# The HPBW of a helical antenna

can someone tell me what are the formulas of HPBW for a helical antenna?

I've searched a lot and I saw that there are two different formulas of HPBW for the helical antenna,

this one,

$$\mathbf{(HPBW)} = [\frac{52}{C} \sqrt{\frac{\lambda^2}{NS}}]$$

and this one,

$$\mathrm{HPBW} \simeq \frac{52}{\frac C\lambda \sqrt\frac{NS}{\lambda}} \mathrm{degrees}$$

so what is the difference between both ?

• One of them is wrong by an exponent in $\lambda$. Otherwise, with applying the basic calculus rules for division and roots, they are identical. Sep 18, 2020 at 20:13
• Hello Abdullah, and welcome to this site! :-) Sep 18, 2020 at 21:28
• The Gain is extremely sensitive to the error in winding geometry from an ideal helical shape thus the latter equation from Kraus leads to higher gain than best effort by a few dB using $$HPBW = k \lambda ^{\dfrac{3}{2}}$$ Sep 19, 2020 at 15:26
• Hello Abdullah, I replaced your equations in .png files with MathJax equations. Here's a quick introduction to MathJax. Sep 29, 2020 at 16:21

$${52}\over{{C\over\lambda} \sqrt{n{S\over\lambda}}}$$
Be aware that this only holds for a narrow range of diameters and spacings: $$0.8<{C\over{\lambda}} <1.8$$ ; $$12<\alpha<14$$ and $$n\ge4$$