- logarithmically...

On practically everyone’s wish list these days, it seems, is a very short antenna with an immense bandwidth, high gain and consistent performance across the range – all at a VSWR of close to 1.5:1. Well, unless the laws of physics have changed, something has to give somewhere. Or does it?

It all depends on what frequencies we are talking about and if we want omnidirectional coverage or not.

The antenna that offers consistent performance over relatively wide bandwidths is the log-period. While log periods are directional, the addition of a rotary system, manual or automated, can at least achieve omnidirectional performance to some degree if not simultaneous.

The log periodic is not like many other antennas. This is the first fractral antenna array invented by D.E. Isbell in the late 1950s, although the significance of how it differed fundamentally from existing antennas was not recognised and understood at the time.

What sets fractal antennas apart is that being made up of a number of elements of the same shape, they can be split into parts that are iterations or smaller scale copies of the whole. This is known as self similarity.

The length and the spacing of these elements are arranged so that they increase logarithmically from one end of the antenna to the other. The ratio of the length of each element to its next longest neighbour, referred to as tau, is constant, as is the relative spacing between adjacent elements, designated sigma. Sigma and tau determine the angle at the apex of the antenna, alpha where the antenna is fed.

The ratio of the length of an element must be the same as the ratio of the distance of the element to the apex. This ratio needs to be as close as possible to 1.0. At 1.0, however, the result becomes parallel lines which is unworkable. To achieve a range of double the base frequency, the length needs to be more than doubled. With a ratio close to 1.0, a very long boom and many elements are required.

Elements are normally fed alternately by two wires in a balanced transmission line. The centre points of each element are connected so that they are 180 degrees out of phase. A cycle of variation results in which the impedance and radiation characteristics are regularly repeated as a logarithmic function of the transmit frequency.

This has the effect of increasing the perimeter of material that can receive or transmit electromagnetic signals within the given total surface area.

The result is a narrow beam broadband directional antenna that offers quite good gain over a wide range of frequencies with essentially constant characteristics. This includes radiation resistances (SWR), as relatively constant feed impedance simplifies matching to the transmission line, and also radiation patterns (gain and front-to-back ratio).

Not all elements in the system are active on a single frequency of operation. The active region shifts among the elements with changes in operating frequency. Due to the diagonal feed arrangement, most of the elements cancel each other out. The two elements closest to the resonant length, however, due to the distance between them, are 180 degrees out of phase. This combined with the cross feed makes the two elements reinforce each other.

Many elements may contribute to radiation, depending on the design. Generally, the larger elements are involved on the lower frequencies, and smaller ones on the higher frequencies.

Those elements not contributing to radiation receive little direct power. The smaller elements in front that resonate above the operational frequency are capacitive, and act like director elements. The longer elements below the operational frequency are inductive and act like reflectors. The direction of maximum radiation is towards the feed point – the “sharp” end. This produces a Yagi-like pattern.

Generally speaking a log periodic will provide around 4-6 dB gain with an SWR of better than 1.3:1 over an operating bandwidth of 2:1.

Bandwidth is only limited by the number of elements it is practical to use. The highest frequency is usually double the lowest but this is not always the case. Bandwidths can vary from a little over 3 octaves covering 3-30 MHz to more commonly 1 octave, for example 14-30 MHz in the HF range.

As current phasing between adjacent elements changes with frequency, it is not possible to achieve flat performance curves. Gain, front to back ratio and SWR should fall within good operating limits rather than follow the same peaks and troughs.

Gain is relatively uniform but has some variation, undulating across the frequency range with a number of peaks and tapering off at either end of the design bandwidth. The amount of variation is dependent on the chosen ratio and consequent number of elements used. Average gain is determined by the length of the array in relation to the frequency range. The greater the length, the higher the gain.

Generally front-to-back ratio and gain performance go hand in hand. When the gain is below 5dBi, the front-to-back ratio will be around 10dB. Increasing the gain to around 7dBi, will provide a front-to-back ratio of around 20dB. When gains are over 8.5dBi, the front-to-back ratio can approach 40dB. Good designs will have well controlled rear patterns with only small differences between the 180 degree front-to-back ratio and the averaged front-to-rear ratio. Large diameter elements provide improved gain and front-to-back ratios.

So, log periodic performance will be dependent on the number of elements used in the design. Economising on elements will reflect in variations in gain in excess of 1dB across the band, increased front-to-back ratios and higher VSWR.

Some log periodics have reduced performance at each end of the desired frequency range where there are not enough active elements to provide good gain and front-to-back ratios. When this occurs passive reflectors or directors have been used to boost performance. Parasitic elements may also be used to achieve desired results.

A shorted length of parallel feed line or stub is sometimes added at the other end, usually to eliminate or move frequencies that show gain and front to back weakness. This, however, can also have the effect of transferring weakness to other frequencies. So, additional stubs located at specific elements may also be needed if the full range is required.

Often the elements are linear, as in the well known Log Periodic Dipole Array (LPDA), which is made up of number of dipole elements in an arrowhead configuration. However, this need not always be the case.

Due to their good gain over a very wide range of frequencies log periodics are often a good solution for directional multi-band transceiver operation. They are used extensively at HF, almost always horizontally, but vertical types are also available, as seen above.

In the HF frequency band, with 5 to 7 elements they can typically achieve gains of around 5-10 dBi with 1.5:1 VSWR. These are antennas of appreciable size, in the region of 70 to 170 metres by 40 to 120 metres by 25 to 80 metres, and therefore require large sites. Power capabilities can be high too. It is also possible to rotate antennas at these frequencies when of aluminium tube or wire type construction. Below HF they are not normally a practical consideration due to size.

Above HF, they are much simpler to handle and can be mast mounted and easily rotated through 360 degrees to obtain omnidirectional coverage. Commonly they are used for TV reception over the whole VHF/UHF bands.

Inverted V type elements and even vertically oriented quarter wave elements over an earth system, have been used experimentally.

When wideband communications are required, don’t forget the log periodic. You may need more elements for the same length boom than in a yagi, but with good designs and the space to locate them, you will get better front-to-back ratios over a wider frequency range.

Today more uses are being found for log periodics, especially in the military arena where they are proving their worth in direction finding and jamming of signals in the field. Moonraker types feature foldable elements for fast deployment and easy stowage.