Re: ferrite vs sensitivity

George Magiros

I'm still on my quest to simulate ferrite loop antennas, this time for their signal to noise ratios.  I hope I'm not proving that 17 swallows are as strong as a horse with all my graphs.  Experimentation and actual DXing comes next I promise.

Let me point out a few simple design observations that I gleamed from the graphs.

First, use as many turns as possible without making the Q too high.  My Sony ICF-S10MK2 apparently uses a small loopstick with an inductance of 650 uH.  That is more than enough turns I would think.  300 uH is probably sufficient too, maybe lower.  Having a good number of turns puts you into a kind of linear region where increasing the length of the rod improves the SNR the most.  While increasing the number of turns on the loop does improve the SNR, best results come from increasing the length of the rod. 

Second, increasing the diameter of rod does not improve the SNR that much, unless of course your rod has a very small diameter to begin with.  It appears to be better SNR-wise, and less costly, to simply increase the length of the rod rather than its diameter.  In addition there appears to be, for a given rod diameter, a maximum rod length beyond which no increase in the SNR occures. 

Now here are the graphs.  First for a ferrite loopstick antenna with an initial permeability of 125.  One graph plots rod length against turns and the other plots rod diameter against turns.  For a loopstick with a diameter of 12.7mm the best length seems to be between 200mm and 300mm FYI.

Next, here are the graphs for a loopstick antenna with a mu of 800.  The best length for a rod with a 12.7mm diameter seems to be between 300mm to 450mm.


Ps. Just to be sure I haven't made any glaring mistakes here is the Matlab/Octave function I used to calculate the signal to noise ratio.

% mui: initial relative permeability of the rod
% n: number of turns
% lr: length of rod in mm
% dw: diameter of wire in mm
% f: frequency in Hz
% E: E-field in V/m
function [ snr Rac Rdc ] = loopstick (mui, n, d, lr, f, dw, E)
  Kb = 1.38e-23;                  % boltzmann constant
  T = 293;                        % room temperature 20C (293K)
  muo = 4 * pi * 1e-7;            % permeability of free space
  sigma = 5.96e7;                 % conductivity of copper at 20C (293K)
  B = 3e3;                        % bandwidth (3 khz)

  lw = n .* pi .* d;                          % length of wire need
  delta = 1 ./ sqrt(pi * muo * sigma * f);    % skin depth of wire
  Rdc = lw * .001 ./ (pi / 4 .* (dw * .001).^2 * sigma);
  Rac = lw * .001 ./ (pi * sigma * delta .* dw * .001);
  en = sqrt(4 * Kb * T * B * Rac);            % noise voltage

  mu = 1./(1./mui+(d./lr).^2.*(log(lr./(d/2))-1)); % rod relative permeability
  a = pi / 4 * (d * .001).^2;                 % rod winding area
  es = 2 * pi * n .* a .* mu * E / (3e8 / f); % signal voltage
  snr = 20 * log10(es ./ en);          

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