# Transmission Line (Cable) SPICE Model

Characteristic Impedance (Ohm)
Velocity ratio (0.66 for PE insulation)
Attenuation constant at below frequency (dB/m)
frequency defining the above attenuation (MHz)
highest frequency of transmission signal spectrum (MHz)
length of the cable (m)
Model accuracy
Model type

The circuit simulator SPICE has built-in Lossless Transmission Lines (T), Lossy Transmission Lines (O) and Uniform Distributed RC Lines (U) Model. However both T and U model does not cosider frequency-dependent conductor resistance. So it is not possible to calculate the transmossion characteristic of the long cable.

This form generates adequate SPICE model for real taransmission line of specfied attenuation and length.

The velocity raio is the ratio of the phase velocity of the electromagnetic wave propergating througu the cable to the speed of light in vacuum. This value is determined by the dielectric constant of cable insulation as following relation.

```  Vr = 1 / sqrt(k)
Where
Vr = velocity ratio (0 < Vr <= 1)
k = relative dielectric constant
= 2.3 (PE - Polyethylene insutation)
= 1.5 (CPE - Celler/foamed Polyethylene insutation)
= 2.1 (PTFE, PFA, FEP fluorocarbon polymer insulation)
= 1.0 (Aire insulation)
..
```
If insulation of the cable is composed of two or more dielectric materials, it uses the equivalent dielectric constant which is determind actual measurement or computed value by the finit element method etc.

Frequency that defines the attenuation must be at several tens of MHz or higher.

The highest frequency of transmission signal spectrum is the highest frequency limit of this SPIE model. If this value is not sure, please be calculated by the following equation.

```  The highest frequency = 0.35 / the raise time of the pulse / 1e6 (MHz)
```
For example, if the rise time is 25 nS, this frequency is about 14 MHz.

The precision of this model is about 2 % in the high accuracy model, about 6 % in the statndard accuracy model, about 12 % in the low accuracy model.

This model can apply wide range of transmission lines dielectric losses are negligible in comparison with the conductor loss, including coaxial cables, twin leads and strip lines.

Kouichi Hirabayashi, 2003-10