Total Resistance of Coaxial Cable Calculator

Total Resistance of Coaxial Cable Formula:

\[ R_t = \frac{1}{2\pi\delta\sigma_c} \left( \frac{1}{a_r} + \frac{1}{b_r} \right) \]

Skin Depth (δ):

Electrical Conductivity (σc):

S/m

Inner Radius of Coaxial Cable (ar):

Outer Radius of Coaxial Cable (br):

Total Resistance of Coaxial Cable (Rt):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Total Resistance of Coaxial Cable?

The Total Resistance of Coaxial Cable is a measure of the opposition that the conductor of the coaxial cable presents to the flow of electric current. It accounts for both the inner and outer conductors' resistance, considering skin depth effects at high frequencies.

2. How Does the Calculator Work?

The calculator uses the coaxial cable resistance formula:

\[ R_t = \frac{1}{2\pi\delta\sigma_c} \left( \frac{1}{a_r} + \frac{1}{b_r} \right) \]

Where:

\( R_t \) — Total resistance of coaxial cable (Ω)
\( \delta \) — Skin depth (m)
\( \sigma_c \) — Electrical conductivity (S/m)
\( a_r \) — Inner radius of coaxial cable (m)
\( b_r \) — Outer radius of coaxial cable (m)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: The formula calculates the total resistance by considering the skin effect, which causes current to flow primarily near the surface of the conductor at high frequencies.

3. Importance of Total Resistance Calculation

Details: Accurate resistance calculation is crucial for signal integrity analysis, power loss estimation, and proper cable design in high-frequency applications. It helps in determining the attenuation characteristics and overall performance of coaxial cables.

4. Using the Calculator

Tips: Enter skin depth in meters, electrical conductivity in Siemens per meter, and both inner and outer radii in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is skin depth and why is it important?
A: Skin depth is the depth at which current density drops to 1/e of its surface value. It's crucial because at high frequencies, current flows mostly in a thin layer near the conductor surface, increasing effective resistance.

Q2: How does cable geometry affect total resistance?
A: Smaller radii result in higher resistance due to the inverse relationship in the formula. The combination of inner and outer conductor sizes determines the overall resistance.

Q3: What materials are commonly used in coaxial cables?
A: Copper is most common due to its high conductivity. Silver-plated copper and aluminum are also used in some applications for better performance or cost considerations.

Q4: How does frequency affect coaxial cable resistance?
A: As frequency increases, skin depth decreases, causing current to concentrate near the surface and increasing the effective resistance of the cable.

Q5: Are there limitations to this formula?
A: This formula assumes uniform current distribution within the skin depth and may not be accurate for extremely high frequencies or unusual conductor geometries where additional effects become significant.