Line loss is composed of conductor (wire) loss and insulation (dielectric) loss. Conductor loss increases (very closely) in proportion to the square root of frequency, whereas insulation loss increases (very closely) in direct proportion to frequency. The total matched line loss at any frequency is given by the formula
ML(dB) = K1 * SQRT(Freq) + K2 * Freq
where (in this case):
ML is in dB / 100 feet,
Freq is in MHz, and
K1,K2 depend on the characteristics of the line.
Given two or more pairs of frequency and loss values, it is possible to compute a "least squares" best fit for K1 and K2 using multiple linear regression with "SQRT(Freq)" as one independent variable and "Freq" as a second independent variable. The BestFit workbook uses the Excel LINEST function to do this computation.
For example, the following BestFit partial screen capture shows a table (blue border) with the manufacturer's specifications for Belden 9258 (RG-8X). As each data pair is entered the workbook will compute the values (red border) for K1 and K2. Also shown are the C1 and C2 coefficients, which may be used with those modeling programs which expect to have the loss coefficients expressed in terms of GHz and dB/meter as opposed to MHz and dB/100 feet. (Ansoft Serenade and ARRL Radio Designer are two such programs.)
BestFit has a chart sheet showing the matched line loss per the specification points (blue markers) and as computed using the K1 and K2 coefficients (red line). This chart is similar to those shown in the ARRL Antenna Book and other references dealing with transmission lines.
Note that the "Best Fit" line does not pass exactly through each of the specification points. However, the K1 and K2 coefficients have been calculated to minimize the combined delta between the specification points and the computed points. For this particular transmission line, as an example, the manufacturer's specification at 10 MHz is 0.98 dB/100 feet while the computed value is approximately 0.91 dB/100 feet. These small differences will usually have no practical significance and in fact may be well within ordinary manufacturing tolerances. If desired, you may use the K1/K2 button on the Transmission Line Details screen to explicitly set the Matched Loss to any value, in order to determine the effect of such small differences.
The BestFit workbook contains the manufacturer's specifications for all the transmission lines that are built-in to the TLDetails stand-alone program. By doing some copy/paste operations you may transfer this data to the table (blue border) and thus produce a chart showing how well the "per K1,K2" curve matches the "per spec" points. BestFit may also used to determine K1 and K2 for user-defined lines in TLDetails. Merely enter the manufacturer's loss specifications into the table, then enter the K1 and K2 values into the appropriate text boxes.
Caution: The computed values for K1 and K2, like all computed results in the TLDetails program, are shown with a precision of a few digits beyond what is reasonable in normal engineering practice. This is done to allow you to spot trends and do theoretical studies. Don't allow yourself to become overly concerned with the exact values for K1 and K2. The loss characteristics for any transmission line will vary with manufacturing tolerances, age, bending, exposure to heat and sunlight, and even changes in the ambient temperature. The values used here, and indeed in any modeling package, must be considered as "best guess" estimates of the actual attenuation for any given line.
Download a zip file containing the BestFit workbook (14 KB). Free. Requires Excel 97 or later.