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: ggplot2 3.5.1 | R 4.4.1
#' Quality: 89/100 | Created: 2026-05-20
library(ggplot2)
library(ragg)
# --- Theme tokens -----------------------------------------------------------
THEME <- Sys.getenv("ANYPLOT_THEME", "light")
PAGE_BG <- if (THEME == "light") "#FAF8F1" else "#1A1A17"
INK <- if (THEME == "light") "#1A1A17" else "#F0EFE8"
INK_SOFT <- if (THEME == "light") "#4A4A44" else "#B8B7B0"
IMPRINT <- c("#009E73", "#C475FD", "#4467A3", "#BD8233",
"#AE3030", "#2ABCCD", "#954477")
# --- Smith chart grid -------------------------------------------------------
theta <- seq(0, 2 * pi, length.out = 361)
# Outer unit circle (|Gamma| = 1 boundary)
outer_circle <- data.frame(x = cos(theta), y = sin(theta))
# Constant resistance circles: r/(1+r) center, 1/(1+r) radius
r_vals <- c(0, 0.2, 0.5, 1, 2, 5)
r_circles <- do.call(rbind, lapply(r_vals, function(r) {
cx <- r / (1 + r)
rad <- 1 / (1 + r)
data.frame(
x = cx + rad * cos(theta),
y = rad * sin(theta),
grp = paste0("r", r)
)
}))
# Constant reactance arcs: center (1, 1/x), radius 1/|x|, clipped to unit disc
x_vals <- c(0.2, 0.5, 1, 2, 5)
x_arcs <- do.call(rbind, lapply(c(x_vals, -x_vals), function(x) {
cy <- 1 / x
rad <- abs(1 / x)
pts_x <- 1 + rad * cos(theta)
pts_y <- cy + rad * sin(theta)
inside <- (pts_x^2 + pts_y^2) <= 1.001
if (sum(inside) < 3) return(NULL)
data.frame(x = pts_x[inside], y = pts_y[inside], grp = paste0("x", x))
}))
# VSWR = 2 reference circle (|Gamma| = 1/3)
vswr_circle <- data.frame(
x = (1 / 3) * cos(theta),
y = (1 / 3) * sin(theta)
)
# --- Impedance locus: RLC antenna resonant near 2 GHz ----------------------
set.seed(42)
Z0 <- 50
freqs_ghz <- seq(1, 3, length.out = 80)
omega <- 2 * pi * freqs_ghz * 1e9
R_ant <- 45
L_ant <- 5e-9
C_ant <- 1 / ((2 * pi * 2e9)^2 * L_ant) # resonance exactly at 2 GHz
zr <- R_ant / Z0
zx <- (omega * L_ant - 1 / (omega * C_ant)) / Z0
# Reflection coefficient Gamma = (z - 1) / (z + 1)
denom <- (zr + 1)^2 + zx^2
gamma_re <- ((zr - 1) * (zr + 1) + zx^2) / denom
gamma_im <- 2 * zx / denom
locus <- data.frame(gre = gamma_re, gim = gamma_im, freq = freqs_ghz)
# Labels at 1 GHz, 2 GHz, 3 GHz
label_freqs <- c(1, 2, 3)
label_idx <- sapply(label_freqs, function(f) which.min(abs(locus$freq - f)))
label_pts <- locus[label_idx, ]
label_pts$lbl <- c("1 GHz", "2 GHz\n(res.)", "3 GHz")
# Directional arrow at 3 GHz end to show sweep direction
n_loc <- nrow(locus)
dx <- locus$gre[n_loc] - locus$gre[n_loc - 5]
dy <- locus$gim[n_loc] - locus$gim[n_loc - 5]
norm <- sqrt(dx^2 + dy^2)
arr_len <- 0.055
arr_x0 <- locus$gre[n_loc] - (dx / norm) * arr_len
arr_y0 <- locus$gim[n_loc] - (dy / norm) * arr_len
# --- Plot -------------------------------------------------------------------
p <- ggplot() +
# Grid: outer circle
geom_path(data = outer_circle, aes(x = x, y = y),
color = INK_SOFT, linewidth = 0.7) +
# Grid: constant-r circles
geom_path(data = r_circles, aes(x = x, y = y, group = grp),
color = INK_SOFT, linewidth = 0.22, alpha = 0.65) +
# Grid: constant-x arcs
geom_path(data = x_arcs, aes(x = x, y = y, group = grp),
color = INK_SOFT, linewidth = 0.22, alpha = 0.65) +
# Real axis
geom_segment(aes(x = -1, xend = 1, y = 0, yend = 0),
color = INK_SOFT, linewidth = 0.3) +
# VSWR = 2 reference circle
geom_path(data = vswr_circle, aes(x = x, y = y),
color = IMPRINT[3], linewidth = 0.5, linetype = "dashed") +
annotate("text", x = -0.38, y = 0.06,
label = "VSWR = 2", size = 3.0, color = IMPRINT[3]) +
# Matched-load centre marker
geom_point(aes(x = 0, y = 0),
color = INK_SOFT, size = 1.8, shape = 3) +
# Impedance locus
geom_path(data = locus, aes(x = gre, y = gim),
color = IMPRINT[1], linewidth = 1.4) +
# Directional arrow at 3 GHz end showing sweep direction
annotate("segment",
x = arr_x0, xend = locus$gre[n_loc],
y = arr_y0, yend = locus$gim[n_loc],
color = IMPRINT[1], linewidth = 1.4,
arrow = arrow(length = unit(0.1, "inches"), type = "closed")) +
# Start (1 GHz) and end (3 GHz) markers
geom_point(data = locus[1, ], aes(x = gre, y = gim),
color = IMPRINT[1], size = 3.5, shape = 16) +
geom_point(data = locus[nrow(locus), ], aes(x = gre, y = gim),
color = IMPRINT[2], size = 3.5, shape = 17) +
# Frequency labels
geom_text(data = label_pts, aes(x = gre, y = gim, label = lbl),
color = INK, size = 3.2, hjust = -0.15, lineheight = 0.9) +
# Resistance value labels along real axis
annotate("text",
x = (r_vals - 1) / (r_vals + 1),
y = -0.06,
label = as.character(r_vals),
size = 3.0, color = INK_SOFT, vjust = 1) +
coord_fixed(xlim = c(-1.15, 1.35), ylim = c(-1.15, 1.15)) +
labs(
title = "smith-chart-basic · r · ggplot2 · anyplot.ai",
x = "Re(Γ)",
y = "Im(Γ)"
) +
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_blank(),
panel.grid.minor = element_blank(),
panel.border = element_blank(),
axis.title = element_text(color = INK, size = 10),
axis.text = element_text(color = INK_SOFT, size = 8),
plot.title = element_text(color = INK, size = 12),
axis.line = element_blank()
)
# --- Save -------------------------------------------------------------------
ggsave(
filename = sprintf("plot-%s.png", THEME),
plot = p,
device = ragg::agg_png,
width = 6,
height = 6,
units = "in",
dpi = 400
)
Part of Smith Chart for RF/Impedance on anyplot.ai.