update

Author: EMDLAB-Package

functions/emdlab_extend_hbcurve_linear.m

@@ -0,0 +1,11 @@
+
+function [h,b] = emdlab_extend_hbcurve_linear(h, b, h_final)
+
+mu0 = 4*pi*1e-7*1.1;
+x_tmp = linspace(h(end),h_final,1e2)';
+y_tmp = b(end) + mu0 * (x_tmp - h(end));
+
+h = [h;x_tmp(2:end)];
+b = [b;y_tmp(2:end)];
+
+end

functions/emdlab_flib_smooth_extend_bvcurve_arctan.m

@@ -0,0 +1,38 @@
+function [B_ext, v_ext] = emdlab_flib_smooth_extend_bvcurve_arctan(B, v, v_final)
+% emdlab_flib_smooth_extend_bvcurve_arctan
+% extend B and reluctivity v to v_final using smooth arctangent decay
+%
+% inputs:
+%   B       : original B vector (t)
+%   v       : original reluctivity vector (1/mu or v=B/H)
+%   v_final : asymptotic v value for high B
+%
+% outputs:
+%   B_ext   : extended B vector
+%   v_ext   : extended v vector
+
+    % last point
+    Bs = B(end);
+    vs = v(end);
+
+    % last slope
+    slope_last = (v(end) - v(end-1)) / (B(end) - B(end-1));
+
+    % characteristic B width for arctan transition
+    Bk = (B(end)*0.5);  % you can tune this fraction
+
+    % compute amplitude to match slope at B=end
+    A = (slope_last - 0) * (pi/2) * Bk;  % slope decays from slope_last to near 0
+
+    % generate extension points
+    B_tail = linspace(B(end), 1e2*B(end), 100)'; 
+    B_tail = B_tail(2:end); % skip first point
+
+    % arctangent decay
+    v_tail = v_final + A * (atan((B_tail - Bs)/Bk) - atan(0));
+
+    % combine original + extension
+    B_ext = [B; B_tail];
+    v_ext = [v; v_tail];
+
+end

functions/emdlab_flib_smooth_extend_bvcurve_exp.m

@@ -0,0 +1,31 @@
+function [B_ext, v_ext] = emdlab_flib_smooth_extend_bvcurve_exp(B, v, B_final)
+% extend_exponential
+% extend B and reluctivity v to B_final using smooth exponential decay
+%
+% inputs:
+%   B       : original B vector (T)
+%   v       : original reluctivity vector (1/mu or v=B/H)
+%   B_final : asymptotic B value for v
+%
+% outputs:
+%   B_ext   : extended B vector
+%   v_ext   : extended v vector
+
+    % compute slope from last segment
+    slope = (v(end) - v(end-1)) / (B(end) - B(end-1));
+
+    % characteristic decay constant
+    tau = (B_final - v(end)) / slope;
+
+    % create extension points
+    B_tail = linspace(B(end), 1e2*B(end), 100)';  % 100 points beyond last B
+    B_tail = B_tail(2:end); % skip first point (already included)
+
+    % exponential decay for v
+    v_tail = B_final + (v(end) - B_final) * exp(-(B_tail - B(end))/tau);
+
+    % combine original + extension
+    B_ext = [B; B_tail];
+    v_ext = [v; v_tail];
+
+end

functions/emdlab_flib_smooth_extend_hbcurve_arctan.m

@@ -0,0 +1,31 @@
+function [h_full,b_full] = emdlab_flib_smooth_extend_hbcurve_arctan(h, b, h_final)
+% emdlab_flub_smooth_extend_hbcurve_arctan
+% extend b-h curve to h_final using arctangent, smoothly decreasing
+% incremental permeability from last slope to mu0.
+
+    mu0 = 4*pi*1e-7;  % vacuum permeability
+
+    % last point
+    Hs = h(end);
+    Bs = b(end);
+
+    % incremental permeability at last point
+    mu_last = (b(end) - b(end-1)) / (h(end) - h(end-1));
+
+    % arctangent scale parameter to control slope decrease
+    Ht = linspace(Hs, h_final, 100);  % extension points
+    Ht = Ht(2:end);  % skip Hs
+
+    % compute amplitude so that slope decreases from mu_last -> mu0
+    % dB/dH = mu0 + Bk*(2/pi)*(1/(1+(H/Hk)^2))*(1/Hk)
+    % at H = Hs, slope = mu_last => Bk formula:
+    Hk = (h_final - Hs)/2;           % characteristic width, adjustable
+    Bk = (mu_last - mu0) * (pi/2) * Hk;  % ensures slope starts at mu_last
+
+    % arctangent extension
+    b_ext = Bs + mu0*(Ht - Hs) + Bk*(2/pi)*(atan(Ht/Hk) - atan(Hs/Hk));
+
+    % combine original + extension
+    h_full = [h; Ht(:)];
+    b_full = [b; b_ext(:)];
+end

functions/emdlab_flib_smooth_extend_hbcurve_exp.m

@@ -0,0 +1,57 @@
+function [h_ext, b_ext] = emdlab_flib_smooth_extend_hbcurve_exp(h, b, h_final)
+% emdlab_flib_smooth_extend_hbcurve_exp
+% smooth maxwell-compatible extension of b-h curve
+%
+% inputs:
+%   h       : original h vector (a/m), monotonic increasing
+%   b       : original b vector (t)
+%   h_final : final h value for extension (a/m)
+%
+% outputs:
+%   h_ext   : extended h vector
+%   b_ext   : extended b vector
+
+    % constants
+    mu0 = 4*pi*1e-7;
+
+    % ensure column vectors
+    h = h(:);
+    b = b(:);
+
+    % last data point (saturation entry)
+    Hsat = h(end);
+    Bsat = b(end);
+
+    % incremental permeability at last segment
+    mu_last = (b(end) - b(end-1)) / (h(end) - h(end-1));
+
+    % smoothing length (maxwell-like)
+    DeltaH = 0.1 * Hsat;
+
+    % interpolation inside measured range
+    pp = pchip(h, b);
+
+    % generate extended h grid
+    if h_final <= Hsat
+        h_ext = h;
+        b_ext = b;
+        return
+    end
+
+    dh = mean(diff(h));
+    h_tail = (Hsat+dh : dh : h_final).';
+    h_ext  = [h; h_tail];
+
+    % allocate b
+    b_ext = zeros(size(h_ext));
+
+    % inside data range
+    idx_in = h_ext <= Hsat;
+    b_ext(idx_in) = ppval(pp, h_ext(idx_in));
+
+    % smooth asymptotic extension
+    idx_out = h_ext > Hsat;
+    Ht = h_ext(idx_out) - Hsat;
+    b_ext(idx_out) = Bsat + mu0 * Ht + (mu_last - mu0) * DeltaH .* (1 - exp(-Ht / DeltaH));
+
+end

functions/emdlab_flib_smooth_extend_hbcurve_polyc.m

@@ -0,0 +1,45 @@
+function [h_full, b_full] = emdlab_flib_smooth_extend_hbcurve_polyc(h, b, h_final, n)
+% emdlab_flib_smooth_extend_hbcurve_polyc
+% smooth polynomial-based extension of B-H curve
+% decreasing incremental permeability from last slope to mu0
+%
+% inputs:
+%   h       : original h vector (a/m)
+%   b       : original b vector (t)
+%   h_final : final h value for extension (a/m)
+%   n       : polynomial exponent for decay (default 2)
+%
+% outputs:
+%   h_full  : extended h vector
+%   b_full  : extended b vector
+
+    if nargin < 4
+        n = 2; % default exponent
+    end
+
+    mu0 = 4*pi*1e-7; % vacuum permeability
+
+    % last point
+    Hs = h(end);
+    Bs = b(end);
+
+    % incremental permeability at last segment
+    mu_last = (b(end) - b(end-1)) / (h(end) - h(end-1));
+
+    % generate extended H vector
+    Ht = linspace(Hs, h_final, 100);
+    Ht = Ht(2:end); % skip Hs
+
+    % polynomial decay function (normalized)
+    f = (1 - (Ht - Hs)/(h_final - Hs)).^n;
+
+    % incremental permeability along extension
+    mu_ext = mu0 + (mu_last - mu0) .* f;
+
+    % integrate mu(H) to get B(H)
+    b_ext = Bs + cumtrapz(Ht, mu_ext);
+
+    % combine original + extension
+    h_full = [h; Ht(:)];
+    b_full = [b; b_ext(:)];
+end

functions/extend_exponential.m

@@ -1,18 +1,13 @@
 
-function [x,y] = extend_exponential(x, y, y_final)
+function [B,v] = extend_exponential(B, v, B_final)
 
-% p = spline(x,y);
-% c = p.coefs(end,:);
-% x_tmp = x(end) - x(end-1);
-% slope = 3*c(4)*x_tmp^2 + 2*c(3)*x_tmp + c(2);
+slope = (v(end)-v(end-1))/(B(end)-B(end-1));
+tau = (B_final-v(end))/slope;
 
-slope = (y(end)-y(end-1))/(x(end)-x(end-1));
-tau = (y_final-y(end))/slope;
+x_tmp = linspace(B(end),1e2*B(end),1e2)';
+y_tmp = B_final + (v(end)-B_final) * exp(-(x_tmp-B(end))/tau);
 
-x_tmp = linspace(x(end),1e2*x(end),1e2)';
-y_tmp = y_final + (y(end)-y_final) * exp(-(x_tmp-x(end))/tau);
-
-x = [x;x_tmp(2:end)];
-y = [y;y_tmp(2:end)];
+B = [B;x_tmp(2:end)];
+v = [v;y_tmp(2:end)];
 
 end