# RF Arbitrary Transmission Line Loss Calculator

## Calculator input form

 Ro: vf: Loss type: Loss/m k0, k1, k2 Conductor loss (dB/m): Dielectric loss (dB/m): k0: k1: k2: Length: metres wavelengths degrees picoseconds Frequency: MHz Mismatch:  None Zload Yload Zin GAMMAload Yin GAMMAin Source end VSWR Midpoint VSWR Load end VSWR Load end VSWR - bad case Zload Title: No symbols in output: New results window for each calc: Long output: Use Lint: 0 1 2

TLLC 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 supplied Ro, vf, k1 and k2 (explained below). 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; or

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 model used for matched line loss in a length of line is:

$Loss=(k_0+k_1 \sqrt f + k_2 f)l$

$$Loss=(k_0+k_1 \sqrt f + k_2 f)l$$

 Where Loss = loss per unit length f = frequency k1 = constant k2 = constant l = length

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. The model assumes:

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

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. The calculator shows the lowest frequency on which the loss model is based (Loss model source data frequency range), and results at or above that frequency should be reasonably accurate. Results may be usable below that frequency depending on the cable construction, for example the loss model for a generic RG6 cable based on data above 20MHz may be quite usable for lower frequency predictions provided the centre conductor is copper or has sufficient copper thickness. (See the notes on modelling loss.)

ATLLC does not attempt to model the transition region between DC and frequencies where developed skin effect is fully developed.

Fig 1 shows the (RLGC) modelled loss (red line) against the data points used for the regression (blue diamonds) for Belden 8262 (RG58C/U type coaxial line).

Fig 2 shows the modelled Ro (resistive component of Zo) of Belden 8262 against frequency.

Fig 3 shows the modelled Xo (reactive component of Zo) Belden 8262 against frequency.

## Implementation

The calculator involves this page and a results page which are 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. The model assumes that R is proportional to the square root of frequency (R=k1*f^0.5) which is a reasonable assumption where the conductor is homogenous to a depth of 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).

#### G

G is the shunt admittance and is usually considered to be a result of loss in the dielectric material. The model assumes that G is proportional to frequency (R=k2*f) which is a reasonable assumption for most dielectrics used for low loss cables. Ideally, G would depend on the permittivity (ε) and dielectric factor (D or tan(δ)), however it seems that modelled G is sometimes higher than that which suggests some other contribution to G. The dielectrics used for low loss cables have typically very low losses, dielectric loss factor is a very small number and anecdotally,  is sensitive to quality in the manufacture process.

### 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 loss 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.

## Examples

See ATLLC Examples.

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