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5_Simulations/Slotted_DielectricFilled_Waveguide.m

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+%% ---- Slotted waveguide column (dielectric-filled, alumina) ----
+% Your numbers:
+f0      = 10.5e9;           % Hz
+eps_r   = 9.8;              % alumina (99.5–99.8%)
+a       = 8.5e-3;           % broad wall (m)
+b       = 3.5e-3;           % narrow wall (m)
+Mcols   = 16;               % (for panel-level, not used here)
+Nslots  = 32;               % per column
+
+% Physical constants
+c0   = physconst('LightSpeed');
+lam0 = c0/f0;
+
+%% ---- Rectangular waveguide TE10 cutoff (filled with eps_r) ----
+% fc10 = (c0 / (2*a*sqrt(eps_r)))
+fc10 = c0/(2*a*sqrt(eps_r));
+if f0 <= fc10
+    error('f0 is below TE10 cutoff for the filled waveguide.')
+end
+
+% Guide wavelength in dielectric:  λg = λ0 / sqrt(1 - (fc10/f0)^2)
+lamg = lam0 / sqrt(1 - (fc10/f0)^2);
+
+%% ---- Design rules derived from λg ----
+% Slot spacing: s = λg/2
+slotSpacing = lamg/2;                     % ~ 16.915 mm (with λg=33.83 mm)
+% Slot length (longitudinal): L ≈ 0.47*λg  (trim in proto if needed)
+slotLen     = 0.47*lamg;                  % ~ 15.9 mm
+% Slot width: keep electrically narrow but machinable
+slotWid     = 0.02*lam0;                  % ~ 0.57 mm at 10.5 GHz
+
+% Slot offset from centerline: start ~ 0.25*a (tune per-slot for taper)
+x_offset    = 0.25*a;                     % ~ 2.1 mm
+
+% Probe length inside dielectric (for note/consistency):
+Lprobe      = lam0/(4*sqrt(eps_r));       % ~ 2.28 mm
+
+%% ---- Overall waveguide length and feed locations ----
+% Center the slot train about z=0 (Antenna Toolbox uses feed/slot offsets
+% relative to the waveguide center by default).
+z_first = ((Nslots)/2-0.5)*slotSpacing ;    % first-slot z position (centered array)
+z_feed  = -z_first - lamg/4;               % ~ quarter-wave behind first slot
+z_short = z_feed - lamg/4;                % backshort another quarter-wave behind
+
+% Put some margin beyond the last slot and behind the short:
+z_margin_front = 2*slotSpacing;
+z_margin_back  = 2*slotSpacing;
+wgLength = lamg + (Nslots-1)*slotSpacing;
+% This keeps the backshort inside the model and gives space beyond last slot.
+
+% Antenna Toolbox expects total Length (z extent), Width (y=a), Height (x=b)
+Length = wgLength;
+Width  = a;
+Height = b;
+
+% Slot-to-top: distance from slot center to the top (outer) broad-wall edge.
+% If the slot offset from center is +x_offset toward the top wall,
+% then SlotToTop ≈ (a/2 - x_offset).
+slotToTop = (a/2 - x_offset);
+
+% The SlotOffset property is the lateral offset from the guide centerline.
+% Use +x_offset (sign convention follows object; if inverted, use -x_offset).
+slotOffset = x_offset;
+
+% Feed parameters:
+feedHeight = Lprobe;          % use the probe length as the pin intrusion (model note)
+feedWidth  = 1.2e-3;          % ~1.2 mm hole/pin diameter (adjust to your connector)
+feedOffset = [z_feed, 0];     % [z y] offset (y=0 at column center)
+
+%% ---- Build the slotted waveguide in Antenna Toolbox ----
+slotShape = antenna.Rectangle('Length',slotLen,'Width',slotWid);
+
+ant = waveguideSlotted( ...
+    'Length',        Length, ...
+    'Width',         Width, ...
+    'Height',        Height, ...
+    'NumSlots',      Nslots, ...
+    'Slot',          slotShape, ...
+    'SlotSpacing',   slotSpacing, ...
+    'SlotOffset',    slotOffset, ...
+    'ClosedWaveguide', 1, ...
+    'SlotToTop',     lamg/2, ...
+    'FeedHeight',    feedHeight, ...
+    'FeedOffset',    feedOffset, ...
+    'FeedWidth',     feedWidth);
+
+% For plotting/inspection
+figure; show(ant); title('Dielectric-informed slotted waveguide (geometry driven)');
+
+%% ---- Optional: verify positions quickly in the command window ----
+fprintf('lambda0 = %.3f mm, lambda_g = %.3f mm\n', lam0*1e3, lamg*1e3);
+fprintf('SlotSpacing = %.3f mm, SlotLen = %.3f mm, SlotWid = %.3f mm\n', slotSpacing*1e3, slotLen*1e3, slotWid*1e3);
+fprintf('Slot offset = %.3f mm  (SlotToTop = %.3f mm)\n', slotOffset*1e3, slotToTop*1e3);
+fprintf('z_first = %.2f mm, z_feed = %.2f mm, z_short = %.2f mm\n', z_first*1e3, z_feed*1e3, z_short*1e3);
+fprintf('FeedHeight (probe) ~ %.2f mm, FeedWidth ~ %.2f mm\n', feedHeight*1e3, feedWidth*1e3);