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Saturday, January 11, 2014


Yagi antenna theory - the basics

The key element to the Yagi theory is the phases of the currents flowing in the additional elements of the antenna.

The parasitic elements of the Yagi antenna operate by re-radiating their signals in a slightly different phase to that of the driven element. In this way the signal is reinforced in some directions and cancelled out in others. As a result these additional elements are referred to as parasitic elements.
In view of the fact that the power in these additional elements is not directly driven, the amplitude and phase of the induced current cannot be completely controlled. It is dependent upon their length and the spacing between them and the dipole or driven element.

As a result, it is not possible to obtain complete cancellation in one direction. Nevertheless it is still possible to obtain a high degree of reinforcement in one direction and have a high level of gain, and also have a high degree of cancellation in another to provide a good front to back ratio. The Yagi antenna is able to provide very useful levels of gain and front to back ratios.

Yagi Uda antenna showing element types

To obtain the required phase shift an element can be made either inductive or capacitive.


If the parasitic element is made inductive it is found that the induced currents are in such a phase that they reflect the power away from the parasitic element. This causes the RF antenna to radiate more power away from it. An element that does this is called a reflector. It can be made inductive by tuning it below resonance. This can be done by physically adding some
inductance to the element in the form of a coil, or more commonly by making it longer than the resonant length. Generally it is made about 5% longer than the driven element.


If the parasitic element is made capacitive it will be found that the induced currents are in such a phase that they direct the power radiated by the whole antenna in the direction of the parasitic element. An element which does this is called a director. It can be made capacitive tuning it above resonance. This can be done by physically adding some capacitance to the element in the form of a capacitor, or more commonly by making it about 5% shorter than the driven element.

It is found that the addition of further directors increases the directivity of the antenna, increasing the gain and reducing the beamwidth. 

The addition of further reflectors makes no noticeable difference.
In summary:

Reflectors - longer than driven element = Inductive
Directors - shorter than driven element = Capacitive

Yagi Uda antenna showing direction of maximum radiation

Yagi antenna history

The full name for the antenna is the Yagi-Uda antenna. The Yagi antenna derives its name from its two Japanese inventors Hidetsugu Yagi and Shintaro Uda. The RF antenna design concept was first outlined in a paper that Yagi presented in 1928. Since then its use has grown rapidly to the stage where today a television antenna is synonymous with an RF antenna having a central boom with lots of elements attached.

The design for the Yagi antenna appears to have been initially developed not by Yagi who was a student, but his colleague Professor Shintaro Uda. However all the original papers were all in Japanese and accordingly the design was not publicised outside Japan.

It was Hidetsugu Yagi who wrote papers in English and as a result the design is often incorrectly only attributed only to Yagi.
Yagi himself did not aim to steal the publicity, in view of his English papers, and as a result the design now bears the names of both men and is known as the Yagi-Uda antenna.

Yagi antenna - the basics

The Yagi antenna design has a dipole as the main radiating or driven element. Further 'parasitic' elements are added which are not directly connected to the driven element.

These parasitic elements within the Yagi antenna pick up power from the dipole and re-radiate it. The phase is in such a manner that it affects the properties of the RF antenna as a whole, causing power to be focussed in one particular direction and removed from others.

basic concept of Yagi Uda antenna

The parasitic elements of the Yagi antenna operate by re-radiating their signals in a slightly different phase to that of the driven element. In this way the signal is reinforced in some directions and cancelled out in others. It is found that the amplitude and phase of the current that is induced in the parasitic elements is dependent upon their length and the spacing between them and the dipole or driven element.

Yagi Uda antenna showing element types

There are three types of element within a Yagi antenna:

Driven element:   

The driven element is the Yagi antenna element to which power is applied. It is normally a half wave dipole or often a folded dipole.

Reflector :  

 The Yagi antenna will generally only have one reflector. This is behind the main driven element, i.e. the side away from the direction of maximum sensitivity.

Further reflectors behind the first one add little to the performance. However many designs use reflectors consisting of a reflecting plate, or a series of parallel rods simulating a reflecting plate. This gives a slight improvement in performance, reducing the level of radiation or pick-up from behind the antenna, i.e. in the backwards direction.

Typically a reflector will add around 4 or 5 dB of gain in the forward direction.


 There may be none, one of more reflectors in the Yagi antenna. The director or directors are placed in front of the driven element, i.e. in the direction of maximum sensitivity. Typically each director will add around 1 dB of gain in the forward direction, although this level reduces as the number of directors increases.
The antenna exhibits a directional pattern consisting of a main forward lobe and a number of spurious side lobes. The main one of these is the reverse lobe caused by radiation in the direction of the reflector. The antenna can be optimised to either reduce this or produce the maximum level of forward gain. Unfortunately the two do not coincide exactly and a compromise on the performance has to be made depending upon the application.

Yagi antenna radiation pattern

Yagi antenna advantages

The Yagi antenna offers many advantages for its use. The antenna provides many advantages in a number of applications:

Antenna has gain allowing lower strength signals to be received.
Yagi antenna has directivity enabling interference levels to be minimised.
Straightforward construction. - the Yagi antenna allows all constructional elements to be made from rods simplifying construction.
The construction enables the antenna to be mounted easily on vertical and other poles with standard mechanical fixings
The Yagi antenna also has a number of disadvantages that need to be considered.

For high gain levels the antenna becomes very long
Gain limited to around 20dB or so for a single antenna

Typical Yagi Uda antenna used for television reception

The Yagi antenna is a particularly useful form of RF antenna design. It is widely used in applications where an RF antenna design is required to provide gain and directivity. In this way the optimum transmission and reception conditions can be obtained.

Yagi gain / beamwidth considerations

It is found that as the Yagi gain increases, so the beam-width decreases. Antennas with a very high level of gain are very directive. Therefore high gain and narrow beam-width sometimes have to be balanced to provide the optimum performance for a given application

Yagi-Uda antenna gain vs beam-width

Yagi-Uda antenna gain considerations

A number of features of the Yagi design affect the overall gain:

Number of elements in the Yagi: 

  One of the main factors affecting the Yagi antenna gain, is the number of elements in the design. Typically a reflector is the first element added in any yagi design as this gives the most additional gain. Directors are then added.

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.

The gain of a Yagi antenna is governed mainly by the number of elements in the particular RF antenna. However the spacing between the elements also has an effect. As the overall performance of the RF antenna has so many inter-related variables, many early designs were not able to realise their full performance. Today computer programmes are used to optimise RF antenna designs before they are even manufactured and as a result the performance of antennas has been improved.

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.




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.

Yagi front to back ratio

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.

Feed impedance of Yagi driven element

It is possible to vary the feed impedance of a Yagi antenna over a wide range. Although the impedance of the dipole itself would be 73 ohms in free space, this is altered considerably by the proximity of the parasitic elements.
The spacing, their length and a variety of other factors all affect the feed impedance presented by the dipole to the feeder. In fact altering the element spacing has a greater effect on the impedance than it does the gain, and accordingly setting the required spacing can be used as one design technique to fine tune the required feed impedance.
Nevertheless the proximity of the parasitic elements usually reduces the impedance below the 50 ohm level normally required. It is found that for element spacing distances less than 0.2 wavelengths the impedance falls rapidly away.

Yagi matching techniques

To overcome this, a variety of techniques can be used. Each one has its own advantages and disadvantages, both in terms of performance and mechanical suitability. No one solution is suitable for all applications.
The solutions below are some of the main solutions used and applicable to many types of antenna. There also not the only ones:

  A balun is an impedance matching transformer and can be used to match a great variety of impedance ratios, provided the impedance is known when the balun is designed.

Folded dipole: 
One method which can effectively be implemented to increase the feed impedance is to use a folder dipole. In its basic form it raises the impedance four fold, although by changing various parameters it is possible t raise the impedance by different factors.

Delta match:   
This method of Yagi impedance matching involves "fanning out" the feed connection to the driven element.

Gamma match:   
The gamma match solution to Yagi matching involves connecting the out of the coax braid to the centre of the driven element, and the centre via a capacitor to a point away from the centre, dependent upon the impedance increase required.

Balun for Yagi matching

The balun is a very straightforward method of providing impedance matching. 4:1 baluns are widely available for applications including matching folded dipoles to 75Ω coax.

Baluns like these are just RF transformers. They should have as wide a frequency range as possible, but like any wound components they have a limited bandwidth. However if designed for use with a specific Yagi antenna, this should not be a problem.

One of the problems with a balun is the cost - they tend to be more costly than some other forms of Yagi impedance matching. They may also be power limited for a given size.

Folded dipole

The folded dipole is a standard approach to increasing the Yagi impedance. It is widely used on Yagi antennas including the television and broadcast FM antennas.

The simple folded dipole provides an increase in impedance by a factor of four. Under free space conditions, the dipole impedance on its own is raised from 75Ω for a standard dipole to 300Ω for the folded dipole.

Note on folded dipole:

The folded dipole is a from of dipole that has a higher impedance than the standard half wave dipole - in the standard version it has four times the impedance. However different ratios can be obtained by changing the mechanical attributes.

Another advantage of using a folded dipole for Yagi impedance matching is that the folded dipole has a flatter impedance versus frequency characteristic than the simple dipole. This enables it and hence the Yagi to operate over a wider frequency range.

While a standard folded dipole using the same thickness conductor for the top and bottom conductors within the folded dipole will give a fourfold increase in impedance, by varying the thickness of both, it is possible to change the impedance multiplication factor to considerably different values.

Delta match

The delta match for of Yagi matching is one of the more straightforward solutions. It involves fanning out the ends of the balanced feeder to join the continuous radiating antenna driven element at a point to provide the required match.

Delta match for dipole - often used for Yagi impedance matching
Both the side length and point of connection need to be adjusted to optimise the match.

One of the drawbacks for using the Delta match for providing Yagi impedance matching is that it is unable to provide any removal of reactive impedance elements. As a result a stub may be used.

Gamma match

The gamma match is often used for providing Yagi impedance matching. It is relatively simple to implement.

Gamma match for dipole - often used for Yagi impedance matching
As seen in the diagram, the outer of the coax feeder is connected to the centre of the driven element of the Yagi antenna where the voltage is zero. As a result of the fact that the voltage is zero, the driven element may also be connected directly to a metal boom at this point without any loss of performance.

The inner conductor of the coax is then taken to a point further out on the driven element - it is taken to a tap point to provide the correct match. Any inductance is tuned out using the series capacitor.

When adjusting the RF antenna design, both the variable capacitor and the point at which the arm contacts the driven element are adjusted. Once a value has been ascertained for the variable capacitor, its value can be measured and a fixed component inserted if required.

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