A Smith chart is a specialized circular diagram used in RF engineering to display complex impedance and reflection coefficients on a normalized polar grid. The chart features constant resistance circles (centered along the horizontal axis) and constant reactance arcs (curving from the right edge), enabling engineers to visualize impedance matching, transmission line behavior, and antenna characteristics. It reveals relationships between impedance, admittance, and reflection coefficient that would be difficult to interpret in Cartesian coordinates.
""" anyplot.ai
smith-chart-basic: Smith Chart for RF/Impedance
Library: matplotlib 3.10.9 | Python 3.13.13
Quality: 92/100 | Updated: 2026-05-20
"""
import os
import sys
# Remove script directory from path to avoid name collision (this script is named matplotlib.py)
sys.path = [p for p in sys.path if p != "" and "implementations" not in p]
import matplotlib.patches as mpatches
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.collections import LineCollection
from matplotlib.colors import Normalize
# Theme
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
OI_2 = "#C475FD" # Okabe-Ito position 2 — VSWR circles
OI_3 = "#4467A3" # Okabe-Ito position 3 — boundary / matched condition
# Data — antenna impedance sweep 1–6 GHz
Z0 = 50
np.random.seed(42)
frequency = np.linspace(1e9, 6e9, 50)
z_real = 50 + 30 * np.sin(2 * np.pi * (frequency - 1e9) / 2e9) + 10 * np.cos(4 * np.pi * (frequency - 1e9) / 5e9)
z_imag = 20 * np.cos(2 * np.pi * (frequency - 1e9) / 1.5e9) + 15 * np.sin(3 * np.pi * (frequency - 1e9) / 5e9)
z_norm = (z_real + 1j * z_imag) / Z0
gamma = (z_norm - 1) / (z_norm + 1)
freq_ghz = frequency / 1e9
# Plot — square canvas for Smith chart (2400×2400 px)
fig, ax = plt.subplots(figsize=(6, 6), dpi=400, facecolor=PAGE_BG)
ax.set_facecolor(PAGE_BG)
ax.set_aspect("equal")
# Smith chart grid — constant resistance circles
theta = np.linspace(0, 2 * np.pi, 500)
for r in [0, 0.2, 0.5, 1, 2, 5]:
center = r / (r + 1)
radius = 1 / (r + 1)
x_c = center + radius * np.cos(theta)
y_c = radius * np.sin(theta)
mask = x_c**2 + y_c**2 <= 1.001
ax.plot(np.where(mask, x_c, np.nan), np.where(mask, y_c, np.nan), color=INK_MUTED, linewidth=0.7, alpha=0.35)
if r > 0:
label_x = center + radius
if label_x <= 1.0:
ax.text(label_x + 0.02, 0.02, f"{r}", fontsize=6, color=INK_MUTED, ha="left", va="bottom")
# Constant reactance arcs
arc_theta = np.linspace(0, np.pi, 500)
for x in [0.2, 0.5, 1, 2, 5]:
center_y = 1 / x
radius = 1 / x
x_arc = 1 + radius * np.cos(arc_theta + np.pi)
# Inductive (upper half)
y_arc_pos = center_y + radius * np.sin(arc_theta + np.pi)
mask = x_arc**2 + y_arc_pos**2 <= 1.001
ax.plot(
np.where(mask, x_arc, np.nan), np.where(mask, y_arc_pos, np.nan), color=INK_MUTED, linewidth=0.7, alpha=0.35
)
# Capacitive (lower half)
y_arc_neg = -center_y + radius * np.sin(arc_theta)
mask = x_arc**2 + y_arc_neg**2 <= 1.001
ax.plot(
np.where(mask, x_arc, np.nan), np.where(mask, y_arc_neg, np.nan), color=INK_MUTED, linewidth=0.7, alpha=0.35
)
if x <= 1:
angle = 2 * np.arctan(1 / x)
lx, ly = np.cos(angle), np.sin(angle)
ax.text(lx, ly + 0.06, f"+j{x}", fontsize=6, color=INK_MUTED, ha="center", va="bottom")
ax.text(lx, -ly - 0.06, f"-j{x}", fontsize=6, color=INK_MUTED, ha="center", va="top")
# Real axis
ax.axhline(y=0, color=INK_MUTED, linewidth=0.7, alpha=0.35)
# Unit circle boundary
ax.plot(np.cos(theta), np.sin(theta), color=INK_SOFT, linewidth=1.5)
# VSWR circles via matplotlib.patches.Circle — distinctive matplotlib feature
for vswr in [1.5, 2, 3]:
gamma_mag = (vswr - 1) / (vswr + 1)
vswr_circle = mpatches.Circle(
(0, 0), gamma_mag, fill=False, linestyle="--", edgecolor=OI_2, linewidth=1.0, alpha=0.55, zorder=3
)
ax.add_patch(vswr_circle)
ax.text(0, gamma_mag + 0.04, f"VSWR={vswr}", fontsize=6, color=OI_2, ha="center", alpha=0.8)
# Matched condition marker
ax.plot(0, 0, "o", color=OI_3, markersize=7, zorder=6, label="Matched (Z=Z₀)")
# Impedance locus via LineCollection colored by frequency — distinctive matplotlib feature
# cividis colormap chosen for sequential continuous data (perceptually uniform + colorblind-safe)
points = np.array([gamma.real, gamma.imag]).T.reshape(-1, 1, 2)
segments = np.concatenate([points[:-1], points[1:]], axis=1)
norm = Normalize(vmin=freq_ghz[0], vmax=freq_ghz[-1])
lc = LineCollection(segments, cmap="cividis", norm=norm, linewidth=2.5, zorder=5, label="Impedance Locus")
lc.set_array(freq_ghz[:-1])
ax.add_collection(lc)
# Key frequency markers, color-matched to the locus colormap
key_indices = [0, 12, 24, 36, 49]
ax.scatter(
gamma.real[key_indices],
gamma.imag[key_indices],
c=freq_ghz[key_indices],
cmap="cividis",
norm=norm,
s=40,
edgecolors=PAGE_BG,
linewidths=0.8,
zorder=7,
)
# Frequency labels at key points
for idx in key_indices:
x_pos, y_pos = gamma.real[idx], gamma.imag[idx]
offset_x = 0.10 if x_pos < 0.5 else -0.10
offset_y = 0.08 if y_pos >= 0 else -0.08
ax.annotate(
f"{freq_ghz[idx]:.1f} GHz",
(x_pos, y_pos),
xytext=(x_pos + offset_x, y_pos + offset_y),
fontsize=7,
color=INK,
arrowprops={"arrowstyle": "->", "color": INK_SOFT, "lw": 0.8},
zorder=10,
)
# Colorbar — frequency scale for the cividis locus
cbar = plt.colorbar(lc, ax=ax, shrink=0.72, pad=0.02, fraction=0.03)
cbar.set_label("Frequency (GHz)", fontsize=8, color=INK)
cbar.ax.tick_params(labelsize=7, labelcolor=INK_SOFT)
cbar.outline.set_edgecolor(INK_SOFT)
# Style
ax.set_xlim(-1.3, 1.3)
ax.set_ylim(-1.3, 1.3)
ax.set_xlabel("Real(Γ)", fontsize=10, color=INK)
ax.set_ylabel("Imag(Γ)", fontsize=10, color=INK)
ax.set_title("smith-chart-basic · python · matplotlib · anyplot.ai", fontsize=12, fontweight="medium", color=INK)
ax.tick_params(axis="both", labelsize=8, colors=INK_SOFT)
ax.set_xticks([])
ax.set_yticks([])
for spine in ax.spines.values():
spine.set_color(INK_SOFT)
# Cardinal direction labels
ax.text(1.18, 0, "Open\n(Γ=1)", fontsize=7, ha="center", va="center", color=INK_SOFT)
ax.text(-1.18, 0, "Short\n(Γ=-1)", fontsize=7, ha="center", va="center", color=INK_SOFT)
ax.text(0, 1.18, "+jX\n(Inductive)", fontsize=7, ha="center", va="center", color=INK_MUTED)
ax.text(0, -1.18, "-jX\n(Capacitive)", fontsize=7, ha="center", va="center", color=INK_MUTED)
# Legend
leg = ax.legend(fontsize=7, loc="upper left")
if leg:
leg.get_frame().set_facecolor(ELEVATED_BG)
leg.get_frame().set_edgecolor(INK_SOFT)
plt.setp(leg.get_texts(), color=INK_SOFT)
plt.tight_layout()
plt.savefig(f"plot-{THEME}.png", dpi=400, bbox_inches="tight", facecolor=PAGE_BG)
Part of Smith Chart for RF/Impedance on anyplot.ai.