Characteristic Impedance Calculator
Enter any two of Z0, inductance per unit length L and capacitance per unit length C. The third is solved, along with phase velocity, velocity factor, delay, wavelength, electrical length and, if you enter R, G and frequency, the lossy line values.
Z0 = √(L / C)v = 1 / √(L·C)Step-by-step solution (SI base units)
Companion quantities
Transmission line model
A lossless line is a ladder of series inductance and shunt capacitance. With loss, series R and shunt G are added per unit length.
Z0 versus capacitance at your L
Typical lines
| Line | Z0 (Ω) | C (pF/m) | L (nH/m) | Velocity factor |
|---|
Approximate catalogue values. L is derived as Z0²·C. Your Z0 row is highlighted when it is within 10%.
FAQ
Does Z0 depend on line length?
No. Z0 depends only on L and C per unit length, so it is set by the cross-section geometry and dielectric, not by how long the cable is.
Why does a lossy line give a complex Z0?
With loss, Z0 = √((R + jωL)/(G + jωC)). At high frequency R ≪ ωL and G ≪ ωC, so it approaches the real value √(L/C). At low frequency it becomes noticeably complex.
How do I get the velocity factor?
VF = v/c = 1/√(εeff), where v = 1/√(LC). A solid polyethylene coax has VF around 0.66.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Z₀ | Characteristic impedance of the transmission line | Ω |
| L | Inductance per unit length (distributed inductance) | H/m |
| C | Capacitance per unit length (distributed capacitance) | F/m |
What it means
The characteristic impedance Z₀ of a transmission line is the ratio of the voltage to the current of a single traveling wave on the line. It is given by Z₀ = √(L/C), where L is the distributed inductance per unit length and C is the distributed capacitance per unit length. Z₀ is purely resistive for a lossless line. It is a crucial parameter for matching the line to the source and load to minimise reflections. Common values are 50Ω for coaxial cables, 75Ω for video cables, and 100Ω for twisted‑pair Ethernet. The characteristic impedance depends on the geometry of the line and the dielectric material. Example: A coaxial cable with L=0.5µH/m and C=0.2nF/m has Z₀ = √(0.5e-6/0.2e-9) = √(2500) = 50Ω. This is standard for RF applications.
Worked example
Characteristic Impedance – Practical Example
Real‑World| Parameter | Value |
|---|---|
| L | 0.25 µH/m = 0.25×10⁻⁶ H/m |
| C | 100 pF/m = 100×10⁻¹² F/m |
| Formula | Z₀ = √(L/C) |
Common mistakes
Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.Applications
Characteristic impedance Z₀ = √(L/C) of a transmission line is the ratio of voltage to current for a forward wave. It depends only on the line's geometry and dielectric. Engineers use it to design cables, to match loads, and to ensure efficient power transfer. By matching the load to Z₀, reflections are minimised. This is crucial for RF and high‑speed digital signal integrity.
- Transmission line design and cable selection
- Impedance matching for maximum power transfer
- Signal integrity and reflection control in high‑speed circuits
- Antenna and RF circuit design
- Educational understanding of transmission lines
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