antenna-theory.com

[kurt]

I have been trying to implement the formulas on this page http://www.antenna-theory.com/antennas/travelling/helix.php in order to design my WLAN helix

After creating a spreadsheet and X-Y graph to of the E-field radiation pattern and gotten plausible results with three-degree data points for the example 0.5 meter helix.

I need first to know what the variable "k" is supposed to mean? When graphing and changing k I see that lower values simplify the curve and higher ones complexify it. A k value around 0.012 gives 12 zero-crossings in X-Y for the example 0.5 meter - which I believe is equivalent to the 12 lobes in Figure 2 on that page. Am I right? How to chose a value for my design at 2440 MHz?

Second, I was somewhat surprised that my spreadsheet energy formula:
Omega is =k*S*(COS(theta)-1)-PI()*(2+1/N) and
E is =Sin(pi()/(2*N))*COS(theta)*SIN(N*omega/2)/SIN(omega/2)
gives negative values on-axis (z positive, at theta=0) for N values that are even. I had been thinking polar and that would mean the antenna's main lobe is backwards. Is it? Or is it really just a phase reversal? Subsequently, I've been always specifying an odd number of turns to get a positive main lobe.

Third, considering the Gain formula and the radiation pattern I am confused about how much power is actually available on beam vs. in the side-lobes. To illuminate that I computed the field energy (by summing narrow rings of E) around the z-axis: the primary lobe and then all of the rest - the side-lobes. To me the ratio of those two energies reflects the directivity of the antenna. Is that right? How is that related to gain? And I found (barring my errors) that the example design had a 0.21 ratio (with 11 turns; 0.19 with 10). The Figure 2 suggests that a lot of energy is going to side-lobes.

Surprisingly, as I adjust N I see that the computed Gain (=6.2*C_turn_ln^2*N*S/Lambda^3) varies inversely to N. On the other hand, my intuition was rewarded when I saw that the computed main/side-lobe energy ratio varies with N. Is there an issue with the gain (empirical?) formula? These relationships held while the turns angle, alpha, was inside or outside the 12 - 14 degree limits.

Fourth, I'm planning a backplane slightly larger than one wavelength - based on materials at hand. Since there are no parameters for a non-infinite backplane, what adjustments or considerations are needed for reality?

Fifth, the author said that helical antennas function well at pitch angles between 12 and 14 degrees. But the formulas seem to give me better results at lower angles. Can someone describe what happens to the radiation field (or anything else) as the angle is changed? I.e. as the same N is spread over a greater or lesser total length?

Thanks in advance for any help.

[bigSteve]

Some quick notes:


k is the wavenumber:
http://www.antenna-theory.com/definitions/wavenumber.php

Wavenumber (k) is analogous to frequency (oscillation in time), where k is a measure of oscillation in space. It is not a variable, rather it is defined when the frequency is determined.


Don't worry about E-field being negative. The E-field varies in time as sin(2*pi*f*t), so if it is positive at one time, it will be negative a half-cycle later. If it is negative at the peak of the main beam, this simply means it is out of phase with some arbitrary reference. When you get the gain pattern (proportional to magnitude of E-field squared), the negative signs go away.



Directivity is not really a measure of the ratio of the energy in the primary lobe to that of the side lobes. If it was, then an antenna with a single beam would have an infinite directivity. It is a measure of the peak radiation direction relative to the energy in the rest of the beam. The ratio metric you mention may be useful, but you can't call it directivity.


The gain should vary directly with N. It is a general rule of antenna that larger antennas give larger gain (more directive). So if you see the gain vary inversely with N then something isn't right.