Calculate ideal lossless transmission-line impedance, velocity, wavelength, one-way delay and unwrapped electrical length, or find reflection coefficient, VSWR and return loss for a nonnegative real load.

Ideal uniform lossless line. Use the fixed per-meter units shown; length gives one-way delay and unwrapped electrical length.

Optional settings

Related Calculators

Transmission Line Formula

The general characteristic impedance of a uniform transmission line is determined by series resistance, series inductance, shunt conductance and shunt capacitance per unit length. The full equation below provides context; this calculator uses the ideal lossless simplification and does not solve complex or lossy line parameters. Characteristic impedance describes a traveling wave and is the terminating impedance that eliminates load reflections on an ideal matched line.

Z₀ = √((R + jω L) / (G + jω C))

In this expression:

Symbol Meaning Typical Unit Physical Interpretation
Z0 Characteristic impedance Ω The natural impedance of the line for a traveling wave
R Resistance per unit length Ω/m or Ω/ft Conductor loss
L Inductance per unit length H/m or H/ft Magnetic energy storage along the line
G Conductance per unit length S/m or S/ft Leakage through the dielectric
C Capacitance per unit length F/m or F/ft Electric energy storage between conductors
ω Angular frequency rad/s Signal frequency in angular form
j Imaginary unit — Represents phase-sensitive reactive behavior

Useful Simplifications

For many practical lines, the losses are small compared with the reactive terms. In that low-loss case, the characteristic impedance is often approximated by the square root of the inductance-to-capacitance ratio.

Z₀ ≈ √((L) / (C))

If the line is treated as perfectly lossless, this same relation becomes exact.

Z₀ = √((L) / (C))

If your known signal frequency is given in hertz rather than radians per second, convert it before using the full equation.

ω = 2π f

How to Use the Transmission Line Calculator

  1. Choose Lossless line properties and enter inductance in µH/m, capacitance in pF/m, frequency in MHz and line length in meters.
  2. Use the fixed units printed on the inputs. Convert per-foot values to per-meter values before entering them.
  3. Alternatively, choose Real-load reflection and VSWR, then enter a positive real reference impedance and a nonnegative real load in ohms. The default reference is 50 Ω; a 0 Ω load represents an ideal short circuit.
  4. Select Calculate. The line mode assumes a uniform ideal lossless model; the matching mode is limited to real resistive loads.
  5. Interpret characteristic impedance as a traveling-wave property, not end-to-end DC resistance. Delay is one-way, and electrical length is not reduced modulo 360°.

What the Result Means

  • When a real load equals the real characteristic impedance, the ideal load reflection coefficient is zero, VSWR is 1:1, reflected power is 0% and return loss is unbounded.
  • When the load does not equal the characteristic impedance, part of the wave reflects back toward the source.
  • When losses are very small, the characteristic impedance is usually close to a real number and is often treated as a nominal value such as 50 Ω, 75 Ω, or 100 Ω in design work.
  • When losses are significant, the characteristic impedance can be complex, meaning both magnitude and phase matter.

Example

Suppose a low-loss line has an inductance per unit length of 2.5 × 10-7 H/m and a capacitance per unit length of 1.0 × 10-10 F/m. With conductor and dielectric losses small enough to ignore, the characteristic impedance is:

Z₀ ≈ √((2.5 × 10⁻⁷) / (1.0 × 10⁻¹⁰)) = √(2500) = 50 Ω

This means the line should ideally be terminated with 50 Ω to avoid reflections.

Why Line Length Is Not in the Formula

Characteristic impedance is a property of the line’s geometry and materials, captured through the distributed parameters per unit length. Total length affects other behavior, including attenuation, phase shift, and propagation delay, but it does not change the nominal characteristic impedance of a uniform line.

Related Transmission-Line Quantities

If you are analyzing more than matching alone, two other quantities are especially useful: the propagation constant and the reflection coefficient.

γ = √((R + jω L)(G + jω C))
Gamma = (ZL - Z₀) / (ZL + Z₀)
VSWR = (1 + |Gamma|) / (1 - |Gamma|)

For the calculator’s real-load mode, return loss is −20 log₁₀|Γ| dB and reflected power is 100|Γ|² percent. An ideal short circuit has Γ = −1, unbounded VSWR, 0 dB return loss and 100% reflected power. These equations also provide broader transmission-line context; the tool does not compute the lossy propagation constant above.

Practical Notes

  • Do not confuse characteristic impedance with resistance. A line can have a 50 Ω characteristic impedance without having 50 Ω of end-to-end DC resistance.
  • Keep unit systems consistent. Mixing per-meter and per-foot values will produce a wrong answer.
  • Use the full formula for lossy or frequency-sensitive analysis. The simplified form is best when resistance and leakage are small.
  • Fast digital edges can behave like high-frequency signals. Even when the clock rate seems moderate, long interconnects may still need transmission-line treatment.
  • Matching is application-dependent. RF systems usually target a specific nominal impedance, while high-speed digital links focus on controlling reflections and preserving waveform shape.

Common Input Mistakes

  • Entering Hz or rad/s when the line-mode input expects ordinary frequency in MHz
  • Confusing line-mode inductance per meter with total inductance, or treating a complex load as a real resistance
  • Mixing unit bases such as H/m with F/ft
  • Assuming a longer cable automatically changes the characteristic impedance
  • Ignoring dielectric leakage in cases where the insulation is not ideal