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: altair 6.1.0 | Python 3.13.13
Quality: 92/100 | Updated: 2026-05-20
"""
import importlib
import os
import sys
# Drop script directory from sys.path so the `altair` package resolves, not this file
sys.path[:] = [p for p in sys.path if os.path.abspath(p or ".") != os.path.dirname(os.path.abspath(__file__))]
alt = importlib.import_module("altair")
np = importlib.import_module("numpy")
pd = importlib.import_module("pandas")
# Theme tokens
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"
BRAND = "#009E73" # Okabe-Ito position 1 — impedance locus
VSWR_COLOR = "#C475FD" # Okabe-Ito position 2 — VSWR circles
# Reference impedance
Z0 = 50 # ohms
# Generate Smith chart grid — constant resistance circles
theta = np.linspace(0, 2 * np.pi, 200)
resistance_circles = []
resistance_values = [0, 0.2, 0.5, 1.0, 2.0, 5.0]
for r in resistance_values:
center_x = r / (r + 1)
radius = 1 / (r + 1)
x = center_x + radius * np.cos(theta)
y = radius * np.sin(theta)
mask = x**2 + y**2 <= 1.0
for i in range(len(x)):
if mask[i]:
resistance_circles.append({"x": x[i], "y": y[i], "group": f"r_{r}", "idx": i})
resistance_df = pd.DataFrame(resistance_circles)
# Generate constant reactance arcs
reactance_arcs = []
reactance_values = [0.2, 0.5, 1.0, 2.0, 5.0]
arc_theta = np.linspace(-np.pi, np.pi, 200)
for x_val in reactance_values:
center_y = 1 / x_val
radius = 1 / x_val
x = 1 + radius * np.cos(arc_theta)
y = center_y + radius * np.sin(arc_theta)
mask = (x**2 + y**2 <= 1.0) & (x >= -0.01)
y_neg = -center_y - radius * np.sin(arc_theta)
for i in range(len(x)):
if mask[i]:
reactance_arcs.append({"x": x[i], "y": y[i], "group": f"x_pos_{x_val}", "idx": i})
reactance_arcs.append({"x": x[i], "y": y_neg[i], "group": f"x_neg_{x_val}", "idx": i})
# Zero reactance line (horizontal axis)
x_line = np.linspace(-1, 1, 50)
for i, xi in enumerate(x_line):
reactance_arcs.append({"x": xi, "y": 0, "group": "x_zero", "idx": i})
reactance_df = pd.DataFrame(reactance_arcs)
# VSWR circles — constant reflection coefficient magnitude
vswr_theta = np.linspace(0, 2 * np.pi, 200)
vswr_circles = []
vswr_entries = [(1.5, (1.5 - 1) / (1.5 + 1)), (2.0, 1 / 3), (3.0, 0.5)]
for vswr_val, gamma_mag in vswr_entries:
x = gamma_mag * np.cos(vswr_theta)
y = gamma_mag * np.sin(vswr_theta)
for i in range(len(x)):
vswr_circles.append({"x": x[i], "y": y[i], "group": f"vswr_{vswr_val}", "idx": i})
vswr_df = pd.DataFrame(vswr_circles)
# VSWR labels at 45° (upper-right of each circle, away from impedance curve)
vswr_labels_data = [
{"x": v * np.cos(np.pi / 4), "y": v * np.sin(np.pi / 4), "label": f"VSWR {w}"} for w, v in vswr_entries
]
vswr_labels_df = pd.DataFrame(vswr_labels_data)
# Unit circle boundary
unit_theta = np.linspace(0, 2 * np.pi, 200)
unit_circle_df = pd.DataFrame({"x": np.cos(unit_theta), "y": np.sin(unit_theta), "idx": range(len(unit_theta))})
# Antenna impedance sweep 1–6 GHz
np.random.seed(42)
n_points = 50
frequency = np.linspace(1e9, 6e9, n_points)
t = np.linspace(0, 2.5 * np.pi, n_points)
z_real = 50 * (1 - 0.7 * np.exp(-t / 3))
z_imag = 40 * np.sin(t) * np.exp(-t / 4)
z_norm = (z_real + 1j * z_imag) / Z0
gamma = (z_norm - 1) / (z_norm + 1)
impedance_df = pd.DataFrame(
{
"x": gamma.real,
"y": gamma.imag,
"frequency_ghz": frequency / 1e9,
"z_real": z_real,
"z_imag": z_imag,
"idx": range(n_points),
}
)
# Frequency labels — per-label dx/dy offsets; 4.7 GHz skipped (converges with endpoint)
label_configs = [(0, 18, -18), (12, 18, -18), (24, 18, -18), (49, 18, -20)]
label_layers = []
for row_idx, dx, dy in label_configs:
row = impedance_df.iloc[[row_idx]].copy()
row["label"] = f"{row['frequency_ghz'].values[0]:.1f} GHz"
label_layers.append(
alt.Chart(row)
.mark_text(fontSize=14, fontWeight="bold", color=INK, dx=dx, dy=dy)
.encode(
x=alt.X("x:Q", scale=alt.Scale(domain=[-1.2, 1.2])),
y=alt.Y("y:Q", scale=alt.Scale(domain=[-1.2, 1.2])),
text="label:N",
)
)
scale_x = alt.Scale(domain=[-1.2, 1.2])
scale_y = alt.Scale(domain=[-1.2, 1.2])
# Unit circle boundary
boundary = (
alt.Chart(unit_circle_df)
.mark_line(color=INK, strokeWidth=3, opacity=0.8)
.encode(x=alt.X("x:Q", scale=scale_x), y=alt.Y("y:Q", scale=scale_y), order="idx:O")
)
# Resistance circles
res_circles = (
alt.Chart(resistance_df)
.mark_line(strokeWidth=1.0, opacity=0.3)
.encode(
x=alt.X("x:Q", scale=scale_x),
y=alt.Y("y:Q", scale=scale_y),
detail="group:N",
order="idx:O",
color=alt.value(INK_SOFT),
)
)
# Reactance arcs
react_arcs = (
alt.Chart(reactance_df)
.mark_line(strokeWidth=1.0, opacity=0.3)
.encode(
x=alt.X("x:Q", scale=scale_x),
y=alt.Y("y:Q", scale=scale_y),
detail="group:N",
order="idx:O",
color=alt.value(INK_SOFT),
)
)
# VSWR circles (dashed, subtle)
vswr_layer = (
alt.Chart(vswr_df)
.mark_line(strokeWidth=1.2, opacity=0.4, strokeDash=[5, 4])
.encode(
x=alt.X("x:Q", scale=scale_x),
y=alt.Y("y:Q", scale=scale_y),
detail="group:N",
order="idx:O",
color=alt.value(VSWR_COLOR),
)
)
# VSWR labels
vswr_labels = (
alt.Chart(vswr_labels_df)
.mark_text(fontSize=11, color=VSWR_COLOR, fontStyle="italic", dx=6, dy=-8)
.encode(x=alt.X("x:Q", scale=scale_x), y=alt.Y("y:Q", scale=scale_y), text="label:N")
)
# Impedance locus curve
impedance_line = (
alt.Chart(impedance_df)
.mark_line(strokeWidth=4, color=BRAND)
.encode(x=alt.X("x:Q", scale=scale_x), y=alt.Y("y:Q", scale=scale_y), order="idx:O")
)
# Impedance data points with interactive tooltips
impedance_points = (
alt.Chart(impedance_df)
.mark_circle(size=80, color=BRAND, stroke=PAGE_BG, strokeWidth=1)
.encode(
x=alt.X("x:Q", scale=scale_x),
y=alt.Y("y:Q", scale=scale_y),
tooltip=[
alt.Tooltip("frequency_ghz:Q", title="Frequency (GHz)", format=".2f"),
alt.Tooltip("z_real:Q", title="R (Ω)", format=".1f"),
alt.Tooltip("z_imag:Q", title="X (Ω)", format=".1f"),
],
)
)
# Center point marker (matched condition Z = Z₀)
center_df = pd.DataFrame({"x": [0], "y": [0]})
center_point = (
alt.Chart(center_df)
.mark_point(size=200, shape="cross", color=INK, strokeWidth=3)
.encode(x=alt.X("x:Q", scale=scale_x), y=alt.Y("y:Q", scale=scale_y))
)
# Resistance value labels along real axis
r_labels_data = [
{"x": 0.0, "y": 0.08, "label": "0"},
{"x": 0.17, "y": 0.08, "label": "0.2"},
{"x": 0.33, "y": 0.08, "label": "0.5"},
{"x": 0.5, "y": 0.08, "label": "1"},
{"x": 0.67, "y": 0.08, "label": "2"},
{"x": 0.83, "y": 0.08, "label": "5"},
]
r_labels_df = pd.DataFrame(r_labels_data)
r_labels = (
alt.Chart(r_labels_df)
.mark_text(fontSize=12, fontWeight="bold")
.encode(x=alt.X("x:Q", scale=scale_x), y=alt.Y("y:Q", scale=scale_y), text="label:N", color=alt.value(INK_SOFT))
)
# Compose all layers
chart = (
alt.layer(
res_circles,
react_arcs,
vswr_layer,
vswr_labels,
boundary,
center_point,
impedance_line,
impedance_points,
*label_layers,
r_labels,
)
.properties(
width=600,
height=600,
background=PAGE_BG,
title=alt.Title(
"smith-chart-basic · python · altair · anyplot.ai",
fontSize=16,
anchor="middle",
color=INK,
subtitle="Antenna Impedance Sweep (1–6 GHz, Z₀ = 50 Ω)",
subtitleFontSize=12,
subtitleColor=INK_SOFT,
),
)
.configure_view(fill=PAGE_BG, stroke=INK_SOFT, strokeWidth=0)
.configure_axis(grid=False, domain=False, labels=False, ticks=False, title=None)
.interactive()
)
chart.save(f"plot-{THEME}.png", scale_factor=4.0)
chart.save(f"plot-{THEME}.html")
Part of Smith Chart for RF/Impedance on anyplot.ai.