Yagi Antenna Gain, Directivity & Front to Back Ratio

Yagi antenna gain is dependent upon many factors including the number of elements, spacing and several other minor factors..

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The key advantages for using a Yagi antenna are the gain and directivity it provides.

The Yagi or Yagi-Uda antenna gain is particularly useful because it enables all the transmitted power to be directed into the area where it is required, or when used for reception, it enables the maximum signal to be received from the same area. Coupled to this the fact that it has reduced gain in other directions means that it receives or transmits less signal in other directions thereby reducing the levels of interference.

It is worth understanding that the performance of a passive antenna (i.e. one with no active elements like transistors, etc) like the Yagi is equal for both transmit and receive, and therefore gain for transmitting will be the same as gain when receiving.

Yagi gain / beamwidth factors

There are many factors that affect the overall Yagi antenna gain. There is a link between the gain and the beamwidth. If the Yagi gain increases, then the beamwidth decreases. This can be reasoned by thinking of the available transmit power. As there is only a certain amount of power available, to create gain, power must be taken from one direction to put into the main beam.

Gain and beamwidth options for Yagi antenna shown on polar diagram
Gain and beamwidth options for Yagi antenna

This means that very high gain antennas are very directive. Therefore high gain and narrow beam-width sometimes have to be balanced to provide the optimum performance.

Yagi-Uda antenna gain considerations

There are several features of the design of a Yagi antenna that affect its gain:

  • Number of elements in the Yagi:   The most obvious factor that affects the Yagi antenna gain is the number of elements in the antenna. Typically a reflector is the first element added in any Yagi design as this gives the most additional gain, often around 4 to 5 dB. Directors are then added. For mid ranges of the number of directors, each director provides very roughly 1 dB of gain.
  • Element spacing:   The spacing can have an impact on the Yagi gain, although not as much as the number of elements. Typically a wide-spaced beam, i.e. one with a wide spacing between the elements gives more gain than one that is more compact. The most critical element positions are the reflector and first director, as their spacing governs that of any other elements that may be added.
  • Antenna length:   When computing the optimal positions for the various elements it has been shown that in a multi-element Yagi array, the gain is generally proportional to the length of the array. There is certain amount of latitude in the element positions.

One of the major factors controlling the Yagi antenna gain is the number of elements in the design. However the spacing between the elements also has an effect.

The overall performance of the RF antenna very many inter-related variables and as a result many early designs were not able to realise their full potential. Today computer programmes are used to optimise the designs before they are manufactured and this means that their performance is better than the early designs.

Yagi gain vs number of elements

Although there is variation between different designs and the way Yagi-Uda antennas are constructed, it is possible to place some very approximate figures for anticipated gain against the number of elements in the design. This can be a useful rule of thumb guide to the expected Yagi antenna gain.

Approximate Yagi-Uda antenna Gain levels
Number of elements Approx anticipated gain
dB over dipole
2 5
3 7.5
4 8.5
5 9.5
6 10.5
7 11.5

It should be noted that these figures are only very approximate.

As an additional rule of thumb, once there are around four or five directors, each additional director adds around an extra 1dB of gain for directors up to about 15 or so directors. The figure falls with the increasing number of directors.

Yagi Front to Back ratio

One of the figures associated with the Yagi antenna gain is what is termed the front to back ratio, F/B. This is simply a ratio of the signal level in the forward direction to the reverse direction. This is normally expressed in dB.

Radiation pattern or polar diagram of a Yagi antenna showing front and back radiation for front to back ratio
Yagi antenna radiation pattern and front to back ratio
Front to back ratio = Signal in forward direction Signal in reverse direction

Front to back ratio = F B

The front to back ratio for a Yagi antenna, or any antenna for that matter, is normally expressed in decibels. Accordingly it is necessary to take the log10 for the ratio.

Front to back ratio (dB) = log ( F B )

The front to back ratio is important in circumstances where interference or coverage in the reverse direction needs to be minimised. Unfortunately the conditions within the antenna mean that optimisation has to be undertaken for either front to back ratio, or maximum forward gain. Conditions for both features do not coincide, but the front to back ratio can normally be maximised for a small degradation of the forward gain.

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