Coaxial Line Impedance Calculator

What is Coaxial Line Impedance?

Coaxial line impedance, also known as characteristic impedance (Z0), is a fundamental property of a coaxial cable or transmission line. It represents the ratio of the voltage to the current of a wave traveling along the line when there are no reflections. This impedance is determined by the physical dimensions of the cable – specifically the inner diameter of the outer conductor (D), the outer diameter of the inner conductor (d), and the dielectric constant (εr) of the insulating material between them – and is ideally independent of the line’s length or the signal frequency (at high frequencies where skin effect is dominant and losses are low).

Anyone working with radio frequency (RF) systems, high-frequency signals, video signals, or data transmission over coaxial cables should use a Coaxial Line Impedance Calculator. This includes RF engineers, technicians, amateur radio enthusiasts, and anyone designing or analyzing systems using coax. Maintaining impedance matching is crucial to prevent signal reflections, minimize power loss, and ensure signal integrity.

A common misconception is that the impedance of a coaxial cable is like the DC resistance of a wire. However, characteristic impedance is an AC property related to the distributed inductance and capacitance along the line and governs how energy propagates along it. It’s not measured with a simple ohmmeter.

Coaxial Line Impedance Formula and Mathematical Explanation

The characteristic impedance (Z0) of a coaxial line can be calculated using the following formula:

Z0 = (1 / (2 * π * √(μ / ε))) * ln(D/d)

Where μ is the permeability and ε is the permittivity of the dielectric material. For non-magnetic dielectrics (like those used in most coax cables, μ = μ0) and considering relative permittivity εr (ε = εr * ε0), the formula simplifies to:

Z0 = (√(μ0 / ε0) / (2 * π * √εr)) * ln(D/d)

The term √(μ0 / ε0) is the impedance of free space, approximately 377 Ohms (or 120π Ohms). Using the natural logarithm (ln) and this value, we get:

Z0 ≈ (60 / √εr) * ln(D/d) Ohms

Alternatively, using the base-10 logarithm (log₁₀), and knowing ln(x) ≈ 2.3026 * log₁₀(x), the formula becomes:

Z0 ≈ (138 / √εr) * log₁₀(D/d) Ohms

Our Coaxial Line Impedance Calculator uses this last formula.

Variables Table

Variable	Meaning	Unit	Typical Range
Z0	Characteristic Impedance	Ohms (Ω)	30 – 150 Ω
D	Outer conductor inner diameter	mm, inches (consistent with d)	1 – 50 mm
d	Inner conductor outer diameter	mm, inches (consistent with D)	0.2 – 10 mm
εr	Relative dielectric constant of insulator	Unitless	1.0 – 10 (commonly 1.5 – 2.5)

Practical Examples (Real-World Use Cases)

Example 1: RG-58/U Coaxial Cable

RG-58/U is a common 50 Ohm coaxial cable. Let’s see if our Coaxial Line Impedance Calculator matches this. Typical dimensions for RG-58/U with a solid polyethylene dielectric are:

Outer conductor inner diameter (D): ~3.6 mm (approximate, depends on shield type)
Inner conductor outer diameter (d): ~0.9 mm
Dielectric constant (εr) for polyethylene: ~2.25

Using the formula: Z0 = (138 / √2.25) * log₁₀(3.6/0.9) = (138 / 1.5) * log₁₀(4) = 92 * 0.602 ≈ 55.4 Ohms. This is close to 50 Ohms, variations depend on the exact D and d values used in manufacturing and the shield construction which can affect the effective D.

Example 2: RG-6/U Coaxial Cable

RG-6/U is typically a 75 Ohm cable used for cable TV and satellite. Typical values with FPE (Foam Polyethylene) dielectric:

Outer conductor inner diameter (D): ~4.7 mm
Inner conductor outer diameter (d): ~1.0 mm
Dielectric constant (εr) for FPE: ~1.5 (foaming reduces it)

Using the Coaxial Line Impedance Calculator formula: Z0 = (138 / √1.5) * log₁₀(4.7/1.0) ≈ (138 / 1.225) * log₁₀(4.7) ≈ 112.65 * 0.672 ≈ 75.7 Ohms. Again, close to the nominal 75 Ohms.

How to Use This Coaxial Line Impedance Calculator

Enter Outer Diameter (D): Input the inner diameter of the outer conductor. Ensure you know the units (e.g., mm, inches).
Enter Inner Diameter (d): Input the outer diameter of the inner conductor, using the SAME units as for D.
Enter Dielectric Constant (εr): Input the relative dielectric constant (permittivity) of the insulating material between the conductors. This is unitless.
Calculate: Click the “Calculate” button or observe the real-time update if enabled.
Read Results: The primary result is the calculated characteristic impedance (Z0) in Ohms. Intermediate values like D/d ratio, √εr, and log₁₀(D/d) are also shown for clarity.
Interpret: The result tells you the characteristic impedance of the coaxial line with the given dimensions and material. This is crucial for matching to antennas, transmitters, receivers, or other lines to minimize reflections and power loss. Check out our Impedance Matching Calculator for more.

Key Factors That Affect Coaxial Line Impedance Results

D/d Ratio: The ratio of the outer conductor’s inner diameter to the inner conductor’s outer diameter is the most significant factor. A larger ratio increases impedance.
Dielectric Constant (εr): The material between the conductors greatly influences impedance. A higher dielectric constant lowers the impedance. Foaming the dielectric reduces its effective εr. Our Dielectric Materials Guide has more info.
Conductor Diameters (D and d): While it’s the ratio that primarily matters, the absolute values can be influenced by manufacturing tolerances, affecting the final impedance.
Uniformity: The formula assumes D, d, and εr are constant along the line’s length. Variations or imperfections will cause impedance bumps and reflections.
Frequency (Indirectly): While the basic formula is frequency-independent, at very high frequencies, skin effect confines current to the surface of conductors, and dielectric losses can become more significant. However, the characteristic impedance itself remains largely constant over the typical operating range. Learn about Transmission Lines Basics here.
Manufacturing Tolerances: Small variations in D, d, or the dielectric’s composition and density during manufacturing can lead to deviations from the nominal impedance.

Frequently Asked Questions (FAQ)

What are the most common coaxial line impedances?: The most common are 50 Ohms (used in RF, test equipment, and data communications) and 75 Ohms (used in video, cable TV, and satellite systems). 93 Ohms was also used in some older systems.
Why are 50 and 75 Ohms so common?: 50 Ohms is a good compromise between power handling capability and low loss. 75 Ohms offers very low loss and is well-suited for video signals.
How do I find the dielectric constant of my cable’s insulator?: You can usually find this in the cable’s datasheet or manufacturer’s specifications. Common materials are Polyethylene (PE, εr ~2.25), Foamed Polyethylene (FPE, εr ~1.5-1.8), Polytetrafluoroethylene (PTFE/Teflon, εr ~2.1), and Air (εr ~1.0006).
What units should I use for D and d in the Coaxial Line Impedance Calculator?: As long as D and d are in the SAME units (e.g., both in mm, or both in inches), the ratio D/d will be unitless, and the calculator will work correctly.
Does the length of the cable affect its characteristic impedance?: No, the characteristic impedance is a property per unit length and is independent of the total length, assuming the cable is uniform. However, total loss does depend on length (Signal Loss Calculator).
What happens if I connect cables with different impedances?: An impedance mismatch occurs, leading to signal reflections at the junction. This causes power loss, standing waves, and potential signal distortion. Impedance matching techniques are used to minimize this.
Can I measure the impedance with a multimeter?: No, you cannot measure characteristic impedance with a standard multimeter. It requires specialized equipment like a Time Domain Reflectometer (TDR) or a Vector Network Analyzer (VNA).
Is the formula accurate for all frequencies?: The formula is very accurate for the frequencies where coaxial cables are typically used (from kHz to many GHz). At very low frequencies, the cable behaves more like discrete components, and at extremely high frequencies, other effects might become more prominent.

Coaxial Line Impedance Calculator

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Results

Impedance vs. D/d Ratio (at εr = 2.25)

Impedance vs. D/d Ratio for Different Dielectrics