Coaxial Cable Impedance Calculator
Calculate coaxial cable characteristic impedance, capacitance, inductance per unit length, and cutoff frequency from inner/outer conductor dimensions and dielectric.
Formula
Z_0 = \frac{60}{\sqrt{\varepsilon_r}} \ln\!\left(\frac{D}{d}\right)
Reference: Wadell, "Transmission Line Design Handbook" 1991, Chapter 3
How It Works
Coaxial cable impedance is a critical parameter in RF system design, determined by the geometric relationships between the inner conductor and outer shield. The fundamental equation Z0 = (60/√εr)·ln(D/d) reflects how the dielectric constant (εr) and physical dimensions influence signal transmission characteristics. The inner conductor diameter (d) and outer shield diameter (D) create a logarithmic relationship that determines the cable's characteristic impedance. This impedance represents the complex ratio of voltage to current at any point along an infinitely long transmission line, ensuring optimal signal transfer and minimal reflections. Lower impedance cables typically have wider conductors, while higher impedance designs feature narrower spacing. The dielectric material between conductors plays a crucial role, with its permittivity directly affecting signal propagation velocity and impedance matching.
Worked Example
Consider a coaxial cable with an inner conductor diameter of 0.5mm and an outer shield diameter of 4.2mm, using a Teflon dielectric with εr of 2.1. Plugging these values into the impedance formula: Z0 = (60/√2.1)·ln(4.2/0.5) = (60/1.449)·ln(8.4) = 41.4 · 2.13 = 50.2 Ω. This calculation matches standard 50Ω RF cable specifications, demonstrating how precise geometric relationships determine transmission line characteristics. The resulting impedance would be suitable for many RF applications like test equipment, signal generators, and communications systems.
Practical Tips
- ✓Always use precision calipers when measuring conductor diameters for accurate calculations
- ✓Consider using vector network analyzers to validate theoretical impedance calculations
- ✓Select cable impedance matching network components within ±2% tolerance for critical RF designs
Common Mistakes
- ✗Neglecting conductor surface roughness which can impact high-frequency signal transmission
- ✗Assuming linear impedance across all frequencies without considering skin effect
- ✗Overlooking temperature and mechanical stress effects on cable impedance
Frequently Asked Questions
Why is 50Ω a common coaxial cable impedance?
50Ω represents an optimal compromise between power handling, signal integrity, and connector/component standardization across various RF applications.
How does cable length affect impedance?
Ideal coaxial cables maintain consistent impedance regardless of length, but practical factors like connector interfaces and manufacturing tolerances can introduce minor variations.
Can I use this calculator for all cable types?
The formula applies primarily to air/solid dielectric coaxial cables. Specialized cables like semi-rigid or foam dielectric may require more complex calculations.
What impact does temperature have on cable impedance?
Temperature variations can cause slight dimensional changes in conductors and dielectric, potentially shifting impedance by 1-2% in extreme environments.
How precise must conductor measurements be?
For professional RF design, conductor diameter measurements should be accurate within ±0.01mm to ensure meaningful impedance calculations.
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