Transmission Line Impedance Calculator Formula

Understand the math behind the transmission line impedance calculator. Each variable explained with a worked example.

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Formulas Used

Characteristic Impedance

z0 = 138 / sqrt(dielectric_constant) * log10(outer_diameter_mm / inner_diameter_mm)

Velocity Factor

velocity_factor = 1 / sqrt(dielectric_constant)

Capacitance per Meter

capacitance_pf_m = 24.13 * dielectric_constant / log10(outer_diameter_mm / inner_diameter_mm)

Variables

VariableDescriptionDefault
outer_diameter_mmOuter Conductor Inner Diameter(mm)7
inner_diameter_mmInner Conductor Outer Diameter(mm)1.63
dielectric_constantDielectric Constant (Er)2.3

How It Works

Coaxial Cable Characteristic Impedance

The characteristic impedance of a coaxial transmission line depends on the ratio of conductor diameters and the dielectric material.

Formula

Z_0 = (138 / sqrt(Er)) x log10(D / d)

Where D is the outer conductor inner diameter, d is the inner conductor outer diameter, and Er is the relative dielectric constant.

Common Values

  • 50 ohm: Standard for RF and instrumentation
  • 75 ohm: Video and cable TV
  • 93 ohm: Early computer networks

    • The velocity factor is 1/sqrt(Er), which determines signal propagation speed.

    Worked Example

    Coaxial cable with D=7.0 mm, d=1.63 mm, polyethylene dielectric (Er=2.3).

    outer_diameter_mm = 7inner_diameter_mm = 1.63dielectric_constant = 2.3
    1. 01Diameter ratio: 7.0 / 1.63 = 4.294
    2. 02log10(4.294) = 0.633
    3. 03Z0 = 138 / sqrt(2.3) x 0.633 = 138 / 1.517 x 0.633 = 57.6 ohms
    4. 04Velocity factor: 1 / sqrt(2.3) = 0.659

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