SWE_basics

Basic routines for Spherical Wave modelling in the Far-Field

Main functions:

q = myVc_swe(F,J,varargin)

Vector field Series expansion in terms of Vector spherical harmonics Inputs

• F: Vector Field to expand. (Struct with fields theta and phi)
• J: Number of harmonics, J = 2N(N+2)
• varargin: theta, phi (rad) Outputs
• q: Vector with odd (s=1) and even (s=2) expansion coefficients in alternate fashion

F = myVc_sws(q,varargin)

Vectorial farfield reconstruction from a Spherical wave expansion Synthesis, given the coefficients of a series expansion in spherical harmonics Inputs

• q: Vector of coefficients
• varargin: theta, phi Outputs:
• Reconstructed field. (Struct with fields theta and phi)

[F,Pnm,mP,dP] = my_SHgen(m,n,s,varargin)

Vectorial spherical harmonics generator, Inputs

• n: (scalar) Degree
• m: (scalar) Order
• s: (scalar) Function (1: odd <-> TE, 2: even <-> TM)
• varargin:
  • theta: vector
  • phi: vector
  • test: boolean, enables the comparison between the calculated Functions and direct and (selected) theoretical expressions taken from Hansen book p.322-324, for n == 2 | n == 3 | n == 4 Outputs
• F: Vectorial Spherical Harmonic (struct with fields theta and phi)
• Pnm: normalized associated Legendre function
• mP: normalized associated Legendre function, times m, over sin\theta
• dP: derivative of normalized associated Legendre function

plotPattern(E,theta,phi,varargin)

Flexible routine for Radiation pattern plot, in a given coordinate system (1D: Rectangular, polar, 2D: Rectangular grid, Projected, 3D: Polar) Inputs:

• E: (Array), Supported sizes: N_theta x N_Phi x N_Pats, N_theta x N_Phi, N_theta x N_Pats, N_theta x 1, N_phi x 1
• theta: (Array), 1D or 2D
• phi: (Array), 1D or 2D
• varargin:
  • norma: (Logic), true if normalized plot is desired
  • scale: (String), indicate the field axis scaling, 'dB', 'lin'
  • plStyle: (String), representation of the input field, 'asis' -> E, 'fld' -> abs(E), 'pwr' -> abs(E).^2, 'dir' -> dir*abs(E)/max(abs(E))
  • coords: (String), format of the axes, 1D fields: 'rect','polar', 2D fields: 'rect','proj2D','pol3D' 'rect' for 3D patterns creates a projection on a rectangular (theta, phi) grid 'proj2D' for 3D patterns creates a projection on a Direction cosine coordinate system (u=sin(th)cos(ph),v=sin(th)sin(ph)).
  • limsScale: (Vector), [minScale,maxScale]
  • thetaCut: (scalar), -1 for sweep, other value for an specific angle cut (3D patterns)
  • phiCut: (scalar), -1 for sweep, other value for an specific angle cut (3D patterns)
  • multPatts: (logic), true to indicate that multiple patterns are provided, false by default.
  • aggrPatts: (logic), true to indicate that patterns should be added before plotting, false by default. Outputs:
• No variable neither file output is generated, just the pattern plot