Above is Fig 3A from Severns and is the current distribution at 1MHz for 20.3µm (0.0008″) cladding of a 0.405mm (#26) CCS (Copperweld) conductor.
Above is from (Duffy 2017) and reconciles well with Severns.
Above is Fig 4 from Severns comparing RF resistance 20.3µm (0.0008″) cladding of a 0.405mm (#26) CCS conductor. Note that at some frequencies, the CCS conductor has lower resistance.
As a check, the resistance for this scenario of Duffy at 1MHz is 0.702Ω/m and Severns looks like 0.7Ω/m from the graph, they reconcile well.
Above is Fig 5 from Severns comparing 2.053mm (#12) wire with difference cladding. Again, at some frequencies, the CCS wire may have lower resistance that a plain copper wire.
As a check, the resistance for this scenario of Duffy at 4MHz is 0.075Ω/m and Severns looks like 0.079Ω/m from the graph, they reconcile fairly well. Both models expose the effect of the phase change with depth, eddy currents if you like.
The simplest algorithm often used is that \(MLL \propto \sqrt f\) which assumes only conductor loss, and that skin effect is well developed and estimated based on a simple model of skin effect.
In homogenous conductors, the underlying assumption fails at frequencies where the conductor is less than about 2 skin depths in radius transition towards low frequency behavior.
Clad conductors exhibit a departure at frequencies where the cladding is insufficient, and a further transition where the core material departs from well developed skin effect… a double transition if you like.
Fig 5 shows that at the first transition, departure from well developed skin effect (as in the copper conductor) is more complicated than often described.
Importantly, characteristic impedance Zo depends on the internal impedance of the conductor(s), and not only is the RF resistance affected by current distribution in the conductor, so too is the internal inductance and the combination may significantly change Zo at lower frequencies.
The technique he followed was to make a series of measurements of Rin at low Z resonances of the length of line with open circuit at the far end, and to calculate the MLL using Calculate transmission line Matched Line Loss from Rin of o/c or s/c resonant section.
…
Though the calculator can use high Z resonances, the high Z resonances are very narrow and it is very difficult to measure Rin at the true resonant frequency. So, only his reported low Z measurements will be used.
This article illustrates the response expected from a 13.7m length of Belden 8262 (RG58C/U).
Above, the response at the first low Z resonance with open end. The rate of change of X with frequency is 2.2Ω/kHz, quite modest and given the low slope of the Rin line, frequency need only be set to within 1kHz for reasonably good accuracy of the Rin value obtained. (Slope will be steeper on a lower loss line section.)
Above, the response at the first high Z resonance (antiresonance) with shorted end. The rate of change of X with frequency is -12.7Ω/kHz, quite rapid and smaller frequency steps (~0.1kHz) are needed to resolve an accurate value for Rin. (Slope will be steeper on a lower loss line section.)
The response depends on the line type, length and frequency.
Let’s test the calculator on both the above cases.
The exact length is used in the calcs, it is a nominal 90° of Belden 8262 at 3.6MHz.
The two calcs reconcile, keeping in mind that the calculation is an approximation… but a good approximation if the measurements of Rin and length are accurate, and Ro is known to good accuracy.
A word of warning: measuring on the roll can give unusual results if the cable is deformed significantly on the roll. A higher risk for foamed dielectric cables, and this is one of that type.
The technique he followed was to make a series of measurements of Rin at low Z resonances of the length of line with open circuit at the far end, and to calculate the MLL using Calculate transmission line Matched Line Loss from Rin of o/c or s/c resonant section.
Impedance measurements were made using a nanoVNA which was OSL calibrated in several ranges through the series of measurements. Also notable was that there were several coax adapters used to connect the RG6 to VNA.
Though the calculator can use high Z resonances, the high Z resonances are very narrow and it is very difficult to measure Rin at the true resonant frequency. So, only his reported low Z measurements will be used.
So. let’s graph the measured Rin at zero crossing of Xin.
The circled measurements appear out of line with the others. They were made with a different OSL calibration that the ones immediately below and above, so that hints something may have gone wrong in the calibration. Two of the possible explanations are:
The circled measurements are suspect, it is not known if they are faulty. It is a good idea to plot measurements as they are made as it allows investigation of apparent anomalies.
Above is the calculated MLL from the measured Rin. The calculation can be done in the spreadsheet, \(MLL=\frac{-10log|\frac{R_{in}-R_0}{R_{in}-R_0}|}{length}\). Also show are two datapoints (+) from what appears to be the datasheet for this line. The measured points are not a lot different to the two datapoints from the datasheet.
The shape of the curve is not the classic shape that one might expect, but this is a CCS line and copper like performance will not be observed at lower frequencies where the copper thickness is insufficient.
Above is a comparison of the measured MLL with that from the datasheet for Belden 1694A which uses a solid copper centre conductor. There is a growing departure from copper like performance below about 30MHz.
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.
]]>Above is a pic of the Rose Clip as a line insulator / support. The clips are pretty flimsy but pretty cheap. They click onto the 1.6mm diameter wire reasonably firmly.
Above, a small dob of hot melt glue is used to fix the clip at one end only so that it does not move along the line. The other side is clicked on but free to move to accommodate twists and turns. The clips will probably be needed at intervals of 0.5m or perhaps less in some situations.
The short test section has been in the weather for two years, but has not been subjected to a real trial as a long section of line in all weather.
Above is a calculation of expected performance. The velocity factor is a guess based on experience.
Essentially, though it is very low cost, it achieves Zo around 480Ω with matched line loss around 0.23dB/100m @ 3.5MHz. The clips cost about $6/100 and the wire about $0.07/m, so all up $0.26/m.
Above is a mockup of a dipole leg terminated on an insulator, and the feed line connected using the 3mm stainless steel tap connector. In use, the tap connector will be filled with marine grease or aluminium jointing compound to exclude oxygen and water.
Above is a 2mm stainless connector. The 1.6mm wire has to be bent to follow the path through this smaller connector body. Again it needs to be filled with grease to exclude oxygen and water. These connectors are available on eBay at low cost.
]]>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.
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