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: letsplot 4.9.0 | Python 3.13.13
Quality: 90/100 | Updated: 2026-05-20
"""
import os
import numpy as np
import pandas as pd
from lets_plot import (
LetsPlot,
aes,
coord_fixed,
element_rect,
element_text,
geom_path,
geom_point,
geom_text,
ggplot,
ggsize,
labs,
layer_tooltips,
theme,
theme_void,
)
from lets_plot.export import ggsave
LetsPlot.setup_html()
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
BRAND = "#009E73"
COLOR_START = "#4467A3" # Okabe-Ito position 3
COLOR_END = "#C475FD" # Okabe-Ito position 2
Z0 = 50 # Reference impedance (ohms)
# Simulated antenna impedance sweep 1–6 GHz
np.random.seed(42)
n_points = 60
freq = np.linspace(1e9, 6e9, n_points)
t = np.linspace(0, 2.5 * np.pi, n_points)
r_base = 20 + 80 * (1 - np.exp(-t / 2.5))
x_base = 50 * np.sin(t) * np.exp(-t / 6)
z_real = r_base + 3 * np.random.randn(n_points)
z_imag = x_base + 2 * np.random.randn(n_points)
z_norm = (z_real + 1j * z_imag) / Z0
gamma = (z_norm - 1) / (z_norm + 1)
gamma_real = np.real(gamma)
gamma_imag = np.imag(gamma)
df_locus = pd.DataFrame(
{
"gamma_real": gamma_real,
"gamma_imag": gamma_imag,
"freq_ghz": freq / 1e9,
"z_real": z_real,
"z_imag": z_imag,
"vswr": (1 + np.abs(gamma)) / (1 - np.abs(gamma)),
}
)
# Smith chart grid — constant resistance circles
# Circle centered at (r/(r+1), 0) with radius 1/(r+1)
grid_data = []
r_values = [0, 0.2, 0.5, 1, 2, 5]
for r in r_values:
cx = r / (r + 1)
rad = 1 / (r + 1)
theta = np.linspace(0, 2 * np.pi, 120)
x = cx + rad * np.cos(theta)
y = rad * np.sin(theta)
mask = (x**2 + y**2) <= 1.001
for i in np.where(mask)[0]:
grid_data.append({"x": x[i], "y": y[i], "type": "resistance", "group": f"r_{r}"})
# Constant reactance arcs
# Arc centered at (1, 1/x_val) with radius |1/x_val|
xv_values = [0.2, 0.5, 1, 2, 5]
for xv in xv_values:
for sign in [1, -1]:
x_val = sign * xv
cy = 1 / x_val
rad = abs(1 / x_val)
theta = np.linspace(0, 2 * np.pi, 120)
x = 1 + rad * np.cos(theta)
y = cy + rad * np.sin(theta)
mask = (x**2 + y**2) <= 1.001
for i in np.where(mask)[0]:
grid_data.append({"x": x[i], "y": y[i], "type": "reactance", "group": f"x_{x_val}"})
df_grid = pd.DataFrame(grid_data)
theta_circle = np.linspace(0, 2 * np.pi, 200)
df_boundary = pd.DataFrame({"x": np.cos(theta_circle), "y": np.sin(theta_circle)})
df_axis = pd.DataFrame({"x": [-1, 1], "y": [0, 0]})
# Resistance labels at leftmost point of each r-circle on the real axis
df_r_labels = pd.DataFrame([{"x": (r - 1) / (r + 1), "y": 0, "label": str(r)} for r in r_values])
# Reactance labels at unit-circle boundary intersection
# For xv: boundary at x2=(xv²-1)/(xv²+1), y2=xv*(1-x2)
xv_label_rows = []
for xv in xv_values:
x2 = (xv**2 - 1) / (xv**2 + 1)
y2 = xv * (1 - x2)
scale = 1.12
xv_label_rows.append({"x": x2 * scale, "y": y2 * scale, "label": f"+j{xv}"})
xv_label_rows.append({"x": x2 * scale, "y": -y2 * scale, "label": f"-j{xv}"})
df_x_labels = pd.DataFrame(xv_label_rows)
label_indices = [0, n_points // 2, n_points - 1]
# Per-label nudge to avoid crowding: 1.0 GHz left+up, 3.5 GHz upper-left, 6.0 GHz lower-right
label_nudges = [(-0.18, 0.13), (-0.12, 0.22), (0.26, -0.22)]
df_freq_labels = pd.DataFrame(
{
"x": [gamma_real[i] + nx for i, (nx, ny) in zip(label_indices, label_nudges, strict=True)],
"y": [gamma_imag[i] + ny for i, (nx, ny) in zip(label_indices, label_nudges, strict=True)],
"label": [f"{freq[i] / 1e9:.1f} GHz" for i in label_indices],
}
)
df_start = df_locus.iloc[[0]]
df_end = df_locus.iloc[[-1]]
df_center = pd.DataFrame({"x": [0], "y": [0]})
df_legend = pd.DataFrame(
{
"x": [1.15, 1.15, 1.15],
"y": [0.25, 0.05, -0.15],
"grp": ["locus", "start", "end"],
"label": ["Impedance locus", "Start (1.0 GHz)", "End (6.0 GHz)"],
}
)
plot = (
ggplot()
# Outer boundary
+ geom_path(aes(x="x", y="y"), data=df_boundary, color=INK, size=2.0)
# Real axis
+ geom_path(aes(x="x", y="y"), data=df_axis, color=INK_SOFT, size=0.8)
# Resistance circles
+ geom_path(
aes(x="x", y="y", group="group"),
data=df_grid[df_grid["type"] == "resistance"],
color=INK_SOFT,
size=0.5,
alpha=0.5,
)
# Reactance arcs
+ geom_path(
aes(x="x", y="y", group="group"),
data=df_grid[df_grid["type"] == "reactance"],
color=INK_SOFT,
size=0.5,
alpha=0.5,
)
# Resistance labels along real axis
+ geom_text(aes(x="x", y="y", label="label"), data=df_r_labels, size=8, nudge_y=-0.08, color=INK_SOFT)
# Reactance labels at chart boundary
+ geom_text(aes(x="x", y="y", label="label"), data=df_x_labels, size=9, color=INK_SOFT)
# Impedance locus path
+ geom_path(aes(x="gamma_real", y="gamma_imag"), data=df_locus, color=BRAND, size=3.2)
# Interactive hover points
+ geom_point(
aes(x="gamma_real", y="gamma_imag"),
data=df_locus,
color=BRAND,
size=3,
alpha=0.8,
tooltips=layer_tooltips()
.line("Freq: @freq_ghz GHz")
.line("Z: @z_real + j@z_imag Ω")
.line("VSWR: @vswr")
.format("z_real", ".1f")
.format("z_imag", ".1f")
.format("vswr", ".2f"),
)
# Start marker
+ geom_point(aes(x="gamma_real", y="gamma_imag"), data=df_start, color=COLOR_START, size=10)
# End marker
+ geom_point(aes(x="gamma_real", y="gamma_imag"), data=df_end, color=COLOR_END, size=10)
# Matched condition marker at chart center
+ geom_point(aes(x="x", y="y"), data=df_center, color=INK_SOFT, size=6, shape=3)
# Frequency labels along trajectory (pre-nudged per-label to avoid crowding)
+ geom_text(aes(x="x", y="y", label="label"), data=df_freq_labels, size=11, color=INK)
# Manual legend outside chart area
+ geom_point(aes(x="x", y="y"), data=df_legend[df_legend["grp"] == "locus"], color=BRAND, size=5)
+ geom_point(aes(x="x", y="y"), data=df_legend[df_legend["grp"] == "start"], color=COLOR_START, size=7)
+ geom_point(aes(x="x", y="y"), data=df_legend[df_legend["grp"] == "end"], color=COLOR_END, size=7)
+ geom_text(aes(x="x", y="y", label="label"), data=df_legend, size=10, hjust=0, nudge_x=0.06, color=INK)
+ labs(title="smith-chart-basic · python · letsplot · anyplot.ai")
+ theme_void()
+ theme(
plot_title=element_text(size=16, hjust=0.5, color=INK),
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG),
)
+ coord_fixed(ratio=1, xlim=(-1.35, 2.1), ylim=(-1.35, 1.35))
+ ggsize(720, 600)
)
ggsave(plot, f"plot-{THEME}.png", path=".", scale=4)
ggsave(plot, f"plot-{THEME}.html", path=".")
Part of Smith Chart for RF/Impedance on anyplot.ai.