# RF Two Wire Transmission Line Loss Calculator

## Calculator input form

 Conductivity (ρ): S/m Conductor relative permeability (μr): Conductor diameter (d): mm Centre to centre distance (D): mm Twist rate (t/m): Velocity factor (pu): Dielectric loss tangent (τ): Length: metres wavelengths degrees picoseconds Frequency: MHz Mismatch:  None Zload Yload Zin GAMMAload Yin GAMMAin Source end VSWR Midpoint VSWR Load end VSWR Title: No symbols in output: New results window for each calc: Long output:

TWLLC Help

There is a suite of related transmission line loss calculators:

## Overview

This calculator computes the matched line loss for a transmission line using a model calibrated from data for the transmission line supplied to the calculator. It also gives an estimate of the mismatched loss if the mismatch is specified. Mismatch can be specified as:

• the impedance at the load end of the line;
• the impedance looking into the line from the source;
• the admittance looking into the line from the source;
• the VSWR at the source end of the line;
• the VSWR at the midpoint of the line; or
• the VSWR at the load end of the line.

The calculation of loss using VSWR is an approximation that is reasonably accurate on long lines with low VSWR and low loss. The methods using the impedance of the load or looking into the line produce accurate answers, and are the only way to get reasonably accurate answers with high VSWR or short lines.

The calculator also computes an estimate of the complex characteristic impedance implied by the loss model, nominal Ro, and velocity factor using an RLGC model. At high frequencies, the model assumes:

• R is proportional to square root of frequency;
• L is constant;
• G is proportional to frequency; and
• C is constant.

Adjustments are made for conductor internal impedance in accordance with David Knight's Rac-TED-ML and Li-ACA-3.05 to improve accuracy in the transition region.

These are reasonable assumptions for most practical transmission lines with homogenous conductors down to perhaps 100kHz, depending on line construction. Transmission lines that use conductors that are not homogenous, eg copper clad steel, silver plated copper clad steel, will not conform to the loss model at low frequencies where the outer layer of the conductor is less than a few skin depths in thickness.

## Implementation

The calculator involves this page, and a results page which is written in php and include some java scripting..

## Notes

### Modelling losses

#### R

R is the series resistance in the conductors and is subject to skin effect and proximity effect. The model assumes that the conductor is homogenous to a couple of times the skin depth. That assumption may not be valid at very low frequencies for plated conductors (tinned copper, copper plated steel), laminated or clad conductors (copper clad aluminium, copperweld). A proximity resistance correction is calculated using an algorithm from the program line_zin.pas by Reg Edwards (G4FGQ).

#### G

G is the shunt admittance and is usually considered to be a result of loss in the dielectric material. It is calculated from the Loss Tangent input.

### Mismatched loss

Mismatched loss or loss due to standing waves can be determined accurately knowing the propagation constant (γ) of the line and the complex reflection coefficient (Γ) at a known point on the line. An approximation of the mismatch loss can be made using the propagation constant (γ) and VSWR (which depends only on the magnitude of the complex reflection coefficient (Γ) that is reasonably accurate only on medium length lines with low VSWR and low loss.

### Using k1 and k2 in other programs

Many other programs use the same type of model for transmission line loss. When mismatch=None, the calculator displays the values of k1 and k2 based on distance in metres and frequency in Hz, and C1 and C2 based on metres and GHz.

To use the values of k1 and k2 in other calculators, you may need to adjust the values.

### Errors

The calculator works with precision greater than the probable accuracy of the model or the source data. The results can be no better than the accuracy of the source data.

The calculator derives an RLGC model from the supplied data, and all calculated values are derived consistently from that RLGC model.

The accuracy of the modelling technique depends on compliance with the stated assumptions and the accuracy of the specified data.

Transmission line manufacturing tolerances are the most likely cause of the greatest error for new transmission lines, and for those that have been in service, degradation (eg ingress of water, contamination of dielectric, physical distortion, stretching, crushing etc) is a potential further source of significant error.

### Results window

Results are returned in a separate window. Each instance of the calculator uses its own output window, so different scenarios can be explored in separate browser instances of the calculator and they will return results in separate results windows. The "New results window for each calc" switch on the calculator form will force new results into a new results window. If the calculator window is refreshed, results will be written to a new results window.

V1.01. Use at your own risk, not warranted for any purpose. Do not depend on any results without independent verification.