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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 ?

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  • $\begingroup$ One of them is wrong by an exponent in $\lambda$. Otherwise, with applying the basic calculus rules for division and roots, they are identical. $\endgroup$ Sep 18 '20 at 20:13
  • $\begingroup$ Hello Abdullah, and welcome to this site! :-) $\endgroup$
    – Mike Waters
    Sep 18 '20 at 21:28
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    $\begingroup$ 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 $$HPBW = k \lambda ^{\dfrac{3}{2}}$$ $\endgroup$ Sep 19 '20 at 15:26
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    $\begingroup$ Hello Abdullah, I replaced your equations in .png files with MathJax equations. Here's a quick introduction to MathJax. $\endgroup$
    – rclocher3
    Sep 29 '20 at 16:21
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Kraus says

$${52}\over{{C\over\lambda} \sqrt{n{S\over\lambda}}} $$

Which is your second equation.

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 $n\ge4$

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