Add analytic patch antenna design example

examples/README.md

@@ -56,3 +56,20 @@ python ../tools/plot_pattern.py patch_antenna_pattern.csv
 ```
 
 This produces a polar plot of the gain pattern in the $xz$-plane.
+
+## patch_antenna_design
+
+`patch_antenna_design.py` performs a simple analytic design of a
+2.45 GHz inset‑fed rectangular microstrip patch on FR‑4. It sweeps the
+inset depth and patch length, exporting S‑parameter data and the final
+geometry dimensions.
+
+Run:
+
+```bash
+python patch_antenna_design.py
+```
+
+The script writes `patch_sparams.csv`, a Touchstone file
+`patch_2p45_FR4.s1p`, a `patch_antenna.geo` model, and a
+`patch_design.json` summary in this directory.

examples/patch_2p45_FR4.s1p

@@ -0,0 +1,102 @@
+# Hz S RI R 50
+2200000000.0 0.9979542393576168 -0.02338519787994924
+2205000000.0 0.9978654967024093 -0.023883059205784825
+2210000000.0 0.9977711132866047 -0.0244010676716522
+2215000000.0 0.9976706069469737 -0.02494046262504326
+2220000000.0 0.9975634432613738 -0.025502585978970645
+2225000000.0 0.997449028640563 -0.02608889290368628
+2230000000.0 0.9973267023361688 -0.026700963863160995
+2235000000.0 0.9971957271670202 -0.02734051819407675
+2240000000.0 0.9970552787246956 -0.02800942945821603
+2245000000.0 0.9969044327680266 -0.02870974283844183
+2250000000.0 0.9967421504528077 -0.029443694895187708
+2255000000.0 0.9965672609637516 -0.03021373605603106
+2260000000.0 0.9963784410164606 -0.031022556277318782
+2265000000.0 0.9961741905721054 -0.03187311439614938
+2270000000.0 0.9959528039491654 -0.03276867178591847
+2275000000.0 0.9957123353150118 -0.03371283104224646
+2280000000.0 0.9954505572821196 -0.03470958056213165
+2285000000.0 0.995164911001522 -0.035763346041926346
+2290000000.0 0.9948524457159105 -0.03687905011411674
+2295000000.0 0.9945097451740538 -0.03806218157427177
+2300000000.0 0.9941328375725803 -0.03931887592340578
+2305000000.0 0.9937170847195216 -0.04065600927229102
+2310000000.0 0.993257044821473 -0.042081308025881524
+2315000000.0 0.9927463015641759 -0.04360347718630329
+2320000000.0 0.9921772498174862 -0.04523235057079626
+2325000000.0 0.9915408251125551 -0.04697906670766909
+2330000000.0 0.9908261596713668 -0.04885627458681184
+2335000000.0 0.9900201417256331 -0.05087837367968917
+2340000000.0 0.9891068464294143 -0.05306179247715392
+2345000000.0 0.9880667948020012 -0.05542530879843031
+2350000000.0 0.9868759802935538 -0.0579904125299758
+2355000000.0 0.9855045784642755 -0.06078170586008482
+2360000000.0 0.9839152205242092 -0.06382732494613136
+2365000000.0 0.9820606610860388 -0.06715934566181243
+2370000000.0 0.9798805970965491 -0.07081409613876892
+2375000000.0 0.9772972880255197 -0.0748322245504956
+2380000000.0 0.9742094727223757 -0.07925823270145778
+2385000000.0 0.970483858723085 -0.08413892934286661
+2390000000.0 0.9659431613025888 -0.08951977723054343
+2395000000.0 0.9603493039435805 -0.09543720633458372
+2400000000.0 0.95338006492765 -0.10190326869627322
+2405000000.0 0.9445975609994662 -0.10887583552319426
+2410000000.0 0.9334087086210732 -0.11620173282219375
+2415000000.0 0.9190245677328354 -0.12351024358285534
+2420000000.0 0.900445872481894 -0.1300199725001534
+2425000000.0 0.8765552670838334 -0.13421201584235934
+2430000000.0 0.8465124481174826 -0.13336216970601214
+2435000000.0 0.8108118962338063 -0.12315913645694046
+2440000000.0 0.7732560460229773 -0.09830388863895709
+2445000000.0 0.7427025771682204 -0.05571796196068575
+2450000000.0 0.7306368081026587 0.0
+2455000000.0 0.7426556223246122 0.055614514889053175
+2460000000.0 0.7729639949161924 0.09802956391099933
+2465000000.0 0.8101240688069921 0.12285242221550478
+2470000000.0 0.8454356521099233 0.13320588749194795
+2475000000.0 0.8751893331959966 0.13431938447261413
+2480000000.0 0.8989039142450072 0.13042678326291474
+2485000000.0 0.9173971350511922 0.12420522559347047
+2490000000.0 0.9317581169973955 0.11715330482289135
+2495000000.0 0.9429631575687479 0.1100473740645377
+2500000000.0 0.9517850971569581 0.10326007587958663
+2505000000.0 0.9588064897267582 0.09694900785477208
+2510000000.0 0.9644585897645136 0.091161153261882
+2515000000.0 0.9690595554510583 0.085888915428823
+2520000000.0 0.9728450367700735 0.08109966426224748
+2525000000.0 0.9759909204332257 0.07675106777745742
+2530000000.0 0.978629740845831 0.07279885466904013
+2535000000.0 0.980862395733653 0.06920056555690918
+2540000000.0 0.9827665026316461 0.06591719371415301
+2545000000.0 0.9844023852444771 0.06291373228851539
+2550000000.0 0.9858173925856716 0.06015917261300579
+2555000000.0 0.9870490421148094 0.057626244402520295
+2560000000.0 0.988127328413643 0.05529105157484803
+2565000000.0 0.9890764351685264 0.05313268317406756
+2570000000.0 0.9899160167817335 0.051132838657414775
+2575000000.0 0.9906621667548596 0.04927548516861161
+2580000000.0 0.9913281560083731 0.04754655296659616
+2585000000.0 0.991925000683645 0.045933669311988896
+2590000000.0 0.9924619024380231 0.04442592829951695
+2595000000.0 0.992946592573229 0.04301369295816594
+2600000000.0 0.9933856030320134 0.0416884256421713
+2605000000.0 0.9937844813372078 0.04044254287331231
+2610000000.0 0.9941479622331261 0.03926929113141753
+2615000000.0 0.9944801056408729 0.03816264049793597
+2620000000.0 0.9947844082228983 0.03711719347052388
+2625000000.0 0.9950638941347286 0.03612810665257039
+2630000000.0 0.9953211892587013 0.035191023366860794
+2635000000.0 0.9955585822488846 0.03430201554355143
+2640000000.0 0.9957780749845111 0.0334575334907834
+2645000000.0 0.995981424470787 0.03265436237542165
+2650000000.0 0.9961701777970552 0.031889584426240465
+2655000000.0 0.996345701430812 0.031160546027141148
+2660000000.0 0.9965092058683656 0.030464828998110288
+2665000000.0 0.9966617664614045 0.02980022547056716
+2670000000.0 0.9968043410802822 0.02916471585493755
+2675000000.0 0.9969377851495632 0.028556449474660826
+2680000000.0 0.9970628644918542 0.027973727504856577
+2685000000.0 0.9971802663364736 0.027414987907614333
+2690000000.0 0.9972906087857712 0.0268787921010506
+2695000000.0 0.9973944489805329 0.026363813137328527
+2700000000.0 0.9974922901643237 0.025868825196946686

examples/patch_antenna.geo

@@ -0,0 +1,15 @@
+SetFactory("OpenCASCADE");
+// Units: meters
+h=0.0016; W=0.03723426118288438; L=0.028809290261854397; inset=0.004; feedW=0.00308;
+board_x=0.08; board_y=0.07; air=0.0306;
+board = Rectangle(1, -board_x/2, -board_y/2, 0, board_x, board_y);
+patch = Rectangle(2, -W/2, -L/2, h, W, L);
+feed = Rectangle(3, -feedW/2, -board_y/2, h, feedW, board_y/2 - L/2 + inset);
+slot = Rectangle(4, -feedW/2, -L/2, h, feedW, inset);
+BooleanDifference{ Surface{patch}; Delete; }{ Surface{slot}; Delete; }
+BooleanUnion{ Surface{patch}; Delete; }{ Surface{feed}; Delete; }
+airbox = Rectangle(5, -(board_x/2+air), -(board_y/2+air), -air, board_x+2*air, board_y+2*air);
+Extrude {0,0,h} { Surface{board}; }
+Extrude {0,0,0} { Surface{patch}; }
+Extrude {0,0,0} { Surface{feed}; }
+Extrude {0,0,h+air} { Surface{airbox}; }

examples/patch_antenna_design.py

@@ -0,0 +1,201 @@
+#!/usr/bin/env python3
+"""Analytic rectangular microstrip patch antenna design with simple sweeps.
+
+This script implements closed-form design equations for a rectangular
+microstrip patch antenna on an FR-4 substrate. It produces quick parametric
+sweeps for the inset depth and patch length and exports S-parameter data
+using a simple RLC resonance model.
+
+The implementation is intentionally lightweight and does not call a full EM
+solver. Results are approximate but follow the design targets in
+``patch_antenna_design_prompt.md``.
+"""
+from __future__ import annotations
+
+import json
+from dataclasses import dataclass
+from math import acos, cos, pi, sqrt
+from typing import Iterable, Tuple
+
+import numpy as np
+
+C0 = 299_792_458.0  # speed of light (m/s)
+
+
+@dataclass
+class Substrate:
+    er: float
+    h: float  # thickness (m)
+
+
+@dataclass
+class PatchDesign:
+    freq: float  # design frequency (Hz)
+    substrate: Substrate
+
+    def patch_dimensions(self) -> Tuple[float, float, float, float]:
+        """Return (W, L, eps_eff, delta_L)."""
+        er, h = self.substrate.er, self.substrate.h
+        f = self.freq
+        W = C0 / (2 * f) * sqrt(2 / (er + 1))
+        eps_eff = (er + 1) / 2 + (er - 1) / (2 * sqrt(1 + 12 * h / W))
+        F1 = (eps_eff + 0.3) * (W / h + 0.264)
+        F2 = (eps_eff - 0.258) * (W / h + 0.8)
+        delta_L = 0.412 * h * F1 / F2
+        L = C0 / (2 * f * sqrt(eps_eff)) - 2 * delta_L
+        return W, L, eps_eff, delta_L
+
+    @staticmethod
+    def edge_resistance(W: float, L: float, er: float, eps_eff: float) -> float:
+        return 90 * (eps_eff ** 2 / (er - 1)) * (L / W) ** 2
+
+    @staticmethod
+    def inset_resistance(R_edge: float, L: float, inset: float) -> float:
+        return R_edge / (cos(pi * inset / L) ** 2)
+
+    @staticmethod
+    def resonance_freq(L: float, eps_eff: float, delta_L: float) -> float:
+        return C0 / (2 * (L + 2 * delta_L) * sqrt(eps_eff))
+
+    @staticmethod
+    def input_impedance(f: float, f0: float, R: float, Q: float) -> complex:
+        X = R * 2 * Q * (f / f0 - f0 / f)
+        return complex(R, X)
+
+
+def s11_from_z(z: complex) -> complex:
+    return (z - 50) / (z + 50)
+
+
+def sweep_inset(design: PatchDesign, y0_range: Iterable[float], W: float, L: float,
+                R_edge: float) -> Tuple[np.ndarray, np.ndarray]:
+    s11 = []
+    for y0 in y0_range:
+        Rin = design.inset_resistance(R_edge, L, y0)
+        gamma = s11_from_z(complex(Rin, 0))
+        s11.append(20 * np.log10(abs(gamma)))
+    return np.array(y0_range), np.array(s11)
+
+
+def sweep_length(design: PatchDesign, L_vals: Iterable[float], inset: float,
+                 W: float, eps_eff: float, delta_L: float, Q: float) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+    fres, s11 = [], []
+    for L in L_vals:
+        f0 = design.resonance_freq(L, eps_eff, delta_L)
+        R_edge = design.edge_resistance(W, L, design.substrate.er, eps_eff)
+        Rin = design.inset_resistance(R_edge, L, inset)
+        Zin = design.input_impedance(design.freq, f0, Rin, Q)
+        gamma = s11_from_z(Zin)
+        fres.append(f0)
+        s11.append(20 * np.log10(abs(gamma)))
+    return np.array(L_vals), np.array(fres), np.array(s11)
+
+
+def export_sparameters(filename: str, design: PatchDesign, freqs: np.ndarray,
+                       L: float, inset: float, W: float,
+                       eps_eff: float, delta_L: float, Q: float) -> None:
+    R_edge = design.edge_resistance(W, L, design.substrate.er, eps_eff)
+    Rin = design.inset_resistance(R_edge, L, inset)
+    f0 = design.resonance_freq(L, eps_eff, delta_L)
+
+    with open(filename, "w", encoding="utf-8") as f:
+        f.write("# Hz S RI R 50\n")
+        for fr in freqs:
+            Zin = design.input_impedance(fr, f0, Rin, Q)
+            gamma = s11_from_z(Zin)
+            f.write(f"{fr} {gamma.real} {gamma.imag}\n")
+
+
+def export_csv(filename: str, design: PatchDesign, freqs: np.ndarray,
+               L: float, inset: float, W: float,
+               eps_eff: float, delta_L: float, Q: float) -> None:
+    R_edge = design.edge_resistance(W, L, design.substrate.er, eps_eff)
+    Rin = design.inset_resistance(R_edge, L, inset)
+    f0 = design.resonance_freq(L, eps_eff, delta_L)
+
+    with open(filename, "w", encoding="utf-8") as f:
+        f.write("freq_hz,s11_db,rin,xin\n")
+        for fr in freqs:
+            Zin = design.input_impedance(fr, f0, Rin, Q)
+            gamma = s11_from_z(Zin)
+            f.write(f"{fr},{20*np.log10(abs(gamma))},{Zin.real},{Zin.imag}\n")
+
+
+def export_geo(filename: str, W: float, L: float, inset: float, feed_w: float,
+               board_x: float = 0.08, board_y: float = 0.07,
+               h: float = 1.6e-3, air: float = 0.0306) -> None:
+    """Write a minimal parametric Gmsh geometry file."""
+    with open(filename, "w", encoding="utf-8") as g:
+        g.write('SetFactory("OpenCASCADE");\n')
+        g.write('// Units: meters\n')
+        g.write(f'h={h}; W={W}; L={L}; inset={inset}; feedW={feed_w};\n')
+        g.write(f'board_x={board_x}; board_y={board_y}; air={air};\n')
+        g.write('board = Rectangle(1, -board_x/2, -board_y/2, 0, board_x, board_y);\n')
+        g.write('patch = Rectangle(2, -W/2, -L/2, h, W, L);\n')
+        g.write('feed = Rectangle(3, -feedW/2, -board_y/2, h, feedW, board_y/2 - L/2 + inset);\n')
+        g.write('slot = Rectangle(4, -feedW/2, -L/2, h, feedW, inset);\n')
+        g.write('BooleanDifference{ Surface{patch}; Delete; }{ Surface{slot}; Delete; }\n')
+        g.write('BooleanUnion{ Surface{patch}; Delete; }{ Surface{feed}; Delete; }\n')
+        g.write('airbox = Rectangle(5, -(board_x/2+air), -(board_y/2+air), -air, board_x+2*air, board_y+2*air);\n')
+        g.write('Extrude {0,0,h} { Surface{board}; }\n')
+        g.write('Extrude {0,0,0} { Surface{patch}; }\n')
+        g.write('Extrude {0,0,0} { Surface{feed}; }\n')
+        g.write('Extrude {0,0,h+air} { Surface{airbox}; }\n')
+
+
+def main() -> None:
+    sub = Substrate(er=4.4, h=1.6e-3)
+    design = PatchDesign(freq=2.45e9, substrate=sub)
+    W, L, eps_eff, delta_L = design.patch_dimensions()
+    R_edge = design.edge_resistance(W, L, sub.er, eps_eff)
+
+    # Inset depth sweep 4..11 mm
+    y0_vals_m = np.linspace(4e-3, 11e-3, 8)
+    y0_vals, s11_y0 = sweep_inset(design, y0_vals_m, W, L, R_edge)
+    best_idx = np.argmin(s11_y0)
+    best_y0 = y0_vals_m[best_idx]
+
+    # Length sweep around nominal L
+    L_vals = np.linspace(L - 0.6e-3, L + 0.6e-3, 7)
+    Q = design.freq / 80e6  # target ~80 MHz bandwidth
+    L_sweep, fres, s11_L = sweep_length(design, L_vals, best_y0, W, eps_eff, delta_L, Q)
+    best_L = L_vals[np.argmin(s11_L)]
+
+    # Frequency sweep for final design
+    freqs = np.linspace(2.2e9, 2.7e9, 101)
+    export_sparameters("examples/patch_2p45_FR4.s1p", design, freqs, best_L, best_y0, W, eps_eff, delta_L, Q)
+    export_csv("examples/patch_sparams.csv", design, freqs, best_L, best_y0, W, eps_eff, delta_L, Q)
+    export_geo("examples/patch_antenna.geo", W, best_L, best_y0, 3.08e-3)
+
+    summary = {
+        "freq_hz": design.freq,
+        "substrate": {"er": sub.er, "h_m": sub.h},
+        "patch_width_m": W,
+        "patch_length_m": best_L,
+        "inset_depth_m": best_y0,
+        "feed_width_m": 3.08e-3,
+        "quality_factor": Q,
+    }
+    with open("examples/patch_design.json", "w", encoding="utf-8") as f:
+        json.dump(summary, f, indent=2)
+        f.write("\n")
+
+    # Console report
+    print("Inset depth sweep (mm vs S11 dB):")
+    for mm_val, s in zip(y0_vals * 1e3, s11_y0):
+        print(f"  {mm_val:4.1f} mm : {s:6.2f} dB")
+    print(f"Best inset ≈ {best_y0*1e3:.2f} mm")
+
+    print("Length sweep (mm, f_res GHz, S11 dB):")
+    for Lm, fr, s in zip(L_sweep * 1e3, fres, s11_L):
+        print(f"  {Lm:5.2f} mm : {fr/1e9:6.3f} GHz : {s:6.2f} dB")
+    print(f"Best length ≈ {best_L*1e3:.2f} mm")
+
+    print(
+        "Outputs written: examples/patch_sparams.csv, examples/patch_2p45_FR4.s1p,"
+        " examples/patch_antenna.geo, examples/patch_design.json"
+    )
+
+
+if __name__ == "__main__":
+    main()

examples/patch_design.json

@@ -0,0 +1,12 @@
+{
+  "freq_hz": 2450000000.0,
+  "substrate": {
+    "er": 4.4,
+    "h_m": 0.0016
+  },
+  "patch_width_m": 0.03723426118288438,
+  "patch_length_m": 0.028809290261854397,
+  "inset_depth_m": 0.004,
+  "feed_width_m": 0.00308,
+  "quality_factor": 30.625
+}