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: ggplot2 3.5.1 | R 4.4.1
#' Quality: 92/100 | Created: 2026-06-17
library(ggplot2)
library(ragg)
# Theme tokens (Imprint palette — see prompts/default-style-guide.md)
THEME <- Sys.getenv("ANYPLOT_THEME", "light")
PAGE_BG <- if (THEME == "light") "#FAF8F1" else "#1A1A17"
ELEVATED_BG <- if (THEME == "light") "#FFFDF6" else "#242420"
INK <- if (THEME == "light") "#1A1A17" else "#F0EFE8"
INK_SOFT <- if (THEME == "light") "#4A4A44" else "#B8B7B0"
INK_MUTED <- if (THEME == "light") "#6B6A63" else "#A8A79F"
GRID_COLOR <- adjustcolor(INK, alpha.f = 0.12)
IMPRINT_PALETTE <- c(
"#009E73", # 1 — brand green (first series)
"#C475FD", # 2 — lavender
"#4467A3", # 3 — blue
"#BD8233", # 4 — ochre
"#AE3030", # 5 — matte red
"#2ABCCD", # 6 — cyan
"#954477", # 7 — rose
"#99B314" # 8 — lime
)
# Transfer function G(s) = 10 / (s(s+1)(s+5)) — type-1 system with two real poles
# Phase crossover at omega = sqrt(5), gain margin ~9.54 dB
freq_hz <- 10^seq(log10(0.005), log10(50), length.out = 500)
omega <- 2 * pi * freq_hz
# Analytical magnitude and phase (avoids Arg() wrapping for high-order systems)
magnitude_db <- 20 * log10(10 / (omega * sqrt(1 + omega^2) * sqrt(25 + omega^2)))
phase_deg <- -90 - atan(omega) * (180 / pi) - atan(omega / 5) * (180 / pi)
# Gain crossover frequency: |G| crosses 0 dB downward
gc_idx <- which(diff(sign(magnitude_db)) < 0)[1]
gc_freq <- 10^(log10(freq_hz[gc_idx]) +
(0 - magnitude_db[gc_idx]) *
(log10(freq_hz[gc_idx + 1]) - log10(freq_hz[gc_idx])) /
(magnitude_db[gc_idx + 1] - magnitude_db[gc_idx]))
gc_phase <- approx(freq_hz, phase_deg, xout = gc_freq)$y
phase_margin <- 180 + gc_phase
# Phase crossover frequency: phase crosses -180° downward
pc_idx <- which(diff(sign(phase_deg + 180)) < 0)[1]
pc_freq <- 10^(log10(freq_hz[pc_idx]) +
(-180 - phase_deg[pc_idx]) *
(log10(freq_hz[pc_idx + 1]) - log10(freq_hz[pc_idx])) /
(phase_deg[pc_idx + 1] - phase_deg[pc_idx]))
pc_mag <- approx(freq_hz, magnitude_db, xout = pc_freq)$y
gain_margin <- -pc_mag
# Long-format data for dual-panel faceted plot
panels <- c("Magnitude (dB)", "Phase (°)")
df <- tibble::tibble(
freq = c(freq_hz, freq_hz),
value = c(magnitude_db, phase_deg),
panel = factor(rep(panels, each = 500), levels = panels)
)
# Per-facet reference lines: 0 dB (magnitude) and -180° (phase)
ref_df <- tibble::tibble(
panel = factor(panels, levels = panels),
yint = c(0, -180)
)
# Stability zone shading: vertical band between gain and phase crossover frequencies
shade_df <- tibble::tibble(
panel = factor(panels, levels = panels),
xmin = min(gc_freq, pc_freq),
xmax = max(gc_freq, pc_freq),
ymin = -Inf,
ymax = Inf
)
# Stability margin annotations: place in each panel near the relevant crossover
ann_df <- tibble::tibble(
freq = c(pc_freq * 2.5, gc_freq * 4.0),
value = c(pc_mag / 2, (gc_phase - 180) / 2),
label = c(sprintf("GM = %.1f dB", gain_margin),
sprintf("PM = %.1f°", phase_margin)),
panel = factor(panels, levels = panels)
)
title_str <- "bode-basic · r · ggplot2 · anyplot.ai"
title_size <- max(8, round(12 * min(1.0, 67 / nchar(title_str))))
p <- ggplot(df, aes(x = freq, y = value)) +
# Stability zone: vertical band between crossover frequencies
geom_rect(
data = shade_df,
aes(xmin = xmin, xmax = xmax, ymin = ymin, ymax = ymax),
inherit.aes = FALSE,
fill = adjustcolor(IMPRINT_PALETTE[1], alpha.f = 0.07),
color = NA
) +
# Reference lines per facet (0 dB and -180°)
geom_hline(
data = ref_df, aes(yintercept = yint),
color = INK_MUTED, linetype = "dashed", linewidth = 0.6
) +
# Gain crossover frequency marker (both panels)
geom_vline(
xintercept = gc_freq,
color = IMPRINT_PALETTE[3], linetype = "dotted", linewidth = 0.7
) +
# Phase crossover frequency marker (both panels)
geom_vline(
xintercept = pc_freq,
color = IMPRINT_PALETTE[5], linetype = "dotted", linewidth = 0.7
) +
# Frequency response curves
geom_line(color = IMPRINT_PALETTE[1], linewidth = 1.0) +
# Stability margin annotations
geom_label(
data = ann_df,
aes(x = freq, y = value, label = label),
color = INK, fill = ELEVATED_BG,
label.size = 0.25, size = 3.5, label.r = unit(0.15, "lines")
) +
scale_x_log10(
breaks = 10^(-2:1),
labels = c("0.01", "0.1", "1", "10"),
minor_breaks = as.vector(outer(1:9, 10^(-3:2)))
) +
facet_wrap(~ panel, ncol = 1, scales = "free_y") +
labs(
title = title_str,
x = "Frequency (Hz)",
y = NULL
) +
theme_minimal(base_size = 8) +
theme(
plot.background = element_rect(fill = PAGE_BG, color = PAGE_BG),
panel.background = element_rect(fill = PAGE_BG, color = NA),
panel.grid.major = element_line(color = GRID_COLOR, linewidth = 0.4),
panel.grid.minor = element_line(color = GRID_COLOR, linewidth = 0.2),
panel.border = element_blank(),
axis.line = element_line(color = INK_SOFT, linewidth = 0.4),
axis.title.x = element_text(color = INK, size = 10),
axis.text = element_text(color = INK_SOFT, size = 8),
plot.title = element_text(color = INK, size = title_size, face = "bold"),
strip.text = element_text(color = INK, size = 10, face = "bold"),
strip.background = element_rect(fill = ELEVATED_BG, color = NA),
plot.margin = margin(10, 15, 10, 10, unit = "pt")
)
ggsave(
filename = sprintf("plot-%s.png", THEME),
plot = p,
device = ragg::agg_png,
width = 8,
height = 4.5,
units = "in",
dpi = 400
)
Part of Bode Plot for Frequency Response on anyplot.ai.