In my recent article RG6/U with CCS centre conductor – shielded twin study I made the point that it is naive to rely upon most line loss calculators for estimating the loss of this cable type partly because of their inability to model the loss at low HF and partly because of the confidence one might have in commonly available product. In that article I relied upon measured data for a test line section.
I have been asked if the nanoVNA could be bought to bear on the problem of measuring actual matched line loss (MLL). This article describes one method.
The nanoVNA has been OSL calibrated from 1-299MHz, and a 35m section of good RG6 quad shield CCS cable connected to Port 1 (Ch0 in nanoVNA speak).
A sweep was made from 1-30MHz with the far end open and shorted and the sweeps saved as .s1p files.
Above is a screenshot of one of the sweeps.
MLL can be calculated from the two sweep files.
#!/usr/bin/python3
import math
import cmath
import skrf as rf
import os
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
name='RG6-35'
len=35
nwo=rf.Network('RG6-35-o.s1p')
nws=rf.Network('RG6-35-s.s1p')
mll=np.sqrt(nws.z[:,0]/nwo.z[:,0])
mll=20*np.log10(np.absolute(((1+mll)/(1-mll))))/2/len
plt.figure(figsize=(10.24,7.68),dpi=100)
print(nwo.f.shape)
f=nwo.f/1e6
print(mll.shape)
def func(x,a,b):
return a+b*np.log(x)
popt, pcov = curve_fit(func,f,mll[:,0],bounds=((0,1)),maxfev=5000)
print(popt)
perr=np.sqrt(np.diag(pcov))
print(perr)
plt.xscale('log')
plt.plot(f,mll,label='Measured') plt.plot(f,popt[0]+popt[1]*np.log(f),label='MLL={:0.2e}+{:0.2e}ln(f/1e6)'.format(popt[0],popt[1]))
plt.ylabel('MLL (dB/m)')
plt.xlabel('Frequency (MHz)')
plt.title('Matched Line Loss - {}'.format(name))
plt.legend()
plt.ylim(0,None)
plt.savefig('{}-MLL.png'.format(name))
f=7.1
print(popt[0]+popt[1]*np.log(f))
Above is a snippet of Python code to perform the calculation and plot the results. On review of the plotted measured loss, it seems to be approximately linear on a plot with log x scale, so a least squares curve fit to y=a+b*ln(x) was done.
The slope of the curve is quit different to the traditional approximation of copper coax that \(MLL \propto \sqrt f\). In this instance \(MLL= 0.0300+0.00539 ln(f)\) (f in MHz) over this range.
Using the curve fit, the MLL at 7.1MHz is 0.0405dB/m whereas Simsmith calculates the loss for Belden 8215 (AC6LA) (a similar construction) at 0.0239dB/m, 59% of that based on measurement and curve fitting of this cable.
This demonstrates that it is relatively easy to make sufficiently good measurements of such a line using the nanoVNA, and that the approach is warranted in the case of this RG6 CCS cable at HF.
It is worth noting that Belden gives MLL for its 1694A solid copper centre conductor RG6 a 0.0201dB/m @ 7MHz, half of that of the measured CCS section. Unfortunately copper RG6 has become very expensive.