Coaxial Line Parameter Calculator
Use this calculator to determine the characteristic impedance, velocity factor, capacitance, inductance, and propagation delay per unit length for a coaxial transmission line based on its physical dimensions and dielectric material.
Calculated Parameters:
Understanding Coaxial Transmission Lines
A coaxial cable, often simply called a coax, is a type of electrical cable consisting of an inner conductor surrounded by a concentric conducting shield, with the two separated by a dielectric insulating material. Many coaxial cables also have an insulating outer sheath or jacket for protection.
Coaxial cables are widely used for transmitting radio frequency (RF) signals, such as in television distribution, broadband internet, and various communication systems. Their design provides excellent shielding against external electromagnetic interference and minimizes signal leakage, making them ideal for high-frequency applications.
Key Parameters Explained:
- Characteristic Impedance (Z0): This is one of the most critical parameters of a transmission line. It represents the impedance that an infinitely long line would present to a signal. For coaxial cables, common characteristic impedances are 50 Ohms (for RF and data communication) and 75 Ohms (for video and broadcast applications). Matching the source and load impedance to the characteristic impedance of the cable is crucial to prevent reflections and maximize power transfer.
- Velocity Factor (VF): The velocity factor is the ratio of the speed at which an electromagnetic wave travels through the cable to the speed of light in a vacuum. It is always less than 1 because the dielectric material slows down the signal. A higher velocity factor means faster signal propagation.
- Capacitance per Unit Length (C): This parameter describes how much electrical charge the cable can store per unit of its length. It's influenced by the dielectric constant and the physical dimensions of the conductors. Measured in Farads per meter (F/m) or more commonly picoFarads per meter (pF/m).
- Inductance per Unit Length (L): This parameter describes the magnetic field energy stored per unit length of the cable when current flows through it. It's also influenced by the physical dimensions. Measured in Henries per meter (H/m) or nanoHenries per meter (nH/m).
- Propagation Delay per Unit Length (Td): This is the time it takes for a signal to travel a certain distance along the cable. It's directly related to the velocity factor and is crucial for timing-sensitive applications, especially in digital systems. Measured in seconds per meter (s/m) or nanoSeconds per meter (ns/m).
How the Calculator Works:
This calculator uses the following inputs to determine the coaxial line parameters:
- Inner Conductor Diameter (d): The diameter of the central wire.
- Outer Conductor Inner Diameter (D): The inner diameter of the outer shield.
- Dielectric Constant (εr): A dimensionless value representing the permittivity of the insulating material relative to the permittivity of a vacuum. Common values range from 1.0 (for air/vacuum) to around 2.2-2.3 (for solid polyethylene) or 1.5-1.7 (for foamed polyethylene).
The formulas used are derived from electromagnetic theory for transmission lines:
- Z0 = (138 / √εr) × log10(D/d) (Ohms)
- VF = 1 / √εr (Unitless)
- C = (55.63 × εr) / log10(D/d) (pF/meter)
- L = (460.5 × log10(D/d)) (nH/meter)
- Td = (3.33 × √εr) (ns/meter)
Practical Examples:
Let's consider some common coaxial cable types:
- RG-58 (50 Ohm):
- Inner Conductor Diameter (d): ~0.81 mm
- Outer Conductor Inner Diameter (D): ~2.95 mm
- Dielectric Constant (εr) for solid PE: ~2.25
- Using the calculator with these values should yield Z0 close to 50 Ohms.
- RG-59 (75 Ohm):
- Inner Conductor Diameter (d): ~0.58 mm
- Outer Conductor Inner Diameter (D): ~3.71 mm
- Dielectric Constant (εr) for solid PE: ~2.25
- Using the calculator with these values should yield Z0 close to 75 Ohms.
- Low-Loss Coax with Foamed Dielectric:
- Inner Conductor Diameter (d): ~2.74 mm
- Outer Conductor Inner Diameter (D): ~9.40 mm
- Dielectric Constant (εr) for foamed PE: ~1.5
- This would typically result in a 50 Ohm cable with a higher velocity factor due to the lower dielectric constant.
By adjusting the dimensions and dielectric material, engineers can design coaxial cables with specific characteristic impedances and propagation characteristics for various applications.