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: plotly 6.8.0 | Python 3.13.14
Quality: 93/100 | Updated: 2026-06-17
"""
import os
import sys
# This file is named plotly.py — remove its directory from sys.path so
# 'import plotly' resolves to the installed package, not this script.
_here = os.path.dirname(os.path.abspath(__file__))
sys.path = [p for p in sys.path if os.path.abspath(p or os.getcwd()) != _here]
import numpy as np
import plotly.graph_objects as go
from plotly.subplots import make_subplots
# Theme — Imprint palette chrome 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"
GRID = "rgba(26,26,23,0.15)" if THEME == "light" else "rgba(240,239,232,0.15)"
GRID_MINOR = "rgba(26,26,23,0.07)" if THEME == "light" else "rgba(240,239,232,0.07)"
# Imprint palette colors — positions 1→3 in canonical order
CLR_MAIN = "#009E73" # Imprint green (position 1) — main Bode curve
CLR_GAIN = "#C475FD" # Imprint lavender (position 2) — gain margin annotation
CLR_PHASE = "#4467A3" # Imprint blue (position 3) — phase margin annotation
# Data — Third-order transfer function: H(s) = K / [(s/p1+1)(s²/wn²+2ζs/wn+1)]
# Complex pair at wn=10 Hz with ζ=0.2 produces a clear resonance peak;
# single real pole at 200 Hz ensures a finite gain margin (phase crosses -180°).
K = 2
p1 = 2 * np.pi * 200 # real pole at 200 Hz (well above resonance)
wn = 2 * np.pi * 10 # resonance at 10 Hz
zeta = 0.2 # underdamped — visible resonance peak
frequency_hz = np.logspace(-1, 4, 800)
omega = 2 * np.pi * frequency_hz
s = 1j * omega
H = K / ((s / p1 + 1) * (s**2 / wn**2 + 2 * zeta * s / wn + 1))
magnitude_db = 20 * np.log10(np.abs(H))
phase_deg = np.degrees(np.unwrap(np.angle(H)))
# Gain crossover: where magnitude crosses 0 dB
gain_cross_idx = np.where(np.diff(np.sign(magnitude_db)))[0]
gc_found = len(gain_cross_idx) > 0
if gc_found:
gc_idx = gain_cross_idx[-1]
gc_freq = frequency_hz[gc_idx]
gc_phase = phase_deg[gc_idx]
phase_margin = 180 + gc_phase
# Phase crossover: where phase crosses -180 degrees
phase_cross_idx = np.where(np.diff(np.sign(phase_deg + 180)))[0]
pc_found = len(phase_cross_idx) > 0
if pc_found:
pc_idx = phase_cross_idx[0]
pc_freq = frequency_hz[pc_idx]
pc_mag = magnitude_db[pc_idx]
gain_margin = -pc_mag
# Figure — dual-panel Bode layout
fig = make_subplots(rows=2, cols=1, shared_xaxes=True, vertical_spacing=0.08, row_heights=[0.55, 0.45])
# Magnitude trace (Imprint green — first series)
fig.add_trace(
go.Scatter(
x=frequency_hz,
y=magnitude_db,
mode="lines",
line={"color": CLR_MAIN, "width": 2.5},
name="Magnitude",
showlegend=False,
),
row=1,
col=1,
)
# 0 dB reference line (dashed — zeroline suppressed on y-axis to avoid solid overlay)
fig.add_hline(y=0, row=1, col=1, line={"color": INK_SOFT, "width": 1, "dash": "dash"})
# Phase trace (same Imprint green — single-system Bode)
fig.add_trace(
go.Scatter(
x=frequency_hz,
y=phase_deg,
mode="lines",
line={"color": CLR_MAIN, "width": 2.5},
name="Phase",
showlegend=False,
),
row=2,
col=1,
)
# -180 degree reference line
fig.add_hline(y=-180, row=2, col=1, line={"color": INK_SOFT, "width": 1, "dash": "dash"})
# Gain margin annotation (Imprint lavender — position 2)
if pc_found:
fig.add_shape(
type="rect",
x0=pc_freq * 0.8,
x1=pc_freq * 1.25,
y0=pc_mag,
y1=0,
fillcolor=CLR_GAIN,
opacity=0.12,
line={"width": 0},
row=1,
col=1,
)
fig.add_trace(
go.Scatter(
x=[pc_freq, pc_freq],
y=[pc_mag, 0],
mode="lines+markers",
line={"color": CLR_GAIN, "width": 2},
marker={"size": 8, "symbol": "diamond"},
showlegend=False,
),
row=1,
col=1,
)
fig.add_annotation(
x=np.log10(pc_freq),
y=(pc_mag + 0) / 2,
text=f"<b>GM = {gain_margin:.1f} dB</b>",
showarrow=True,
arrowhead=0,
arrowwidth=1.5,
arrowcolor=CLR_GAIN,
ax=65,
ay=0,
font={"size": 12, "color": CLR_GAIN},
bgcolor=ELEVATED_BG,
bordercolor=CLR_GAIN,
borderwidth=1.5,
borderpad=4,
xref="x",
yref="y",
row=1,
col=1,
)
# Cross-panel marker on phase plot
fig.add_trace(
go.Scatter(
x=[pc_freq],
y=[-180],
mode="markers",
marker={"size": 10, "color": CLR_GAIN, "symbol": "diamond"},
showlegend=False,
),
row=2,
col=1,
)
# Phase margin annotation (Imprint blue — position 3)
if gc_found:
fig.add_shape(
type="rect",
x0=gc_freq * 0.8,
x1=gc_freq * 1.25,
y0=gc_phase,
y1=-180,
fillcolor=CLR_PHASE,
opacity=0.12,
line={"width": 0},
row=2,
col=1,
)
fig.add_trace(
go.Scatter(
x=[gc_freq, gc_freq],
y=[gc_phase, -180],
mode="lines+markers",
line={"color": CLR_PHASE, "width": 2, "dash": "dash"},
marker={"size": 8, "symbol": "square"},
showlegend=False,
),
row=2,
col=1,
)
fig.add_annotation(
x=np.log10(gc_freq),
y=(gc_phase + (-180)) / 2,
text=f"<b>PM = {phase_margin:.1f}°</b>",
showarrow=True,
arrowhead=0,
arrowwidth=1.5,
arrowcolor=CLR_PHASE,
ax=-65,
ay=0,
font={"size": 12, "color": CLR_PHASE},
bgcolor=ELEVATED_BG,
bordercolor=CLR_PHASE,
borderwidth=1.5,
borderpad=4,
xref="x2",
yref="y2",
row=2,
col=1,
)
# Cross-panel marker on magnitude plot
fig.add_trace(
go.Scatter(
x=[gc_freq],
y=[0],
mode="markers",
marker={"size": 10, "color": CLR_PHASE, "symbol": "square"},
showlegend=False,
),
row=1,
col=1,
)
# Layout — theme-adaptive chrome
fig.update_layout(
autosize=False,
title={
"text": "bode-basic · python · plotly · anyplot.ai",
"font": {"size": 16, "color": INK},
"x": 0.5,
"y": 0.98,
},
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
font={"color": INK},
showlegend=False,
margin={"l": 80, "r": 40, "t": 70, "b": 60},
)
# X-axes (log scale — shared between both panels)
fig.update_xaxes(
type="log",
row=2,
col=1,
title={"text": "Frequency (Hz)", "font": {"size": 12, "color": INK}},
tickfont={"size": 10, "color": INK_SOFT},
showgrid=True,
gridcolor=GRID,
gridwidth=1,
showline=True,
linecolor=INK_SOFT,
mirror=False,
zeroline=False,
minor={"showgrid": True, "gridcolor": GRID_MINOR},
)
fig.update_xaxes(
type="log",
row=1,
col=1,
tickfont={"size": 10, "color": INK_SOFT},
showgrid=True,
gridcolor=GRID,
gridwidth=1,
showline=False,
linecolor=INK_SOFT,
mirror=False,
zeroline=False,
minor={"showgrid": True, "gridcolor": GRID_MINOR},
)
# Y-axes
fig.update_yaxes(
row=1,
col=1,
title={"text": "Magnitude (dB)", "font": {"size": 12, "color": INK}},
tickfont={"size": 10, "color": INK_SOFT},
showgrid=True,
gridcolor=GRID,
gridwidth=1,
showline=True,
linecolor=INK_SOFT,
mirror=False,
zeroline=False, # suppress solid zeroline so only the dashed add_hline renders
range=[-80, 25],
)
fig.update_yaxes(
row=2,
col=1,
title={"text": "Phase (degrees)", "font": {"size": 12, "color": INK}},
tickfont={"size": 10, "color": INK_SOFT},
showgrid=True,
gridcolor=GRID,
gridwidth=1,
showline=True,
linecolor=INK_SOFT,
mirror=False,
zeroline=False,
)
# Save — landscape 3200 × 1800 (width=800, height=450, scale=4)
fig.write_image(f"plot-{THEME}.png", width=800, height=450, scale=4)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")
Part of Bode Plot for Frequency Response on anyplot.ai.