Helical Antenna

Description of Antenna

The axial mode helical antenna is a circularly polarised end-fire antenna that has characteristics determined by axial length (L), pitch angle (o), circumference (C) and frequency of operation.

Design Curves

The following design curves enable the prediction of the gain and bandwidth in relation to axial length and pitch angle for any particular helical antenna with an axial length of between 0.5 lambda and 8 lambda.

Points to Note:

* The impedance bandwidth characteristics follow the gain bandwidth unless stated.
* The circumference of the helix is equal to 1 wavelength, although it may vary between 0.9 lambda and 1.2 lambda.
* The ground plane may be either flat or cupped in shape. In the case of a cupped ground plane the optimum dimensions are a diameter of 1 lambda and a depth of 0.2 lambda.
* The diameter of the conductor may vary between 0.005 lambda and 0.05 lambda.

Figure 1 shows the relationship between the gain of a helical antenna and its axial length (also shown in equation 1).
	Figure 1: Gain (G) of a Helical Antenna as a function of Axial Length (L)
G = 10 x log (8.5L + 7.75)...................................................1 The axial length for a given gain, or the gain for a given axial length may be obtained from this curve. The required pitch angle for the given axial length may then be found using figure 2 (or equation 1).
	Figure 2: Pitch Angle (?) vs Axial Length (L) required for Maximum Gain
Figure 3 shows the bandwidth at optimum pitch angle (indicated by the red circles) and also shows the increase in pitch angle required for an increase in bandwidth. An increase in bandwidth will result in a corresponding decrease in boresight gain.
	Figure 3: Percentage Bandwidth (BW%) vs Pitch (p) for Different Axial Lengths (L)

Pitch angles less than the optimum value are indicated by dotted lines (for axial lengths 1.82 lambda, 4.13 lambda, 6 lambda and 8 lambda). Increased pitch angle (in the range 4.5-14 degrees) also results in an improved VSWR. The bandwidth as shown in these curves is normalized to the upper frequency limit using equation 3 and varies with pitch as shown in equation 4.

BW(%) = (upper freq - lower freq) / (upper freq)...........3

BW(%) = 2.5p - 21.9 x log(L) +21......................................4

For a predictable and stable design a pitch angle of between 10 and 13 degrees is preferable, thus requiring a trade off between gain and stability with antennas of axial length shorter than 6 lambda.The dotted lines on the graph (for axial lengths of 0.5 lambda and 0.84 lambda) indicate the saturation of bandwidth (collapse of gain) at high angles of pitch.

Example

An antenna of the following specifications is used to illustrate the design process to be followed when using the curves:

* axial length of 30cm
* operating frequency of 5.15GHz ~ 5.85GHz
* maximum possible gain.

At the centre frequency of 5.5 GHz, a physical axial length of 30 cm corresponds to an electrical axial length of 5.5 lambda (in free space) and from figure 1 the gain for an axial length of 5.5 lambda is approximately 17.5 dBi.

The optimum pitch angle for a length of 5.5 lambda is approximately 9.75° as obtained from figure 2. This is the pitch required for maximum gain. The required bandwidth of the antenna, normalised to the upper frequency limit of 5.85 GHz is 11.97%, and from figure 3 it can be seen that at optimum pitch (red circles) the bandwidth of the antenna is approximately 30%. In order to create a more predictable design, the pitch may be increased to 10° so that it falls in the stable region of pitch (between 10° and 13°). This will cause a slight decrease in the bore sight gain and also an increase in the bandwidth. In a bandwidth-limited application, the percentage bandwidth may be varied by changing the pitch, and the pitch may be kept in the stable range by varying the axial length.

Thus the resulting helical antenna has the following characteristics:

* a pitch angle of 9.75 degrees
* a normalised bandwidth of 30%

as well as the original specifications:

* axial length of 30cm
* operating frequency of 5.15GHz ~ 5.85GHz
* maximum possible gain of 17.5 dBi.

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Reference:
Fourth Year Design Report, "Design Curves for the Axial Mode Helical Antenna" prepared by Wayne Jennings for the School of Electrical and Information Engineering, University of the Witwatersrand, August 2002.