# Twisted Pair

Twisted Pair Cable Impedance Calculator

## Twisted Pair Calculator

### Inputs

Diameter of Wire
D
Seperation Between Wires
S
Substrate Dielectric
Er

### Outputs

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

#### Introduction

Two conductors can create a transmission line. To make an effect transmission line with two wires it is best to create a twisted pair. Often when working with wires it is easy to create large return path loops if one is not paying close attention. The twisted pair helps create a more uniform inductance and capacitance per unit length of wire to ensure a constant impedance, by keeping the return path as close to the signal as possible.

#### Description

The geometries of the twisted pair that we should pay close attention too are the distance between the two conductors (center to center) and the diameter of the conductive wire. The effective permittivity of the material between the two conductors will be somewhere between the permittivity of the insulation on the wires and the relative permittivity of air (1).

#### Characteristic Properties of the Twisted Pair

Characteristic Impedance The characteristic impedance of the twisted pair is the impedance a signal will see as it travels down the conductor.

Propagation Delay The propagation delay of the signal is the time it takes for the signal to travel a specific distance. This tool calculates the time delay in inches per nanosecond.

Inductance Per Unit Length The inductance of the signal is valuable to know. Especially when creating a model for the transmission line in a simulation tool. This tool calculates the inductance in nano-henrys per inch

Capacitance Per Unit Length The capacitance of the signal is often need when creating a model for the transmission line in a simulation tool. This tool calculates the capacitance in pico-farads per inch

#### Twisted Pair Transmission Line Models

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

zo_{twistedpair}(ohms)=\frac{120}{\sqrt{er}}\cdot \ln \left [ \frac{2s}{d} \right ]

delay\left ( \frac{ns}{inch} \right )=84.72\cdot10^{-3}\cdot \sqrt{er}

L_{twistedpair}\left ( \frac{nH}{inch} \right )=10.16\cdot 10^{-9}\cdot \ln \left [ \frac{2s}{d} \right ]

C_{twistedpair}\left ( \frac{pF}{inch} \right )=\left ( \frac{.7065}{\ln \left ( \frac{2s}{d} \right )} \right )\cdot er

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