# Coax

## Coax Calculator

### Inputs

Inner Conductor Diam.
D1
Inner Surface Shield Diam.
D2
Substrate Dielectric
Er

### Outputs

Impedance (Z):
Delay:
Inductance per inch:
Capacitance per inch:

#### Introduction

Perhaps the most common type of transmission line is the coax. The coax is a very nice way to create a transmission line. Understanding coax can be helpful when working with it. The nice part about coax is that it can be bent and flexible unlike most pcb transmission lines.

#### Description

The basic coax cable is constructed with an inner trace and a shield separated by dielectric. The property of coax that is nice is the transverse electric magnetic (TEM) mode, which means that the magnetic and electric fields are perpendicular to the direction of the wave propagation. The characteristic impedance is primarily determined by the distance from the conductor to the shield as well as the dielectric constant of material separating them.

#### Microstrip Transmission Line Models

Models have been created to approximate the characteristics of the microstrip transmission line.

The characteristic impedance of a coax is:

z_{o}=\frac{60}{\sqrt{er}}\cdot \ln \left ( \frac{d2}{d1} \right )

The time delay in ns/inch is:

delay = 84.72\cdot 10^{-12}\cdot\sqrt{er}\cdot \frac{1}{10^{-9}}

The inductance in nH/inch is:

inductance = 5.08\cdot 10^{-9}\cdot \ln \left ( \frac{d2}{d1} \right )\cdot \frac{1}{10^{-9}}

The capacitance in pF/inch is:

capacitance = 1.41\cdot 10^{-12}\cdot \ln \left ( \frac{d2}{d1} \right )\cdot \frac{1}{10^{-12}}

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