Calculators › Transmission Lines
TL Input Impedance Zin
Calculate the input impedance of a terminated lossless transmission line. Enter load, line and frequency — get Z_in, Γ, VSWR, Smith chart path and full step-by-step working.
Parameters
Load Preset
R_L — Resistance
Ω
X_L — Reactance (+ind, −cap)
Ω
Z₀ — Char. impedance
Ω
f — Frequency
MHz
εᵣ_eff (1 = air)
Line Length Preset
Drag to set length
0.1988λ
0λ/4λ/23λ/4λ5λ/43λ/27λ/42λ
Length (wavelengths)
λ
Length (degrees)
°
Length (mm)
mm
Z_in Result
Input Impedance Z_in
—
—
|Z_in|—Ω
∠ Z_in—°
R_in—Ω
X_in—Ω
|Γ|—
Return Loss—dB
VSWR—
βl—°
tan(βl)—
λ on substrate—mm
▪ Transmission Line Input Impedance
Special Cases
βl = 90° (λ/4 line) → Z_in = Z₀² / Z_L (impedance inverter)
βl = 180° (λ/2 line) → Z_in = Z_L (transparent — line invisible)
Z_L = 0 (SC load) → Z_in = j Z₀ tan(βl) (pure reactance)
Z_L = ∞ (OC load) → Z_in = −j Z₀ cot(βl) (pure reactance)
Z_L = Z₀ (matched) → Z_in = Z₀ (for any length)
βl = 180° (λ/2 line) → Z_in = Z_L (transparent — line invisible)
Z_L = 0 (SC load) → Z_in = j Z₀ tan(βl) (pure reactance)
Z_L = ∞ (OC load) → Z_in = −j Z₀ cot(βl) (pure reactance)
Z_L = Z₀ (matched) → Z_in = Z₀ (for any length)
Z_L = R_L + jX_L load impedance
Z₀ = characteristic impedance of the line
β = 2π/λ phase constant (rad/m)
l = physical length of line
βl = electrical length in radians
tan(βl) = drives the rotation on Smith chart
Derivation: Using the telegrapher's equations, the voltage and current waves
on the line produce V(l) and I(l). Dividing gives Z_in = V(0)/I(0).
For a lossless line: V(x) = V⁺(e−jβx + Γe+jβx), where Γ = (Z_L−Z₀)/(Z_L+Z₀). Evaluating at x = −l (input) and simplifying yields the formula above.
For a lossless line: V(x) = V⁺(e−jβx + Γe+jβx), where Γ = (Z_L−Z₀)/(Z_L+Z₀). Evaluating at x = −l (input) and simplifying yields the formula above.
Smith Chart
Z_L (load)
TL rotation (constant |Γ|)
Z_in
Step-by-Step Working
Enter values — working appears here.