Above is an analysis of KN5L’s published measurements of a 19.93m test section of Seminole 1320 (nominal 300Ω windowed ladder line, 0.812mm (#20) 7 strand copper). The line was purchased around 2015. The plot has:
It can be seen that:
Above is an analysis of KN5L’s published measurements of a 14.54m test section of Seminole 1321 (nominal 300Ω windowed ladder line, 1.024mm (#18) 19 strand copper clad steel). The line was purchased around 2015. The plot has:
It can be seen that:
The measured MLL at 1MHz is 0.12dB/m.
Above is a model of current distribution in a 1.024mm (#18) round CCS conductor with cladding equal to that of the component 0.255mm (#30) strands 30% IACS (17.8µm) as an approximation of the #30×19 conductor. That model suggests that the MLL is 0.11dB/m. We can fully expect that the loss of a stranded conductor will be a little higher, so measurement and prediction reconcile reasonably well.
Loss of ladder line: copper vs CCS (DXE-LL300-1C) – revised for 25/07/2018 datasheet was a revision of an earlier article based on an updated datasheet from DXE. I noted that the specification data had artifacts that one would not expect of such a line, and I questioned whether the datasheet was credible.
John, KN5L, recently purchased, measured and published measurements of a 10.06m (33′) section of new DXE-LL300-1C which provide an independent dataset that might cast some light on the matter.
The chart above plots:
The theoretical line is based on well developed skin effect and \(MLL \propto \sqrt f\), resulting in a straight line on the log-log graph.
KN5L’s 100 point measurement dataset is for the most part smooth and quite credible, though it shows departure from ideal homogenous conductors with well developed skin effect… and for good reason, these are not homogenous conductors and skin effect is only developed at higher frequencies.
At 60MHz, KN5L’s measured MLL is a little worse than theoretical, quite probably due to the fact that these are 19 strand conductors, and the cladding thickness may be just too little to deliver copper like performance even at 60MHz. At lower frequencies, MLL is better, but a good deal worse than the theoretical MLL for copper conductors.
Whilst the MLL might seem small, these types of line are commonly used in scenarios with high VSWR. Let’s calculate the loss under mismatch of a scenario used for some recent articles.
The scenario then is the very popular 132′ multi band dipole:
We will consider the system balanced and only deal with differential currents.
Taking the MLL of the LL300 as 0.018dB/m, the calculated loss under mismatch is 2.3dB. It is not huge, but any assumption that the loss in open wire line is insignificant is wrong.
Lets evaluate the loss using a home made open wire line of 2mm copper conductors spaced 150mm. The calculated loss under mismatch is 0.114dB, a lot better than the previous case.
]]>The original scenario then is the very popular 132′ multi band dipole:
We will consider the system balanced and only deal with differential currents, and matched line loss is based on measurement of a specific sample of line (RG6/U with CCS centre conductor at HF).
This article will calculate the same scenario with three feed line variants:
The loss under mismatch depends not only on the transmission line characteristics and length, but also on the load and the current and voltage distribution.
Above the 150Ω twin line with same CCS conductors as the RG6 has loss almost identical to the synthesised twin shielded in the original article. Almost all of the resistance in the coax is in the CCS centre conductor, so I assume that the loss in the twin CCS is approximately equal to that of the synthesised twin. Dielectric loss is less than 1% and can be ignored.
Above the 600Ω twin line with same CCS conductors as the RG6 (ie the spacing is increased to increase Zo). Almost all of the resistance in the coax is in the CCS centre conductor, so I simply assume that the 600Ω twin line with same CCS conductors has 150/600 times the matched line loss. The loss is considerably lower at 0.354dB in this scenario, due to the higher Zo.
Above the 600Ω twin line with 2mm HDC. The loss is considerably lower again at 0.061dB in this scenario, due to the higher Zo.
Note that in all these cases, the load impedance and length of the line form an important part of the evaluation scenario.
So, we can identify that two factors result in the quite poor performance of the synthesised shielded twin:
Improving both of these factors in the third scenario reduces loss under this mismatch scenario by a factor of 50.
]]>These were very popular at one time, but good voltage baluns achieve good current balance ONLY on very symmetric loads and so are not well suited to most wire antennas.
Above is a pic of the balun with load on test. It is not the greatest test fixture, but good enough to evaluate this balun over HF.
Mine has survived, but many users report the moulding cracking and rusted / loose terminal screws, and signs of internal cracks in the ferrite ring.
InsertionVSWR is often an important parameter of nominally 1:1 baluns. So, let’s measure the balun’s InsertionVSWR by connecting it to Port 0 (Ch0) and connecting a good 50+j0Ω load to the output terminals.
Above is a sweep from 1-41MHz, Insertion VSWR looks pretty good above about 7MHz and up to about 20MHz.
Let’s drill down on the low frequency performance.
Above is a Smith chart view of the sweep from 1-5MHz. If you are familiar with the Smith chart, you will recognise that the curve almost follows a circle of constant G (not drawn on this Smith chart unfortunately). That suggests that Yin is approximately 1/50+jB where B is frequency dependent.
nanoVNA MOD does not have an admittance chart (more’s the pity) but it does have a hammy substitute, the “parallel RLC” chart though it is actually Rp||Xp. Let’s sweep 1-5MHz to focus on the low frequency InsertionVSWR problem.
Above, the Rp||Xp presentation. Note that the Xp (blue line) is fairly straight and if you project it to frequency=0, Xp will be approximately 0 so \(Xp \propto f\). Recall that the reactance of an inductance X=2πfL, so Xp looks like it may be due to a constant parallel inductance, and the equivalent parallel inductance can be calculated. It can be, but no need as nanoVNA MOD conveniently displays the value in the cursor data, 11.9µH in this case. Note also that the value of Rp is approximately 50Ω independent of frequency.
The poor low frequency InsertionVSWR is due to the low equivalent parallel inductance of 11.9µH at low frequencies, the magnetising inductance as it happens.
So, what should it be?
Well that depends on how we might specify performance. If we wanted the balun to have an InsertionVSWR of less than 1.1 from 3.5MHz, then Xp needs to be greater than \(Xp>10Zo=500\Omega\) and therefore magnetising inductance \(Lp>\frac{10 Zo}{2 \pi f}=23µH\).
Increasing the magnetising inductance will typically degrade the high frequency performance, so finding a good design is a compromise between these and other factors.
If we look more widely at the Rp||Xp response, we see a self resonance around 22MHz, and above that, progressively a lower and lower shunt Xc. So, just as low equivalent shunt Xl degraded low end performance, low equivalent shunt Xc degrades high end performance which is the main contribution to increasing InsertionVSWR above 22MHz.
So as voltage baluns go, this has moderately good InsertionVSWR from 7-20MHz, but is a bit shabby above and below that range.
The article has demonstrated how simple measurements made with the nanoVNA (or any other capable VNA or antenna analyser) can be used to evaluate not only the InsertionVSWR, but provide a likely explanation for its behaviour. Insufficient magnetising impedance is a common design flaw. You could use this approach to guide design of a DIY voltage balun.
Further reading: Voltage symmetry of practical Ruthroff 1:1 baluns discusses voltage symmetry of the BL-50A.
]]>This article revises Loss of ladder line: copper vs CCS (DXE-LL300-1C) for revised published datasheet MLL figures with internal PDF date of 25/07/2018.
Let’s start by assuming that the new offered data is credible, let’s take it at face value.
The line is described as 19 strand #18 (1mm) CCS and the line has velocity factor (vf) 0.88 and Zo of 272Ω.
Let us calculate using TWLLC the loss at 2MHz of a similar line but using pure solid copper conductor with same conductor diameter, vf and Zo. We will assume dielectric loss is negligible at 2MHz
Parameters | |
Conductivity | 5.800e+7 S/m |
Rel permeability | 1.000 |
Diameter | 0.00100 m |
Spacing | 0.00650 m |
Velocity factor | 0.880 |
Loss tangent | 0.000e+0 |
Frequency | 2.000 MHz |
Twist rate | 0 t/m |
Length | 30.480 m |
Results | |
Zo | 272.69-j2.59 Ω |
Velocity Factor | 0.8800 |
Length | 83.18 °, 0.231 λ, 30.4800 m, 1.155e+5 ps |
Line Loss (matched) | 0.121 dB |
Spacing has been adjusted to obtain Zo.
At 2MHz MLL of a copper line is 0.121dB for 30.48m (100′) as against 0.32dB measured for the stranded CCS line.
At 50MHz MLL of a copper line is 0.641dB for 30.48m (100′) as against 0.89dB measured for the stranded CCS line.
If the measurement data was valid and correct, the difference would almost certainly attributable to CCS and stranding. The copper cladding on the very thin strands is way less than skin depth at lower frequencies, effective RF resistance is higher than that of a solid copper conductor.
You might regard that the difference is tenths of a dB and insignificant, but this line is almost always used at high VSWR and the difference between the two lines is likely to be significant.
If we take the measured data and fit a model that matched line loss is per unit length of line (m) is:
\(MLL=(k_1 \sqrt f + k_2 f)l\)
Where | Loss = | loss per unit length |
f = | frequency | |
k1 = | constant | |
k2 = | constant | |
l = | length |
Such a model is usually a good fit for practical transmission lines where skin effect is well developed, and dielectric loss is proportional to frequency. A solution for k1 and k2 for least squares error has been found for the DXE published data.
Above is a plot of the measured data and the model.
The measured data curve exhibits some form of oscillation about some possibly smoother curve. The oscillation is unexpected and ought prompt review of the measurement setup to see that there is not some other effect being captured, eg unbalanced drive exciting common mode resonances.
Nevertheless, it we treat the data as correct, the issue that arises is that the value for k2 is significantly negative, and we ought to expect it is positive and smaller than k2 at these frequencies.
We might expect and excuse some obvious departure from the model at frequencies below 5MHz due to the copper clad steel conductors.
So, the extent of oscillation and higher frequencies and poor fit to the model raises some questions about the validity of the measurement data.
]]>These were very popular at one time, but good voltage baluns achieve good current balance ONLY on very symmetric loads and so are not well suited to most wire antennas.
Above is W2AU’s illustration of the internals.
Mine barely saw service before it became obvious that it had an intermittent connection to the inner pin of the coax connector. That turned out to be a poor soldered joint, a problem that is apparently quite common and perhaps the result of not properly removing the wire enamel before soldering.
Having cut the enclosure to get at the innards and fix it (they were not intended to be repaired), I rebuilt it in a similar enclosure made from plumbing PVC pipe and caps, and took the opportunity to fit some different output terminals and an N type coax connector.
Above is the rebuilt balun which since that day has been reserved for test kit for evaluating the performance of a voltage balun in some scenario or another.
My rework did not attempt to duplicate the spark gap arrangement of the top terminals. It is doubtful that it is effective protection of an attached receiver.
InsertionVSWR is often an important parameter of nominally 1:1 baluns. So, let’s measure the balun’s InsertionVSWR by connecting it to Port 0 (Ch0) and connecting a good 50+j0Ω load to the output terminals.
Above is a sweep from 1-41MHz, Insertion VSWR looks pretty good above about 7MHz.
Let’s drill down on the low frequency performance.
Above is a Smith chart view of the sweep from 1-5MHz. If you are familiar with the Smith chart, you will recognise that the curve almost follows a circle of constant G (not drawn on this Smith chart unfortunately). That suggests that Yin is approximately 1/50+jB where B is frequency dependent.
nanoVNA MOD does not have an admittance chart (more’s the pity) but it does have a hammy substitute, the “parallel RLC” chart though it is actually Rp||Xp. Let’s sweep 1-5MHz to focus on the low frequency InsertionVSWR problem.
Above, the Rp||Xp presentation. Note that the Xp (blue line) is fairly straight and if you project it to frequency=0, Xp will be approximately 0 so \(Xp \propto f\). Recall that the reactance of an inductance X=2πfL, so Xp looks like it may be due to a constant parallel inductance, and the equivalent parallel inductance can be calculated. It can be, but no need as nanoVNA MOD conveniently displays the value in the cursor data, 12.9µH in this case. Note also that the value of Rp is approximately 50Ω independent of frequency.
The poor low frequency InsertionVSWR is due to the low equivalent parallel inductance of 12.9µH, the magnetising inductance as it happens.
So, what should it be?
Well that depends on how we might specify performance. If we wanted the balun to have an InsertionVSWR of less than 1.1 from 3.5MHz, then Xp needs to be greater than \(Xp>10Zo=500\Omega\) and therefore magnetising inductance \(Lp>\frac{10 Zo}{2 \pi f}=23µH\).
Increasing the magnetising inductance will typically degrade the high frequency performance, so finding a good design is a compromise between these and other factors.
So as voltage baluns go, this has quite good InsertionVSWR above 7MHz, but is a bit shabby below that.
The article has demonstrated how simple measurements made with the nanoVNA (or any other capable VNA or antenna analyser) can be used to evaluate not only the InsertionVSWR, but provide a likely explanation for its behaviour. Insufficient magnetising impedance is a common design flaw. You could use this approach to guide design of a DIY voltage balun.
]]>There are some popular formulas and charts that purport to properly estimate the loss under standing waves or mismatch conditions, usually in the form of a function of VSWR and MLL, more on this later.
Let’s explore theoretical calculations of loss for a very short section of common RG58 at 3.6MHz with two different load scenarios.
The scenarios are:
Above is the RF Transmission Line Loss Calculator (TLLC) input form. A similar case was run for Zload=500Ω.
Now lets compare the outputs side by side. Items of interest are highlighted.
Note that the input Zload figure is different, 5+j0Ω at left and 500+j0Ω at right, both have VSWR(50)=10. Note also that the loss under mismatch in the 500Ω case is less than the MLL, there is less loss under standing waves in this scenario.
The calculated loss is different in both cases, 0.272 vs 0.0139, one is 20 times the other. Note that in both cases, VSWR(50)=10, yet the loss under standing waves is very different so it is not simply a function of VSWR as popularly held.
For the same reason that the loss under mismatch of these two line sections with similar VSWR are so different, the loss along a line under mismatch of that cable type is not uniform. In fact, more generally, loss under mismatch is not uniform for lines that are not distortionless lines, ie for most practical lines.
]]>Let’s explore theoretical calculations of ReturnLoss for a very short section of common RG58 at 3.6MHz.
By definition, \(ReturnLoss=\frac{ForwardPower}{ReflectedPower}\) and it may be expressed as \(ReturnLoss=10log_{10}\frac{ForwardPower}{ReflectedPower} dB\).
The scenarios are:
Above is the RF Transmission Line Loss Calculator (TLLC) input form. Note that it will not accept Zload of zero or infinity, instead a very small value (1e-100) or very large value (1e100) is used.
Above, the input for the shorted termination.
Now lets compare the outputs side by side. Items of interest are highlighted.
Note that the input Zload figure is different, open at left and shorted at right.
The calculated ReturnLoss wrt Zo=50+j0Ω (RL(50)) is different in both cases, one is 28 times the other.
You might have expected that based on classic transmission line theory that \(ReturnLoss=20log_{10}(2 l |\gamma|) dB\) where l is length, and Zload does not appear in that expression, so ReturnLoss should be independent of Zload.
You would be quite correct in that thinkin, and if you look to the second last line, you will see RL calculated as 0.058dB in both cases… this is the ‘true’ ReturnLoss calculated wrt the actual Zo=50.02-j1.37Ω. You will see also that the calculated matched line loss is exactly twice the ‘true’ ReturnLoss.
Beware of assuming that ReturnLoss(50) as might be measured by nominal 50Ω instruments is the actual ReturnLoss in terms of the transmission line Zo.
]]>Above, the measurement fixture is simply a short piece of 0.5mm solid copper wire (from data cable) zip tied to the external thread of the SMA jack, and the other end wrapped around the core and just long enough to insert into the inner female pin of the SMA jack.
Based on the datasheet, we can calculate the expected impedance at 1MHz.
So, around 0.5+j6Ω is the expectation.
The two cores I measured are 0.16+j5.34Ω and 0.53+j6.32Ω, not a lot of departure though the first has quite a lot less core loss (the R component).
Above is a wider range prediction based on the published data. At the cross over frequency of 14MHz R=X=24Ω.
Now to the two sample cores that I measured.
Above from the first sample, the R curve is quite similar to expectation, but the X curve is quite different, it does not roll off nearly to the extent predicted above. As a result, the cross over frequency (R=X) is well above the expected 14MHz, around 46MHz in this case.
Above from the second sample, the R curve is quite similar to expectation, but the X curve is quite different, it does not roll off nearly to the extent predicted above. As a result, the cross over frequency (R=X) is well above expectation, greater than 50MHz.
So, in summary, the tested cores exhibited X, and therefore µ’, quite similar to the datasheet at 1MHz, but at higher frequencies X and µ’ were quite higher than expected.
I have tested a lot of #43 material in various shapes and sizes of cores, and this is the first time I have observed this effect. Ferrite products have wide tolerances, and certain characteristics are controlled, I could not say whether these meet the controlled parameters.
Such variation certainly makes identification of core material, designs and prototype measurements more challenging.
I might mention that Fair-rite issued a new table of permeability characteristics for type #43 in Feb 2020. The results measured here for two year old purchases are even further from the ‘new’ #43.
]]>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.
]]>