SuperNEC - Dual Band Log Periodic Antenna

Dual Band Log Periodic Antenna

Description of Antenna

The dual band LPDA shown in the diagram below consists of two LPDA antennas, each designed for a specific bandwidth.

The antennas are connected via a twisted transmission line, which is continuous throughout the structure and is fed from the smallest end.

The boom impedance (Z0) of the antenna is the characteristic impedance of the antenna that feeds the dipole elements.

The relationship between element spacing and element length are given by the scale factor tau, as shown in equation 1.
tau = Ln+1/ Ln = dn+1/ dn = Dn+1/ Dn = Xn / Xn+1.............1

Truncation coefficents are used to find the minimum value for L1 (longest dipole element) and the maximum value for LN (shortest dipole element) as shown in equations 2 and 3. K1 and K2 are set at 0.5 and 0.25 respectively for the design curves below.
L1 = K1 lambda max .........................................................................2

LN = K2 lambda min ..........................................................................3

Tau can be calculated using the following equation, if the length and spacing of individual elements is required.
tau = (LN / L1)1/(N-1)............................................................4

The Form Factor (FF) is defined as:
Form Factor = Boom Length / lambda max ................................5

The thickness factor is defined as an element's length divided by it's radius.

The separation of the two antennas is defined in terms of the maximum wavelength, scaled according to a scaling factor:
separation = SpaceFactor(SF) x lambda max .............................6

The LF and HF bands are defined as follows:
LF = (%bandwidth / 100) x LowFrequency

LFBand --> LowFrequency : LowFrequency + LF
HF = (%bandwidth / 100) x HighFrequency

HFBand --> HighFrequency - HF : HighFrequency

Design Curves

The following design curves show the variation of certain parameters which fully characterise a dual-band LPDA in terms of appearance, geometry, physical dimensions and number of elements.

Figure 1 shows the minimum number of elements required (to ensure the antenna is operating in its stable region) as a function of form factor for two different bandwidths (of the HF and LF bands). The overall bandwidth (i.e. the bandwidth of the entire structure) is constant at 2:1 for these curves, with the thickness factor set at 2000 and boom impedance set at 75 ohms.
	Figure 1: Optimal Number of Dipole Elements as a function of Form Factor
Figure 2 shows the Gain as a function of the characteristic impedance, for different values of form factor and thickness factor.
	Figure 2: Average Gain as a function of Characteristic Impedance

It should be noted that certain combinations of parameters tend to give unfavourable results and should be avoided.

Points to note:

* A low form factor should be avoided if high gain is required, however the angle should not be reduced to a point where the form factor is too large, as this will result in a sharp drop in gain.
* Thickness factor should be kept high, this however implies that very thin elements are used, which may affect the strength of the antenna structure.
* The characteristic impedance of the antenna should be kept low, however it will be influenced by the choice of thickness factor. If a high Z0 is used, the thickness factor should be a large as possible, which might be difficult to achieve.

Example

A dual-band LPDA with the following specifications is required:

* operating frequency of 800 - 1600MHz (15% bandwidth in HF and LF bands)
* characteristic impedance of 200 ohms
* average gain of 13dBi

Using figure 2 it can be seen that a form factor of 5 is required, the thickness factor is chosen as 100 to reduce the amount of material used in producing the antenna.

Figure 1 may then be used to determine the minimum number of elements (approximately 35) required for a bandwidth of 15%, form factor of 5 and a space factor of 1. The boom length may be reduced slightly by reducing the space factor.

The resulting antenna may be summarised as follows:

Low Frequency component (frequency band of 800-920MHz):

* Form Factor of 5
* Boom length of 1.875m (equation 5)
* 35 dipole elements, longest being 187.5mm and shortest being 81.5mm
* tau of 0.9758 (from which each individual length can be determined)
* Gain of 13.5dBi
* Characteristic Impedance of 200 ohms

High Frequency component (frequency band of 1360-1600MHz):

* Form Factor of 5
* Boom length of 1.103m (equation 5)
* 35 dipole elements, longest being 110.3mm and shortest being 46.9mm
* tau of 0.9752 (from which each individual length can be determined)
* Gain of 13.5dBi
* Characteristic Impedance of 200 ohms

With a separation of lambda max (0.375m), the total length of the structure is 3.353m.

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Note: these design curves provide only a rough estimate of a particular antenna's dimensions and performance. In order to fully specify the antenna it should be simulated, using the values obtained from the curves if so desired.

Reference:
Fourth Year Design Report, "Investigate the Design of a Dual Band Log Periodic Antenna" prepared by Una Perovic for the School of Electrical and Information Engineering, University of the Witwatersrand, August 2003.