Datastream Cowboys

Helical/helix antenna cookbook recipe for 2.4 GHz wavelans
and/or WiFi applications
by
Dr. Remco den Besten, PA3FYM (mail: helix at remco.tk)

Bookmark/refer to this page as http://helix.remco.tk  I 
innocently made this cookbook recipe and placed it on my local
ADSL-connected machine, never expecting that so many of you 
want to have this information.
This (co-located) bandwidth is kindly donated by ds9a.nl

Abstract
The helix antenna, invented in the late fourties by 
John Kraus (W8JK), can be considered as the genious ultimate 
simplicity as far as antenna design is concerned. Especially 
for frequencies in the range 2 - 5 GHz this design is very easy,
practical, and, non critical. This contribution describes how 
to produce a helix antenna for frequencies around 2.4 GHz which
can be used for e.g. high speed packet radio (S5-PSK, 1.288 
Mbit/s), 2.4 GHz wavelans, and, amateur satellite (AO40). 
Developments in wavelan equipment result in easy possibilities
for high speed wireless internet access using the 802.11b 
(aka WiFi) standard.

Theory in a birds eye view
The helix antenna can be considered as a spring with N turns 
with a reflector. The circumference (C) of a turn is 
approximately one wavelength (l), and, the distance (d) between
the turns is approx. 0.25C. The size of the reflector (R) is 
equal to C or l, and can be a circle or a square. The design 
yields circular polarization (CP), which can be either 'right 
hand' or 'left hand' (RHCP or LHCP respectively), depending 
upon how the helix is wound. To have maximum transfer of 
energy, both ends of the link must use the same polarization, 
unless you use a (passive) reflector in the radio path.
The gain (G) of the antenna, relative to an isotrope (dBi), 
can be estimated by:

G = 11.8 + 10 * log {(C/l)^2 * N * d} dBi               (1)

According to Dr. Darrel Emerson (AA7FV) of the National Radio 
Astronomy Observatory, the results from [1], also known as the 
'Kraus formula',  are 4 - 5 dB too optimistic. Dr. Ray Cross 
(WK0O) inserted the results from Emerson in an antenna analysis
program called 'ASAP'.

The characteristic impedance (Z) of the resulting 'transmission
line' empirically seems to be:

Z = 140 * (C/l) Ohm                                     (2)
 

Practical design for 2.43 GHz (aka S-band, ISM band, 13 cm
amateur band)

l = (0.3/2.43) = 0.1234567 m  ;-)(12.34 cm)             (3)

The diameter (D) of one turn = (l/pi) = 39.3 mm         (4)

Standard PVC sewer pipe with an outer diameter of 40 mm is 
perfect for the job and can be obtained easily (at least in 
The Netherlands ;-) from a 'do it yourself' shop or a plumber. 
The helix will be wound with standard wire used to interconnect
220V AC outlets in (Dutch ;-) house holds. This wire has a 
colourized PVC isolation and a 1.5 mm thick copper core. 
Winding it around the PVC pipe will result in D = ca. 42 mm, 
due to the thickness of the isolation.

With D = 42 mm, C = 42*pi = 132 mm (which is 1.07 l)    (5)

Now d = 0.25C = 0.25*132 = 33 mm                        (6)

For distances ranging from 100 m - 2.5 km with line of sight, 
12 turns (N = 12) are sufficient. The length of the PVC pipe 
therefore will be 40 cm (3.24 l). Turn the wire around the PVC
pipe and glue it with PVC glue or any other glue containing 
tetrahydrofurane (THF). The result will be a very solid helix 
wound along the pipe, see figure 1 below.

Figure 1. Overview of some of the materials used and 
dimensions.

The impedance of the antenna, which is:

Z = 140 * (C/l) = 140*{(42*pi)/123.4} = 150 Ohm       (7)

requires a matching network on order to apply standard 50 Ohm
UHF/SHF coax and connectors.

The use of a 1/4-wave matching stub with an impedance (Zs) of:

Zs = sqrt(Z1*Z2) = sqrt(50*150) = 87 Ohm                (8)

is very common. Due to the helix design, this equals 1/4 turn.
However, from a mechanical point of view -bearing water proof 
aspects in mind when using the antenna outdoors- there are 
more preferred methods to match the helix to 50 Ohm. My first 
thoughts were to empirically decrease d for the first and 
second turn and match the helix using the 'trial and error'
-method, while measuring the results with a directional couple
r, and signal generator. Browsing the internet for while I 
found helices matched this way, but surprisingly I bumped into
the page of Jason Hecker. He really used an elegant way to 
match his helix by using a copper vane, referring to the ARRL 
Handbook. So, full credits go to the ARRL and Jason, and I 
used his dimensions for the vane. To be honest, this page 
seems to be a duplicate of his page, except that our helices a
re wound the other way around!! Yes, and I am left handed, so,
is this a coincidence? It is funny anyway :-)) For details, 
see figure 2 (below). 

Figures 2a and 2b. The idea, the dimensions, and, mounting the
stub. The hypotenusa of the stub should follow the wire.

Now with some luck and skills solder the stub to the helix, glue 
it, and prepare the contrapsion to be inserted into the cap, 
see figure 3. 

Figure 3. Almost finished helix antenna.

And.... ready! (figure 4)

Figure 4.  Finished 12 turn 2.4 GHz helix antenna, G = 17.5 
dBi or 13.4 dBi (Kraus or Emerson respectively)
 

The antenna was sweeped an measured. The results are given 
below (figures 5a and 5b) 

Figure 5a Return loss (dB) from 2300 - 2500 MHz

Figure 5b Smith chart 2300 - 2500 MHz