AntCal Documentation

Radiation Pattern

  • Currently all sources are positioned at the origin
  • Amplitudes are normalized to the maximum radiation of E-/M-dipole respectively
  • Far fields are sampled with limited resolution of 1°

E-dipole:

  • Gain θθ: sin⁡(θ)cos⁡(ϕ)\sin(\theta)\cos(\phi)
  • Gain ϕϕ: sin⁡(ϕ)\sin(\phi)

Demo

Module Parameters: [lpwl_,theta_,phi_,mesh_,opac_,step_,pg_][lpwl\_, {theta\_, phi\_}, mesh\_, opac\_, step\_, pg\_]

fun⁡={∣πLpwlsin⁡(πLpwlcos⁡Ξ)sin⁡π∣cos⁡Ξif ∣cos⁡(πLpwlcos⁡Ξ)−cos⁡(πLpwl)∣sin⁡Ξ=Indeterminate∣cos⁡(πLpwlcos⁡Ξ)−cos⁡πLpwl∣sin⁡Ξotherwise\operatorname{fun} = \begin{dcases} \frac{\left|\pi Lpwl \sin{(\pi Lpwl \cos{\Xi})} \sin{\pi}\right|}{\cos{\Xi}} & \text{if } \frac{\left|\cos{(\pi Lpwl \cos{\Xi})}-\cos{(\pi Lpwl)}\right|}{\sin{\Xi}} = \text{Indeterminate} \\ \frac{\left|\cos{(\pi Lpwl \cos{\Xi})} - \cos{\pi Lpwl}\right|}{\sin{\Xi}} & \text{otherwise} \end{dcases}

where Ξ\Xi is [0,π,π/180][0, \pi, \pi / 180].

max⁡=Max(fun⁡)⁡\operatorname{max} = \operatorname{Max(\operatorname{fun})}
l⁡(th_,ph_)=[sin⁡(th deg)cos⁡(ph deg),sin⁡(th deg)sin⁡(ph deg),cos⁡(th deg)]\operatorname{l}(th\_, ph\_) = [\sin(th\ deg)\cos(ph\ deg), \sin(th\ deg)\sin(ph\ deg), \cos(th\ deg)]
lr⁡(th_,ph_,t_,f_)=sin⁡(th deg)cos⁡(ph deg)sin⁡(t)cos⁡(f)+sin⁡(th deg)sin⁡(ph deg)sin⁡(t)sin⁡(f)+cos⁡(th deg)cos⁡(t)\operatorname{lr}(th\_, ph\_, t\_, f\_) = \sin(th\ deg)\cos(ph\ deg)\sin(t)\cos(f) + \sin(th\ deg)\sin(ph\ deg)\sin(t)\sin(f) + \cos(th\ deg)\cos(t)

M-dipole:

  • Gain θθ: sin⁡(ϕ)\sin(\phi)
  • Gain ϕϕ: sin⁡(θ)cos⁡(ϕ)\sin(\theta)\cos(\phi)

Linear Combination with Arbitrary Phase Shift 1

We have

asin⁡(x+θa)+bsin⁡(x+θb)=csin⁡(x+φ)a\sin(x+\theta_a)+b\sin(x+\theta_b)=c\sin(x+\varphi)

where cc and φ\varphi satisfy

c=a2+b2+2abcos⁡(θa−θb),φ=atan2⁡(acos⁡θa+bcos⁡θb, asin⁡θa+bsin⁡θb).\begin{gather*} c=\sqrt{a^2+b^2+2ab\cos(\theta_a-\theta_b)}\text{,} \\ \varphi=\operatorname{atan2}(a\cos\theta_a+b\cos\theta_b,\ a\sin\theta_a+b\sin\theta_b)\text{.} \end{gather*}

Note: atan2(y, x)⁡\operatorname{atan2(y,\ x)} uses Numpy's arctan2 parameter order.

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Reference

See IEEE Author Center.

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While IEEE does accept vector artwork, it is our policy is to rasterize all figures for publication. This is done in order to preserve the figures’ integrity across multiple computer platforms.

All color figures should be generated in RGB or CMYK color space. Grayscale images should be submitted in Grayscale color space. Line art may be provided in grayscale OR bitmap colorspace.

When preparing your graphics IEEE suggests that you use of one of the following Open Type fonts: Times New Roman, Helvetica, Arial, Cambria, and Symbol.

—Preparation of Papers for IEEE Transactions and Journals (April 2013)

Footnotes

  1. Trigonometric Identities ↩