RF Two Wire Transmission Line Loss Calculator
Calculator input form
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 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. The model assumes:
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.
TWLLC does not attempt to model the transition region between DC and frequencies where developed skin effect is fully developed.
The calculator involves this page, and a results page which is written in php and include some java scripting..
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 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.
Calculation of Characteristic Impedance
Characteristic impedance is calculated as Zo=120acosh(D/d). This does not include proximity effect, which will result in an underestimated of Zo for D/d<2 (Zo<160Ω), and the error may become significant.
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.
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 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.
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© Copyright: Owen Duffy 1995, 2012. All rights reserved. Disclaimer.