Transmission Line Input Impedance Calculator | VSWR & Reflection

Preset

Parameters

Characteristic Impedance Z₀ 50 Ω

Load impedance Z_L = R + jX [Ω]

R (real part)

X (imaginary part)

Line length l/λ (wavelength ratio) 0.25 λ

Voltage / Current Standing Wave Pattern

Input impedance Z_in

—

Results

0.33

|Γ| Reflection Coefficient

2.00

VSWR

0°

∠Γ Phase

9.5

Return Loss [dB]

1.33

V_max / V_min

Mismatch

Matched

Incident Wave Reflected Wave Superposition (Actual Voltage) Standing-Wave Envelope

Characteristic Impedance Z₀50 Ω

Load Resistance R_L100 Ω

Load Reactance X_L0 Ω

Line Length / Wavelength1.5 λ

How to read:The incident wave (orange) travels toward the load, while the reflected wave (blue) returns. Their superposition is the actual voltage (yellow), whose amplitude peaks form theEnvelope(light blue) of thestanding wave. With a matched load (Z_L=Z₀), reflection is zero and the envelope is flat, leaving only a traveling wave. A short or open circuit produces total reflection and a complete standing wave. Peaks (V_max) and nulls (V_min) are spaced λ/2 apart.

Voltage / Current Standing Wave Pattern

—

|Γ| Reflection Coefficient

—

VSWR

—

Return Loss [dB]

—

Reflected power [%]

Theory & Key Formulas

$$\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}$$ $$\text{VSWR}= \frac{1+|\Gamma|}{1-|\Gamma|}$$ $$Z_{in}= Z_0 \frac{Z_L + jZ_0\tan(\beta l)}{Z_0 + jZ_L\tan(\beta l)}$$

Worked examples and checks

100-ohm load on a 50-ohm line

Z0=50 Ω, R=100 Ω, X=0 Ω, l/λ=0.25: Γ=1/3, VSWR=2, RL≈9.54 dB, reflected power≈11.11%, Zin=25 Ω. Changing only length to 0.5 restores Zin=100 Ω without changing |Γ|.

A complex load

Z0=50 Ω, R=50 Ω, X=50 Ω, l/λ=0.25: Γ=0.2+j0.4, |Γ|≈0.4472, VSWR≈2.618, RL≈6.99 dB and Zin=25−j25 Ω. Check the reactance sign and the position of standing-wave peaks.

Equations and scope

Assumptions: lossless line, real Z0>0 and passive load R≥0. Γ=(ZL−Z0)/(ZL+Z0), VSWR=(1+|Γ|)/(1−|Γ|), return loss RL=−20log10|Γ|. Zin=Z0[ZL cosθ+jZ0 sinθ]/[Z0 cosθ+jZL sinθ], θ=2πl/λ. The sine/cosine form avoids the tangent pole at a quarter wavelength. Reflected power fraction |Γ|² is not absorption in the cable.

Questions about the model

Is return loss 99 dB at a perfect match?

No. Ideal Γ=0 gives infinite return loss. The calculator does not use 99 dB as an artificial ceiling.

Does changing length reduce reflected power?

Not in this lossless model: |Γ| stays constant while phase and input impedance change. A lossy line requires a separate attenuation model.

How are open and short circuits represented?

A short has R=X=0; its quarter-wave input impedance is ideally infinite. The main open preset approximates an open with 1 MΩ. The animation’s 400 Ω preset is a finite load, not an open circuit.

Transmission Line Input Impedance Calculator | VSWR & Reflection

Inputs and units

Worked examples and checks

100-ohm load on a 50-ohm line

A complex load

Equations and scope

Questions about the model

References

Transmission Line Input Impedance Calculator | VSWR & Reflection

Inputs and units

Worked examples and checks

100-ohm load on a 50-ohm line

A complex load

Equations and scope

Questions about the model

References

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