Coaxial Line Impedance Calculator

Calculate characteristic impedance, capacitance, inductance, and signal velocity for coaxial transmission lines. Essential RF engineering tool for designers and technicians.

Coaxial Cable Cross-Section
d D/2 Inner Conductor Dielectric Outer Conductor
  • d: Inner conductor diameter
  • D: Outer conductor inner diameter
  • εr: Relative permittivity (dielectric constant)
  • μr: Relative permeability (usually 1 for non-magnetic materials)
  • Z0: Characteristic impedance
Units:
mm inch mil

Characteristic Impedance Formula: Z₀ = (138 / √εr) · log₁₀(D/d) Ω

Where: D = inner diameter of outer conductor, d = diameter of inner conductor, εr = relative permittivity

RG-58 (50Ω)
RG-59 (75Ω)
RG-6 (75Ω)
RG-8 (50Ω)
RG-11 (75Ω)
RG-174 (50Ω)
RG-213 (50Ω)
RG-214 (50Ω)
LMR-400 (50Ω)
mm
Diameter of the center conductor
mm
Inner diameter of the outer conductor (shield)
unitless
Dielectric constant of the insulating material
unitless
Usually 1.0 for non-magnetic materials
Air
εr = 1.0
Polyethylene
εr = 2.25
PTFE (Teflon)
εr = 2.1
Polypropylene
εr = 2.3
PVC
εr = 2.55
Polyurethane
εr = 3.0
Epoxy
εr = 3.4
FR-4 (PCB)
εr = 4.0
For wavelength and loss calculations
For total capacitance/inductance calculations
Calculating...

Understanding Coaxial Cable Impedance

Coaxial cable is a type of transmission line used to carry high-frequency electrical signals with low losses. It consists of an inner conductor surrounded by a concentric conducting shield, with the two separated by a dielectric material.

Key Parameters:

  • Characteristic Impedance (Z₀): The ratio of voltage to current in a traveling wave. For coaxial cables, typical values are 50Ω (RF applications) and 75Ω (video applications).
  • Capacitance per Unit Length: Determines how much charge the cable can store per unit length.
  • Inductance per Unit Length: Determines how the cable resists changes in current flow.
  • Velocity Factor: The ratio of signal speed in the cable to the speed of light in vacuum.

Impedance Formula Derivation

1

Electric Field: For a coaxial cable with inner radius a and outer radius b, the electric field at radius r is E = V / (r · ln(b/a)).

2

Capacitance: The capacitance per unit length is C = (2πε₀εr) / ln(b/a), where ε₀ = 8.854×10⁻¹² F/m.

3

Inductance: The inductance per unit length is L = (μ₀μr/2π) · ln(b/a), where μ₀ = 4π×10⁻⁷ H/m.

4

Characteristic Impedance: Z₀ = √(L/C) = (1/2π) √(μ₀μr/ε₀εr) · ln(b/a) = (138/√εr) · log₁₀(b/a) Ω.

Common Coaxial Cable Types

Cable Type Impedance (Ω) Inner Conductor Dielectric Typical Use
RG-58 50 0.9 mm PE (εr=2.25) RF applications, amateur radio
RG-59 75 0.81 mm PE (εr=2.25) Cable TV, video
RG-6 75 1.02 mm PE (εr=2.25) Satellite TV, broadband
RG-8 50 2.17 mm PE (εr=2.25) High-power RF
RG-174 50 0.48 mm PE (εr=2.25) Low-loss patch cords
RG-213 50 2.26 mm PE (εr=2.25) Commercial RF
LMR-400 50 2.74 mm PE (εr=1.56) Low-loss applications

Applications of Coaxial Cables

  • RF and Microwave Systems: Antenna feeds, radio transceivers, radar systems
  • Broadcast and Video: Cable television, CCTV, video distribution
  • Data Communications: Ethernet (10BASE5, 10BASE2), broadband internet
  • Test and Measurement: Oscilloscope probes, network analyzers
  • Medical Equipment: MRI machines, diagnostic equipment

Calculator Features:

  • Calculates characteristic impedance, capacitance, inductance, and velocity factor
  • Supports multiple units (mm, inch, mil) for diameter inputs
  • Includes presets for common coaxial cable types
  • Provides visual graph of impedance vs. diameter ratio
  • Calculates wavelength and total capacitance/inductance for given length

Frequently Asked Questions

50Ω represents a compromise between minimum loss (which occurs at 77Ω for air dielectric) and maximum power handling (which occurs at 30Ω). 75Ω is optimized for minimum loss and is commonly used in video applications where signal integrity is paramount.

Historically, 50Ω became a standard for RF applications because it was a convenient midpoint between these two optimizations, while 75Ω was adopted for television broadcast systems.

Impedance mismatch causes signal reflections at the discontinuity. This results in:
  • Standing waves: Variations in voltage and current along the line
  • Return loss: Power reflected back to the source
  • Insertion loss: Reduced power delivered to the load
  • Signal distortion: Especially problematic for digital signals
The severity is measured by Voltage Standing Wave Ratio (VSWR), where 1:1 represents perfect match.

At higher frequencies, several effects become significant:

  • Skin effect: Current flows primarily near the conductor surface, increasing effective resistance
  • Dielectric losses: The dielectric material dissipates more energy as heat
  • Radiation losses: Higher frequencies can radiate through imperfect shields
  • Higher-order modes: Above the cutoff frequency, multiple propagation modes exist

These effects increase attenuation and can distort signals, limiting the useful frequency range of a coaxial cable.

Velocity factor (VF) is the ratio of signal propagation speed in the cable to the speed of light in vacuum. It's determined by the dielectric constant: VF = 1/√εr.

VF is important for:

  • Timing calculations: Signal delay in long cable runs
  • Antenna design: Length of cable stubs for impedance matching
  • Wavelength determination: Effective wavelength in the cable λ = λ₀ × VF

For example, with polyethylene dielectric (εr=2.25), VF ≈ 0.67, so signals travel at 67% of light speed.

Yes, different transmission line geometries have different impedance formulas:
  • Two-wire line: Z₀ = (120/√εr) · arccosh(D/d) where D is spacing between centers
  • Microstrip: More complex formula depending on trace width, thickness, and dielectric height
  • Stripline: Symmetric formula for traces embedded between two ground planes
  • Coplanar waveguide: Depends on trace width and gap to ground planes

Coaxial cable has the advantage of complete shielding, which prevents radiation and external interference.