Plot complex impedances and admittances on an interactive Smith chart and read off VSWR, return loss, mismatch loss, and reflection coefficient at a glance. Pick any characteristic impedance Z₀ (50 Ω, 75 Ω, 300 Ω, or custom), enter values as R + jX, |Γ|∠θ, or G + jB, and toggle the constant-VSWR circles to see how matched each load is. Everything runs in your browser.
| Label | Z (Ω) | Y (mS) | |Γ| | ∠Γ° | VSWR | RL (dB) | ML (dB) |
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A Smith chart maps the complex reflection coefficient Γ = (Z − Z₀) / (Z + Z₀) onto a unit disk. The grid superimposes circles of constant normalized resistance r = R/Z₀ (the family bowing to the right) and arcs of constant normalized reactance x = X/Z₀ (upper half = inductive, lower half = capacitive). The center is a perfect match (Γ = 0, VSWR = 1), the outer rim is total reflection (|Γ| = 1), the rightmost point is an open (Z = ∞), and the leftmost is a short (Z = 0).
Γ = (z − 1) / (z + 1), where z = Z/Z₀
Z = Z₀ · (1 + Γ) / (1 − Γ)
Y = 1/Z, normalized y = 1/z
VSWR = (1 + |Γ|) / (1 − |Γ|)
Return loss = −20·log₁₀(|Γ|) dB
Mismatch loss = −10·log₁₀(1 − |Γ|²) dB
On the admittance chart, the entire impedance grid is rotated 180°.
• Inductive loads land in the upper half (X > 0). Capacitive in the lower half.
• A constant-VSWR ring is a circle of constant |Γ| centered at the chart center; everything along it has the same reflected power.
• To convert impedance ⇌ admittance graphically, reflect through the center.
• Moving toward the generator (along a lossless line) rotates Γ clockwise; toward the load rotates counter-clockwise.