## Tuesday, November 11, 2008

### Log Periodic Dipole Antennas, Bob, Session 25

Tonight we will talk about another class of antennas, log periodic antennas. There are different forms of log periodic antennas but we will talk about the most common one, the Log Periodic Dipole Array (LPDA).

This antenna looks and acts similar to the Yagi but unlike the Yagi it covers a wide range of frequencies. This is the LPDA's defining characteristic. A typical design will cover a range of frequencies where the highest frequency is double the lowest. For example you could have one antenna that covered 14 MHz to 30 MHz with very good gain, front to back, and SWR figures over the entire range. You are not limited to the 2:1 frequency coverage. In fact you are only limited by the ability to physically construct the antenna and use it.

GENERAL DESCRIPTION
The log periodic antenna looks somewhat like a Yagi but, unlike the Yagi, the length of the parallel elements vary so that the tips form a straight line that gets progressively smaller. If you imagine lines running along the tips of both ends of the elements from the largest element to the smallest and extend the lines beyond the end of the antenna until they meet, they would form an angle with the boom as the bisector. The elements are connected in a criss-cross pattern so that, if you are looking down from the top of the antenna, the smallest element on the left side would be connected to the next larger element on the right side, and vice versa. This crisscrossing continues through all of the elements. The antenna is fed at the small end with a balanced signal.

BASIC THEORY
I found a greatly simplified explanation of how this antenna works at radio-electronics.com. The link is at the bottom of the blog post. Let's say we are feeding our antenna with a signal about in the middle of the range. Because of the crisscross arrangement most of the adjacent elements cancel each other. But at the two elements in the middle of the array, which are closest to resonant length, you also have the width between them such that the wave will be 180 degrees out of phase when it reaches the other element. That combined with the crisscross feed causes the two elements to reinforce each other.

One other point, the smaller elements which don't contribute to the radiation, act like the shorter director elements of a Yagi, while the longer elements act like reflectors. This creates a radiation pattern much like a Yagi.

As you tune up and down the usable frequency range, you find that at the higher frequencies the radiation primarily comes from the smaller elements and at the lower frequencies, the larger elements are the ones that radiate.

Of course it's never quite this simple. Depending on design you may have many of the elements contributing to the radiation.

DESIGN CONSIDERATIONS
Because the imaginary line along the tips is straight, and the extended lines on each side form an angle, there are some relationships that have to hold. Hopefully it is obvious to all that if you go twice as far away from where the lines meet (the vertex) then the length of the line going across (the element length) will be twice as much. This leads to the formula that the ratio of the length of successive elements has to equal the ratio of the distance from the vertex. This ratio is given the Greek letter tau. This ratio defines the relative distance between elements. In our example of doubling the distance, tau would equal 0.5. To make an effective LPDA you want to have a tau that is as close to 1.0 as is feasible. You can see that tau of 1 would result in parallel lines which wouldn't work. To cover the range you want of double the initial frequency you need a change of length that is actually more than double. If tau is very close to 1 then you will need many elements and a very long boom to achieve that. These are the trade-offs to building a LPDA.

BEYOND THE BASICS
There are ways to add true parasitic elements to the LPDA to improve performance. This is beyond the scope of this discussion and can be found in the Antenna Book.

As usual, I want to point you to the ARRL Antenna Book for an excellent in-depth discussion of building real world LPDA's. Also, as a bonus, you get a LPDA Design program for the PC when you buy the Antenna Book.