# Finding the inductance of the outside of LDF4-50A

There are applications for estimating the inductance of the outside of LDF4-50A at radio frequencies.

For the purpose of calculating the inductance, the geometric mean radius is appropriate. This article offers two methods for estimating the geometric mean diameter (GMD) of the conductor. Above a section of LDF4-50A. Above is a magnified view of the profile, it is corrugated copper outer conductor with a shallow but not quite symmetric profile.

## Method 1

Method 1 finds the GMD of the inside of the shield from the key line parameters Z0, VF, and diameter of the inner conductor.

# RF Coaxial Transmission Line Loss Calculator

## LDF4-50A

Parameters
Conductivity 5.800e+7 S/m
Rel permeability 1.000
Inner diameter 0.00460 m
Outer diameter 0.01187 m
Velocity factor 0.880
Loss tangent 0.000e+0
Frequency 10.000 MHz
Length 100.000 m
Results
Zo 50.02-j0.17 Ω
Velocity Factor 0.8800
Length 1364.58 °, 3.791 λ, 100.0000 m, 3.791e+5 ps
Line Loss (matched) 0.690 dB

If we take the shield thickness to be 0.35mm, that would suggest an effective outside diameter of 11.87+0.7=12.6mm

## Method 2

The second method is to integrate the log of radius over the profile length, and then calculate GMR as the exponent of average log of radius, and GMD is twice GMR.

To perform this integration we must develop a function for the profile. Integrations were performed on two similar profiles, a sine profile and an eliptical profile, and they yielded almost equal results so the result is not very sensitive to the profile. It is however sensitive to the symmetry, and the actual profile is not quite symmetric, but it is relatively shallow and so the error should be relatively small.

Method 2 gave a GMD of 12.8mm which is less than 1% different to the mean diameter.

## Conclusions

Method 1 and Method 2 produce results that differ by less than 2%.

For practical purposes, inductance depends on GMD which for shallow fairly symmetric profiles is approximately equal to the mean diameter ((MajorDiameter+MinorDiameter)/2) which can be determined quite easily with a pair of calipers.

The estimated GMD can then be used in inductance calculations, and inductance is even less sensitive to the error in GMD.