Coaxial Line Impedance Calculator
Professional RF Engineering Tool
Calculate Impedance (Z₀)
Determine the characteristic impedance, capacitance, and inductance of a coaxial transmission line.
The inside diameter of the outer conductor (shield) in millimeters.
The outside diameter of the center conductor in millimeters.
Select standard material or enter custom dielectric constant.
Characteristic Impedance (Z₀)
0.00 Ω (Ohms)
Capacitance
Inductance
Velocity Factor
Cutoff Frequency (Approx)
Formula Used: Z₀ = (60 / √εᵣ) × ln(D / d)
Impedance vs. Inner Diameter Ratio
Showing how Impedance (Z₀) changes as Inner Conductor Diameter (d) varies (keeping D constant).
Common Dielectrics Comparison
| Material | Dielectric Constant (εᵣ) | Impedance (Z₀) | Velocity Factor |
|---|
Calculated using current dimensions (D and d).
What is a Coaxial Line Impedance Calculator?
A coaxial line impedance calculator is a specialized RF engineering tool designed to determine the characteristic impedance of a coaxial transmission line based on its physical geometry and material properties. Understanding impedance is critical for minimizing signal reflection, maximizing power transfer, and ensuring the efficient operation of radio frequency (RF) systems.
This tool is essential for electrical engineers, antenna designers, and PCB layout specialists who work with transmission lines. Unlike generic resistance calculators, a coaxial line impedance calculator accounts for the complex interaction between inductance and capacitance per unit length, which determines how RF signals travel through the cable.
Common misconceptions include assuming that cable impedance depends on the length of the cable. In reality, characteristic impedance is independent of length; it is determined solely by the ratio of the conductor diameters and the dielectric material separating them.
Coaxial Line Impedance Formula and Mathematical Explanation
The calculation of characteristic impedance (Z₀) for a coaxial line uses the physical dimensions of the conductors and the electrical properties of the insulating material. The standard formula used in this calculator is derived from Maxwell’s equations applied to a coaxial geometry.
The primary formula is:
Z₀ = (60 / √εᵣ) × ln(D / d)
Alternatively, using Log base 10:
Z₀ ≈ (138 / √εᵣ) × log₁₀(D / d)
Variable Definitions
| Variable | Meaning | Typical Range |
|---|---|---|
| Z₀ | Characteristic Impedance (Ohms) | 50Ω, 75Ω (Standard) |
| D | Inner Diameter of Outer Shield | 2mm – 50mm |
| d | Outer Diameter of Inner Conductor | 0.5mm – 10mm |
| εᵣ (Epsilon_r) | Dielectric Constant (Relative Permittivity) | 1.0 (Air) – 4.4 (FR4) |
| ln | Natural Logarithm | Mathematical Function |
Intermediate Value Formulas
- Capacitance (C): C’ ≈ (24.13 × εᵣ) / log₁₀(D/d) [pF/m]
- Inductance (L): L’ ≈ 460 × log₁₀(D/d) [nH/m]
- Velocity Factor (VF): VF = 1 / √εᵣ
Practical Examples (Real-World Use Cases)
Example 1: Designing a 50Ω Coaxial Cable
A standard RG-58 type cable is required for a radio transmitter. The design goal is exactly 50 Ohms to match the antenna system.
- Inner Conductor (d): 0.9 mm
- Outer Shield Inner Dia (D): 2.95 mm
- Dielectric: Solid Polyethylene (εᵣ = 2.25)
- Calculation:
Ratio D/d = 3.277
ln(3.277) ≈ 1.187
Multiplier = 60 / √2.25 = 60 / 1.5 = 40
Z₀ = 40 × 1.187 ≈ 47.5 Ohms - Interpretation: This geometry results in an impedance slightly lower than 50Ω. To reach 50Ω, the engineer might need to slightly increase D or decrease d.
Example 2: 75Ω Video Cable (Air Dielectric)
Designing a high-quality rigid line for a TV transmitter station where low loss is critical, so air is used as the dielectric.
- Inner Conductor (d): 6 mm
- Outer Shield Inner Dia (D): 21 mm
- Dielectric: Air (εᵣ ≈ 1.0)
- Calculation:
Ratio D/d = 3.5
ln(3.5) ≈ 1.252
Multiplier = 60 / 1.0 = 60
Z₀ = 60 × 1.252 ≈ 75.1 Ohms - Interpretation: This is an excellent match for 75Ω video systems, ensuring minimal ghosting or signal reflection in the broadcast chain.
How to Use This Coaxial Line Impedance Calculator
Using this coaxial line impedance calculator is straightforward, but accuracy in inputting dimensions is crucial.
- Measure Dimensions: Use a caliper to measure the inner diameter of the outer shield (D) and the outer diameter of the center conductor (d). Ensure both are in the same unit (e.g., millimeters).
- Select Material: Choose the dielectric material from the dropdown. If you are using a proprietary foam or composite, select “Custom” and enter the specific dielectric constant found in the material datasheet.
- Review Impedance: The main result will show the Characteristic Impedance (Z₀). Check this against your target (usually 50Ω for RF power or 75Ω for video/signals).
- Analyze Intermediate Values: Check the Capacitance and Inductance per meter. These are vital for timing simulations and signal integrity analysis.
- Check Cutoff Frequency: Ensure your operating frequency is well below the approximate cutoff frequency displayed to avoid higher-order propagation modes.
Key Factors That Affect Coaxial Line Impedance Results
Several physical and environmental factors influence the impedance of a coaxial line. Understanding these helps in troubleshooting and advanced design.
- Dielectric Constant (εᵣ): A higher dielectric constant increases capacitance and lowers impedance. Replacing air (εᵣ=1) with solid plastic (εᵣ=2.3) will drop the impedance significantly if dimensions remain unchanged.
- Diameter Ratio (D/d): This is the most sensitive factor. A small change in the inner conductor size has a logarithmic effect on impedance. Tighter manufacturing tolerances are required for high-frequency cables.
- Temperature: Extreme temperatures can expand or contract the dielectric material, altering the D/d ratio and slightly changing the dielectric constant, leading to impedance drift.
- Frequency Dependence (Skin Effect): While characteristic impedance is theoretically constant at high frequencies, at lower frequencies (near DC), the resistance of the conductors plays a larger role, causing Z₀ to rise slightly.
- Manufacturing Eccentricity: If the inner conductor is not perfectly centered within the shield, the effective impedance drops, and the cutoff frequency decreases.
- Air Gaps: In braided cables, air gaps between the dielectric and the shield effectively lower the average dielectric constant, increasing the impedance slightly compared to a theoretical solid shield model.
Frequently Asked Questions (FAQ)
50 Ohms is a compromise between power handling and signal loss. Historically, 30Ω was best for power, and 77Ω was best for lowest loss (for air dielectric). 50Ω was chosen as a standard “middle ground” for general RF work.
No. Characteristic impedance is a property of the cable’s geometry and material, not its length. A 1-meter cable and a 100-meter cable of the same type have the same Z₀ (e.g., 50Ω).
If the cable impedance (Z₀) does not match the source or load impedance, signal reflections occur. This leads to a high Standing Wave Ratio (VSWR), power loss, and potential damage to transmitters.
The formula assumes a solid outer conductor. For braided shields, the effective “D” is slightly variable, and the effective dielectric constant might be lower due to air gaps. The results are typically accurate within 5% for high-coverage braids.
No. This coaxial line impedance calculator is strictly for coaxial geometries (one conductor inside another). Twin-lead requires a different formula involving the distance between two parallel wires.
Velocity Factor (VF) represents the speed of the signal relative to the speed of light in a vacuum. A VF of 0.66 means the signal travels at 66% of the speed of light.
Consult the manufacturer’s datasheet. Common values are 2.1 for PTFE (Teflon), 2.2-2.3 for Polyethylene (PE), and roughly 1.4-1.6 for foam dielectrics.
It is the frequency above which the coaxial cable begins to support waveguide modes (TE11) rather than just the TEM mode. Using the cable above this frequency results in unpredictable signal behavior and high losses.