A Bode plot displays a system's frequency response as two vertically aligned panels: magnitude (in decibels) on top and phase (in degrees) on the bottom, both plotted against frequency on a shared logarithmic scale. This visualization is fundamental in control systems engineering and signal processing for analyzing how a system responds to sinusoidal inputs across a range of frequencies, revealing stability characteristics, bandwidth, and resonance behavior.
""" anyplot.ai
bode-basic: Bode Plot for Frequency Response
Library: pygal 3.1.0 | Python 3.13.14
Quality: 88/100 | Updated: 2026-06-17
"""
import io
import os
import cairosvg
import numpy as np
import pygal
from PIL import Image, ImageDraw, ImageFont
from pygal.style import Style
# Theme tokens — Imprint palette (theme-independent) + adaptive chrome
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"
BRAND = "#009E73" # Imprint position 1 — ALWAYS first series
IMPRINT_RED = "#AE3030" # Imprint position 5 — stability-critical thresholds
IMPRINT_BLUE = "#4467A3" # Imprint position 3 — margin indicators
# Data — Third-order system: G(s) = K·ωn² / ((s+p)·(s²+2ζωn·s+ωn²))
# Natural frequency 5 Hz, damping 0.2 (clear resonance), extra pole at 50 Hz
frequency_hz = np.logspace(-1, 3, 500)
omega = 2 * np.pi * frequency_hz
wn = 2 * np.pi * 5.0
zeta = 0.2
p = 2 * np.pi * 50.0
s = 1j * omega
G = (wn**2 * p) / ((s + p) * (s**2 + 2 * zeta * wn * s + wn**2))
magnitude_db = 20 * np.log10(np.abs(G))
phase_deg = np.degrees(np.unwrap(np.angle(G)))
log_freq = np.log10(frequency_hz)
# Gain crossover: where magnitude crosses 0 dB (after resonance peak)
peak_idx = np.argmax(magnitude_db)
peak_db = magnitude_db[peak_idx]
peak_freq = frequency_hz[peak_idx]
zero_crossings = np.where(np.diff(np.sign(magnitude_db[peak_idx:])))[0]
if len(zero_crossings) > 0:
gc_idx = peak_idx + zero_crossings[0]
gc_freq = frequency_hz[gc_idx]
gc_phase = phase_deg[gc_idx]
phase_margin = 180 + gc_phase
else:
gc_freq = None
phase_margin = None
# Phase crossover: where phase crosses −180°
pc_indices = np.where(np.diff(np.sign(phase_deg + 180)))[0]
gain_margin = -magnitude_db[pc_indices[0]] if len(pc_indices) > 0 else None
pc_freq = frequency_hz[pc_indices[0]] if len(pc_indices) > 0 else None
# X-axis tick positions — major decades + minor half-decades
x_ticks_major = [0.1, 1, 10, 100, 1000]
x_ticks_minor = [0.5, 5, 50, 500]
x_tick_major_log = [np.log10(v) for v in x_ticks_major]
x_tick_all_log = sorted([np.log10(v) for v in x_ticks_major + x_ticks_minor])
# Subsample for performance
step = 2
mag_pts = [(float(log_freq[i]), float(magnitude_db[i])) for i in range(0, len(log_freq), step)]
phase_pts = [(float(log_freq[i]), float(phase_deg[i])) for i in range(0, len(log_freq), step)]
x_lo, x_hi = float(log_freq[0]), float(log_freq[-1])
ref_0db = [(x_lo, 0.0), (x_hi, 0.0)]
ref_neg180 = [(x_lo, -180.0), (x_hi, -180.0)]
# Margin visual lines — vertical segments between signal and reference
phase_margin_line = None
if gc_freq is not None and phase_margin is not None:
gc_log = np.log10(gc_freq)
phase_margin_line = [(float(gc_log), float(gc_phase)), (float(gc_log), -180.0)]
gain_margin_line = None
if pc_freq is not None and gain_margin is not None:
pc_log = np.log10(pc_freq)
pc_mag = magnitude_db[pc_indices[0]]
gain_margin_line = [(float(pc_log), float(pc_mag)), (float(pc_log), 0.0)]
# Shared pygal style — Imprint palette + canonical sizing for 3200×1800 canvas
_style = Style(
background=PAGE_BG,
plot_background=PAGE_BG,
foreground=INK,
foreground_strong=INK,
foreground_subtle=INK_MUTED,
colors=(BRAND, IMPRINT_RED, IMPRINT_BLUE, INK_MUTED),
title_font_size=66,
label_font_size=56,
major_label_font_size=44,
legend_font_size=44,
value_font_size=36,
stroke_width=2.5,
font_family="'Helvetica Neue', 'Helvetica', 'Arial', sans-serif",
title_font_family="'Helvetica Neue', 'Helvetica', 'Arial', sans-serif",
label_font_family="'Helvetica Neue', 'Helvetica', 'Arial', sans-serif",
value_font_family="'Helvetica Neue', 'Helvetica', 'Arial', sans-serif",
legend_font_family="'Helvetica Neue', 'Helvetica', 'Arial', sans-serif",
opacity=1.0,
opacity_hover=0.85,
transition="200ms ease-in",
)
# Magnitude chart — top panel (3200×900)
mag_chart = pygal.XY(
width=3200,
height=900,
style=_style,
show_legend=True,
legend_at_bottom=True,
legend_at_bottom_columns=3,
show_y_guides=True,
show_x_guides=False,
margin=20,
margin_left=140,
margin_right=70,
margin_bottom=140,
margin_top=40,
dots_size=0,
stroke=True,
truncate_label=-1,
print_values=False,
x_value_formatter=lambda x: f"{10**x:.4g}",
tooltip_fancy_mode=True,
tooltip_border_radius=8,
title="bode-basic · python · pygal · anyplot.ai",
x_title="",
y_title="Magnitude (dB)",
range=(-100.0, 20.0),
interpolate="cubic",
show_minor_x_labels=True,
)
mag_chart.x_labels = x_tick_all_log
mag_chart.x_labels_major = x_tick_major_log
mag_chart.add(
"Magnitude",
mag_pts,
show_dots=False,
formatter=lambda x, y: f"{10**x:.2g} Hz → {y:.1f} dB",
stroke_style={"width": 5, "linecap": "round", "linejoin": "round"},
)
mag_chart.add("0 dB ref", ref_0db, show_dots=False, stroke_style={"width": 2.5, "dasharray": "18,10"})
if gain_margin_line:
mag_chart.add(
f"GM: {gain_margin:.1f} dB @ {pc_freq:.1f} Hz",
gain_margin_line,
show_dots=True,
dots_size=8,
stroke_style={"width": 3, "dasharray": "8,5"},
)
# −3 dB reference — slightly more visible than previous (width 2 vs 1.5)
bw_3db = [(x_lo, -3.0), (x_hi, -3.0)]
mag_chart.add("−3 dB", bw_3db, show_dots=False, stroke_style={"width": 2, "dasharray": "5,8"})
# Phase chart — bottom panel (3200×900)
phase_chart = pygal.XY(
width=3200,
height=900,
style=_style,
show_legend=True,
legend_at_bottom=True,
legend_at_bottom_columns=3,
show_y_guides=True,
show_x_guides=False,
margin=20,
margin_left=140,
margin_right=70,
margin_bottom=140,
margin_top=10,
dots_size=0,
stroke=True,
truncate_label=-1,
print_values=False,
x_value_formatter=lambda x: f"{10**x:.4g}",
tooltip_fancy_mode=True,
tooltip_border_radius=8,
title="",
x_title="Frequency (Hz)",
y_title="Phase (°)",
range=(-280.0, 10.0),
interpolate="cubic",
show_minor_x_labels=True,
)
phase_chart.x_labels = x_tick_all_log
phase_chart.x_labels_major = x_tick_major_log
phase_chart.add(
"Phase",
phase_pts,
show_dots=False,
formatter=lambda x, y: f"{10**x:.2g} Hz → {y:.1f}°",
stroke_style={"width": 5, "linecap": "round", "linejoin": "round"},
)
phase_chart.add("−180° ref", ref_neg180, show_dots=False, stroke_style={"width": 2.5, "dasharray": "18,10"})
if phase_margin_line:
phase_chart.add(
f"PM: {phase_margin:.1f}° @ {gc_freq:.1f} Hz",
phase_margin_line,
show_dots=True,
dots_size=8,
stroke_style={"width": 3, "dasharray": "8,5"},
)
ref_neg90 = [(x_lo, -90.0), (x_hi, -90.0)]
phase_chart.add("−90° ref", ref_neg90, show_dots=False, stroke_style={"width": 2, "dasharray": "5,8"})
# Render each panel to PNG via cairosvg — each panel 3200×900
mag_png = cairosvg.svg2png(bytestring=mag_chart.render(), output_width=3200, output_height=900)
phase_png = cairosvg.svg2png(bytestring=phase_chart.render(), output_width=3200, output_height=900)
# Compose 3200×1800 dual-panel image (landscape canonical canvas)
mag_img = Image.open(io.BytesIO(mag_png))
phase_img = Image.open(io.BytesIO(phase_png))
combined = Image.new("RGB", (3200, 1800), PAGE_BG)
combined.paste(mag_img, (0, 0))
combined.paste(phase_img, (0, 900))
# Refined panel divider
draw = ImageDraw.Draw(combined)
draw.line([(140, 900), (3070, 900)], fill=INK_MUTED, width=1)
# Annotation fonts
try:
font_bold = ImageFont.truetype("/usr/share/fonts/truetype/dejavu/DejaVuSans-Bold.ttf", 32)
font_reg = ImageFont.truetype("/usr/share/fonts/truetype/dejavu/DejaVuSans.ttf", 26)
except OSError:
font_bold = ImageFont.load_default()
font_reg = font_bold
# Magnitude annotation panel — upper right of top panel, below title area
ann_x, ann_y = 1900, 130
ann_w, ann_h = 1250, 195
draw.rounded_rectangle(
[(ann_x, ann_y), (ann_x + ann_w, ann_y + ann_h)], radius=12, fill=ELEVATED_BG, outline=INK_MUTED, width=1
)
draw.text((ann_x + 20, ann_y + 14), f"▲ Peak: {peak_db:.1f} dB @ {peak_freq:.1f} Hz", fill=BRAND, font=font_reg)
if gain_margin is not None and pc_freq is not None:
draw.text(
(ann_x + 20, ann_y + 60),
f"◆ Gain Margin: {gain_margin:.1f} dB @ {pc_freq:.1f} Hz",
fill=IMPRINT_BLUE,
font=font_bold,
)
else:
draw.text((ann_x + 20, ann_y + 60), "◆ Gain Margin: ∞", fill=IMPRINT_BLUE, font=font_bold)
draw.text((ann_x + 20, ann_y + 118), "H(s): 3rd-order · ωₙ=5 Hz · ζ=0.2", fill=INK_MUTED, font=font_reg)
# Phase annotation panel — upper right of bottom panel
ann2_x, ann2_y = 1900, 912
ann2_w, ann2_h = 1250, 120
draw.rounded_rectangle(
[(ann2_x, ann2_y), (ann2_x + ann2_w, ann2_y + ann2_h)], radius=12, fill=ELEVATED_BG, outline=INK_MUTED, width=1
)
if phase_margin is not None and gc_freq is not None:
draw.text(
(ann2_x + 20, ann2_y + 14),
f"◆ Phase Margin: {phase_margin:.1f}° @ {gc_freq:.1f} Hz",
fill=IMPRINT_BLUE,
font=font_bold,
)
stability = "Stable" if phase_margin > 0 else "Unstable"
stability_color = BRAND if phase_margin > 0 else IMPRINT_RED
draw.text((ann2_x + 20, ann2_y + 68), f"Status: {stability}", fill=stability_color, font=font_reg)
combined.save(f"plot-{THEME}.png", dpi=(300, 300))
# HTML export — pygal native SVG interactivity with tooltips
mag_svg = mag_chart.render(is_unicode=True).replace('<?xml version="1.0" encoding="utf-8"?>', "")
phase_svg = phase_chart.render(is_unicode=True).replace('<?xml version="1.0" encoding="utf-8"?>', "")
html_content = (
"<!DOCTYPE html>\n<html>\n<head>\n"
" <title>bode-basic · python · pygal · anyplot.ai</title>\n"
" <style>\n"
f" body {{ font-family: 'Helvetica Neue', sans-serif; background: {PAGE_BG};"
" margin: 0; padding: 40px 20px; }\n"
" .container { max-width: 1200px; margin: 0 auto; }\n"
" .chart { width: 100%; margin: 8px 0; }\n"
f" .divider {{ border: none; border-top: 1px solid {INK_MUTED}; margin: 0; }}\n"
" .info { text-align: center; font-size: 13px; margin-top: 10px; "
f"color: {INK_MUTED}; }}\n"
" </style>\n</head>\n<body>\n"
" <div class='container'>\n"
f" <div class='chart'>{mag_svg}</div>\n"
" <hr class='divider'/>\n"
f" <div class='chart'>{phase_svg}</div>\n"
" <p class='info'>Hover over data points for frequency/value details</p>\n"
" </div>\n</body>\n</html>"
)
with open(f"plot-{THEME}.html", "w") as f:
f.write(html_content)
Part of Bode Plot for Frequency Response on anyplot.ai.