Please enter valid positive values. Ensure D is greater than d.
RESULTS
Diagrams & Theory
The system maps electromagnetic induction paths inside the insulation space separating concentric conductors under specific relative magnetic permeability constants.
Input Parameters Specification
Outer Diameter (D)
The inner shield opening diameter of the coaxial cable assembly, measured in millimeters (mm).
Inner Diameter (d)
The physical outer diameter thickness profile of the active center copper conductor core, in millimeters (mm).
Length (L)
The total linear length scale segment of the coaxial transmission line being analyzed, measured in millimeters (mm).
Relative Permeability (ur)
The magnetic permeability rating constant of the insulating dielectric substrate layer separating the conductor and shield.
Practical Operational Examples
Example 1: RG-58 Coaxial Transmission Line
• Outer Shield ID (D) = 2.95 mm | Inner Conductor OD (d) = 0.90 mm
• Cable Length (L) = 1000.00 mm | Relative Permeability (ur) = 1.00
• Calculated Loop Inductance: 2.37e-7 H | Integrated Value: 237.19 nH
Example 2: Foam Insulated Microwave Feedline
• Outer Shield ID (D) = 4.80 mm | Inner Conductor OD (d) = 1.13 mm
• Cable Length (L) = 500.00 mm | Relative Permeability (ur) = 1.00
• Calculated Loop Inductance: 1.45e-7 H | Integrated Value: 144.75 nH
Formulas & Mathematical Logic
L = (μ0 × μr / 2π) × ln(D / d) × Length
The mathematical passive pad solver evaluates structural impedance properties linearly using standard decibel voltage division multipliers to solve matrix loop parameters securely.
Step-by-Step Example
Example: Outer Diameter (D) = 10 mm, Inner Diameter (d) = 2 mm, Length (L) = 100 mm, Relative Permeability (ur) = 1.
Step 1: Convert all physical dimensions from millimeters to meters: D = 10 / 1000 = 0.01 m, d = 2 / 1000 = 0.002 m, and L = 100 / 1000 = 0.1 m.
Step 2: Calculate the natural logarithm of the diameter ratio: ln(D / d) = ln(0.01 / 0.002) = ln(5) = 1.609438.
Step 3: Solve the coaxial cable inductance using the standard physical equation: Inductance = (4 * pi * 10^-7 * ur / (2 * pi)) * ln(D / d) * L = (2 * 10^-7) * 1.609438 * 0.1 = 3.218876e-8 H.
Step 4: Convert the raw inductance value to nanohenries (nH) for practical RF applications: Inductance = 3.218876e-8 * 10^9 = 32.19 nH.
Result: The calculated parameters are Inductance = 3.22e-8 H (or 32.19 nH), establishing the characteristic magnetic storage threshold.
How to Use This Calculator
Enter the outer diameter of the coaxial shield in the D / Outer Diameter input field in millimeters (mm).
Enter the external diameter of the inner conductor in the d / Inner Diameter input field in millimeters (mm).
Input the total physical length of the coaxial cable segment in the L / Length field in millimeters (mm).
Input the relative magnetic permeability of the insulating dielectric substrate (ur, default is 1 for non-magnetic media).
Click the orange Calculate button to initiate the electromagnetic induction solver.
Read the computed values for Inductance in both Henries (H) and nanohenries (nH) displayed on the colored Results cards.
About This Calculator
Determine high-frequency coaxial cable parasitic inductance with precision.
The CalcBoy Coax Inductance Calculator evaluates the total loop inductance of a coaxial transmission line segment using its physical cross-sectional boundaries, length, and substrate relative permeability.
Every electrical conductor carrying a time-varying alternating current (AC) experiences self-inductance due to the magnetic flux lines linking the current path. In coaxial cables, which consist of an inner wire wrapped inside a cylindrical outer shield, the magnetic flux is concentrated entirely within the insulating dielectric medium sandwiched between the conductors. Calculating this loop inductance is a fundamental task in RF engineering, high-speed printed circuit board (PCB) design, and electromagnetic compatibility (EMC) testing.
The loop inductance per unit length is set strictly by the geometric ratio of the outer shield diameter (D) to the inner conductor diameter (d), multiplied by the magnetic permeability of the dielectric substrate. This calculator uses these geometric inputs and the total cable length to compute both the raw inductance in Henries (H) and the standard radio frequency unit of nanohenries (nH). These parameters are vital for modeling transmission line impedance (Zo), predicting signal propagation velocity, and designing matching networks.
Best UseRF circuit planning, coaxial line selection, and parasitic loop inductance modeling.
Key OutputTotal cable loop inductance in Henries (H) and nanohenries (nH).
Crucial PhysicsConcentrating magnetic flux inside the dielectric limits external magnetic coupling and emissions.
Design RuleA smaller outer-to-inner diameter ratio decreases loop inductance, which increases capacitance.
Tip: Most coaxial cables use non-magnetic dielectrics like polyethylene or Teflon, which have a relative permeability (ur) of exactly 1. Do not increase this value unless using specialized magnetic cores.
Frequently Asked Questions
What physically causes loop inductance in a coaxial cable?
Loop inductance is caused by the magnetic fields generated around the inner conductor when it carries AC current. Because the return current flows in the opposite direction along the outer shield, the magnetic fields are confined entirely to the space between the conductors, creating a loop inductance that stores magnetic energy.
Why does the ratio of outer to inner diameter (D/d) affect inductance?
The distance between the conductors defines how much space is available for the magnetic flux lines to form. A larger outer diameter (D) relative to the inner diameter (d) increases the cross-sectional area of the dielectric, allowing more magnetic flux to link the conductors, which directly increases loop inductance.
How does relative permeability (ur) impact the calculated inductance?
Relative permeability represents how easily a material allows magnetic fields to form inside it. Introducing magnetic materials (ur > 1) inside the coaxial space increases the magnetic flux density for a given current, multiplying the total inductance. For standard RF cables, this value is 1.
What is the relationship between coaxial inductance and characteristic impedance?
Coaxial characteristic impedance (Zo) is mathematically defined as Zo = sqrt(L / C). Because a larger diameter ratio (D/d) increases loop inductance (L) and decreases capacitance (C), it directly increases the characteristic impedance of the cable.
Can this calculator be used for high-frequency microwave lines?
Yes. The fundamental inductance equations are highly accurate from low frequencies up to the gigahertz range, provided the cable is operating in its dominant transverse electromagnetic (TEM) propagation mode.
What happens if the inner diameter (d) is larger than the outer diameter (D)?
This is physically impossible for a coaxial cable because the inner conductor must fit inside the outer shield. The calculator will trigger an error if the input parameters do not satisfy the boundary condition of D > d.
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