Antenna formulas

• Far-field region and maximum directivity:
  • r = 2*D^2/lambda          % start of far-field region of antenna, D is maximum diameter of antenna
  • D0_max = 4*pi*A/lambda^2  % maximum directivity of antenna (linear power)
• Relations between directivity and beam width:
  • D0 = (95.2/theta3dB_deg)^2                    % directivity (linear power) from half 3 dB beam width in degrees
  • D0_dBi = 39.6 - 20*log10(theta3dB_deg)        % directivity from half 3 dB beam width in degrees
  • theta3dB_deg = 10^((39.6-D0_dBi)/20)          % half 3 dB beam width in degrees from directivity
  • theta3dB_deg = sqrt((thE_deg^2+thH_deg^2)/2)  % half 3 dB beam width to use in the formulas above if different in E- and H-plane
• Array antennas with lambda/2 spacing of elements:
  • D0_element_dBi = 5.0            % directivity of ideal antenna element of area (lambda/2)^2
  • D0_dBi = 5.0 + 10*log10(Nx*Ny)  % directivity of ideal antenna array with lambda/2 spacing of elements
  • theta3dB_x_deg = 60/Nx          % half 3 dB beam width in x-direction with lambda/2 spacing of Nx elements in x-direction
  • theta3dB_y_deg = 60/Ny          % half 3 dB beam width in y-direction with lambda/2 spacing of Ny elements in y-direction
  • bw1dB_x_deg = 2*40/Nx           % whole 1 dB beam width in x-direction with lambda/2 spacing of Nx elements in x-direction
  • bw1dB_y_deg = 2*40/Ny           % whole 1 dB beam width in y-direction with lambda/2 spacing of Ny elements in y-direction
  • Nbits = 1 + log2(max(Nx,Ny))    % approximate number of bits required for phase shifters (assuming lambda/2 spacing)

Profile for Ulf Carlberg

• Born 1978
• PhD in antenna engineering, excellent programmer
• Solid academic and industry experience

Employment and educational background

• 2018- Antenna specialist consultant, Huawei, Sweden
• 2016-2017 Antenna specialist consultant, Provinn, Sweden
• 2014-2016 Antenna specialist consultant, Qamcom Research and Technology, Sweden
• 2008-2014 Antenna and EMC Researcher, SP Technical Research Institute of Sweden
• 2006-2008 Employed at the Antenna Group, Chalmers Univ. of Technology, Sweden
• 2002-2006 PhD Student at the Antenna Group, Chalmers Univ. of Technology, Sweden
• 2001-2002 Master thesis, Tokyo Institute of Technology, Japan
• 1997-2002 Master program electrical engineering, Chalmers Univ. of Technology, Sweden

Example of work

• Matlab support to Prof. Per-Simon Kildal's book Foundations of Antenna Engineering
• An open-source channel model code called virmlab implemented in Matlab

Links

• LinkedIn Profile of Ulf Carlberg
• Publications by Ulf Carlberg

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