Tapered Helix Antenna

Description of Antenna

The diagram below shows a monofilar contantly tapered helical antenna (tapered helix) with constant turn spacing, operating in the axial mode. Tapered helices generally exhibit lower gain and greater bandwidth than uniform helices.

Another parameter of interest for the tapered helix is the top to mean radius ratio (R):

R = RT / RM .........................................................................1

Design Curves

The parameters found to be critical to the performance of the antenna are as follows:

* axial length (L)
* top to mean radius ratio (R)
* turn spacing (S)

The curves shown in figure 1 use equation 2 to show the relationship between gain, axial length and R. 'R=0' corrsponds to a perfect cone, and 'R=1' corresponds to a uniform helix (no taper).
	Figure 1: Gain versus Axial Length for different values of R
G(dbi) = 1.568eR + 7.2log(4 + 9.5L) - 0.5554................2 This equation is valid for L>1 lambda, 0<R<1, 0.1?<S<0.3 lambda, and is accurate to within 5%. If size is not a limiting factor in the design, then a longer axial length is preferable due to the gain being more constant across the antenna's bandwidth. The percentage bandwidth of the antenna is defined by equation 3. And the relationship of the bandwidth to both the turn spacing and top to mean radius ratio is shown in figure 3. These curves are described by equation 4. BW(%) = (upper freq - lower freq) / (lower freq)............3
	Figure 2: Percentage Bandwidth versus R
BW(%) = 468.75log(21.67R + 20.498)S - 780.95S - 41.67R + 75.752.......4 This equation is valid for R>0.3, S>0.1?, 1?<L<8 lambda, and is accurate to within 10% (for most cases 5%). It should be noted that the bandwidth centre frequency, as well as the frequency of maximum gain increases with increasing S and R, while decreasing with increasing axial length. The figure shows the gain characteristic as a function of ground plane diameter. It clearly shows the ideal diameter to be 1.1 lambda, just above the knee.
	Figure 3: Gain vs Ground Plane Diameter for 3 specific Antennas

Example

An antenna with the following characteristics is required:

* Axial length of 30cm
* Centre frequency of operation: 5.5Ghz
* Minimum percentage bandwidth of 40%
* Maximum possible gain

This is a bandwidth limited design, and from figure 2 the turn spacing needs to be less than 0.2 wavelengths in order to achieve the required minimum bandwidth of 40%. To maximise gain. R needs to be maximised, and so S should be chosen to be as close to 0.1? as possible. If S is equal to 0.1 lambda, then R = 0.75 for a bandwidth of 40%.

The gain of the antenna may then be determined by using figure 1 (a physical length of 30cm corresponds to 5.5 lambda at 5.5GHz), and in this case is just greater than 15dBi.

The antenna therefore has the following characteristics:

* a turn spacing of 0.1 lambda (5.5mm)
* a top to mean radius ratio of 0.75
* gain of 15 dBi

as well as the original specifications:

* an axial length of 5.5 lambda (30cm)
* bandwidth greater than 40%
* centre operating frequency of 5.5GHz

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