Characteristic Impedance Calculator Cables

Characteristic Impedance Equation:

\[ z_0 = \frac{60 \times \ln\left(\frac{\text{outer\_d}}{\text{inner\_d}}\right)}{\sqrt{\epsilon_r}} \]

Outer Diameter (outer_d):

meters

Inner Diameter (inner_d):

meters

Relative Permittivity (er):

dimensionless

Characteristic Impedance (z0):

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1. What is Characteristic Impedance?

Characteristic impedance (z₀) is the ratio of voltage to current in a transmission line with no reflections. For coaxial cables, it depends on the geometry of the conductors and the dielectric material between them.

2. How Does the Calculator Work?

The calculator uses the characteristic impedance equation for coaxial cables:

\[ z_0 = \frac{60 \times \ln\left(\frac{\text{outer\_d}}{\text{inner\_d}}\right)}{\sqrt{\epsilon_r}} \]

Where:

\( outer\_d \) — Outer conductor diameter (meters)
\( inner\_d \) — Inner conductor diameter (meters)
\( \epsilon_r \) — Relative permittivity of the dielectric (dimensionless)

Explanation: The impedance increases with the ratio of outer to inner diameter and decreases with higher permittivity materials.

3. Importance of Characteristic Impedance

Details: Matching characteristic impedance is crucial for minimizing signal reflections and maximizing power transfer in RF systems. Common values are 50Ω (general RF) and 75Ω (video/cable TV).

4. Using the Calculator

Tips: Enter diameters in meters (convert from mm by dividing by 1000). Typical εᵣ values: ~2.3 for polyethylene, ~2.1 for PTFE, ~1 for air.

5. Frequently Asked Questions (FAQ)

Q1: Why is 50Ω common for RF systems?
A: It represents a compromise between power handling (lower impedance) and low loss (higher impedance) for air-dielectric coaxial lines.

Q2: What happens if impedances don't match?
A: Signal reflections occur, causing standing waves, power loss, and potential damage to transmitters.

Q3: Does frequency affect characteristic impedance?
A: For ideal coaxial cables, no. But real cables may show frequency-dependent effects at very high frequencies.

Q4: How does twisted pair impedance differ?
A: Twisted pair uses a different formula based on conductor size, spacing, and dielectric properties.

Q5: What's typical for PCB traces?
A: Microstrip/stripline impedances range 50-100Ω, calculated differently based on trace geometry and substrate.