lines form an angle, which is also a choice of design, called ALFA.

(I tried to add a drawing made with text characters here but the results were less than acceptable)

Every element is longer than its precedent by a constant factor known by Greek letter TAU. So they DO NOT increase logarithmically but as a geometric progression of reason TAU. This factor TAU is a design choice, usually around 1.1 to 1.2.

The distance of every element to the vertex is also TAU times the distance of its precedent to the vertex. With smaller values of TAU, the distance between elements becomes smaller, and the impedance is lower, and more constant with frequency. With larger values of the angle ALFA, the elements become closer one to another, yielding a lower impedance.

Let be L(i) the length of the i-th element, and L(i-1) the length of its precedent,

and let be D(i), D(i-1) their respective distances to the vertex. Then

(1) ${\displaystyle L(i)/L(i-1)=TAU}$

(2) ${\displaystyle D(i)/D(i-1)=TAU}$

If we take the logarithm of this expressions, we have

(3) ${\displaystyle log[L(i)]-log[L(i-1)]=log(TAU)}$

(4) ${\displaystyle log[D(i)]-log[D(i-1)]=log(TAU)}$

it follows that

(5) ${\displaystyle log[L(i)]=log[L(i-1)]+log[Tau]}$

and

(6) ${\displaystyle log[D(i)]=log[D(i-1)]+log[Tau]}$

If we regard L(i) as the length of both halves of every dipole, and consider it as a halfe wave resonator, the resonant frequency of every element is aproximately

(7) ${\displaystyle f(i)=c/2L(i)}$

where c is the speed of light. L(1)is a half wavelength for the highest frequency of operation,

and the last length, L(n), is a half wavelength for the lowest frequency of operation. The center of L(1) is the feeding point,

and all elements are linked to a line of a pair of conductors,

with alternately reversing polarity,

i.e., one line conductor is connected to the left half of the elements of odd order, and to the right half of the elements of even order.

Conversely, the other line conductor is connected to the right half of the element of odd order and to the left half of the elements of even order.

From (5) and (7) it follows that

(8) ${\displaystyle log[f(n)]=log[f(n-1)]-log(TAU)}$

From (6) and (8) follows that if we plot D(1), D(2), etc. versus the logarithm of frequency, we have values of D(i) distributed with a period equal to log(TAU). Thus it is called a logarithmic periodic antenna. If the antenna has a reasonably large number of elements, namely 5 or more, the plot of [impedance] versus [logarithm of frequency] gives an almost periodic function, with its period being log(TAU), because within every period we have one dipole. This periodical variation is only notticeable for large values of TAU, say 2 or more, which is not practical. For the usual values of TAU there are rather small variations of impedance over the entire range of frequency, including the resonant frequencies of the first and last element. The gain is usually also constant within +/- 2db.

## Self-similar or not

In the lead, the paragraph about self-similarity needs to be completely rewritten so that it speaks with one voice. That's why I put the cleanup tag at the top of the page. Binksternet (talk) 01:07, 26 August 2008 (UTC)

It's nonsense anyway. Contrary to the claim made in the paragraph, subsections of the antenna do resemble the whole thing, as can be seen in the photo. Chop off the biggest element and scale what's left up to the original size and you get something that looks the same as the original. You can't do that forever because you'll run out of elements, but all real-life self-similar objects (such as coastlines) have a similar limitation on the range of scales at which they are self-similar. I think that rather than "many in the research community" finding it "a dubious claim", it's just one confused Wikipedia editor who thinks the antenna is not self-similar. 67.158.74.7 (talk) 00:52, 31 August 2008 (UTC)

It should look more like the Yagi-Uda article or the reference http://www.radio-electronics.com/info/antennas/log_p/log_periodic.php

There has got to be a good basic description that can be gleaned from an antenna text or similar source.

The self-similar / fractal stuff does not belong at all – it just adds noise.

The best way to drive home the operation of a LPDA is to show an image of the current distribution from a moment-method calculation. I didn’t really grasp the concept fully until I saw one of these plots about 25 years ago. It was excited at a frequency such that one of the middle elements was resonant and that element “glowed” bright red in the plot. The element in front and behind this element was less-resonant and showed somewhat less current. The remaining elements had almost zero current on them. That image for me was worth 1000 words. Onoahimahi (talk) 16:20, 12 December 2010 (UTC)

## Is the ZL Special Log-periodic or Phased-array or both?

No references I have (mostly ARRL antenna handbooks) put it in log-periodic, but one ("Some Notes on Two-Element Horizontal Phased Arrays—Part 3 The Limits of a Single Phase Line: The ZL-Special" by the late L.B. Cebik in the March/April 2002 NCJ at http://81.70.242.211/eab/manual/Magazine/National%20Contest%20Journal%20ARRL%20USA%20www.ncjweb.com/200203.pdf) puts it in the phased array camp; the same author said:

"Some call the ZL Special a 135° phased array because they think of the rear element as 180° minus the 45° twisted phase line out of phase with the front element. This is true with respect to impedance values found at each element. However, it is current magnitude and phase which determine the performance of the array, and the target ballpark for that current is 315° (which is also -45°) out of phase with the front element. The half twist of the phase line is equivalent to twisting the element itself 180° with respect to the front element, with an added 45° phase line between them."

I think it could be both, but that's just my thoughts. There are very few authoritative books/texts that mention it... but a few Practical Wireless articles from way back IIRC - I should look 'em up. Thoughts? Maitchy (talk) 01:42, 9 June 2011 (UTC)