In respect of the first part, inductance \(L=\frac{\phi(i)}{i}\) so if the windings are equal, half the total current flows in each winding and each contributes flux due to i/2, total current is i, total flux is twice that due to i/2, so the inductance of the parallel equal windings is the same as if i flowed in a single winding, ie L of the combination is the same as the inductance of each of the equal windings alone.

In the second case, if there is zero flux leakage, it is true that the inductance of the combination of series opposed equal windings is zero. In the case of the cores used for common mode chokes flux leakage varies from less than 1% to over 50%… so the general statement is a bit naive in this application.

Both of these are very easily demonstrated by simple experiment. In fact a measurement of L with series aiding and series opposing connection is a classic way to find the flux coupling factor.

A few years after the ‘information’ was posted, it has not been questioned much less called out as wrong. So given that the understanding of inductance seems lacking… what credibility does the article have when it includes this?

]]>fenceas explained in the following text by one poster.

With a current balun or CM choke, it is the reactance (inductance) that is mostly responsible for the balun action. In the case of the choke balun, beads installed along the coax at the feed with 31 or 43 material, they form a reflective ‘filter’. There is some absorption, but most of the action is due to reflection from the inductive reactance they form installed on a conductor. As such, they form a high-Z isolation point between the feeder and the antenna center, assuming they are installed at the feedpoint of the doublet. In the case of the CM choke, the common mode currents are reflected by the inductive reactance of the windings as with the current balun and the balance of current between the two conductors is forced through induced opposing magnetic currents within the cone. This is the reason I prefer the CM choke for the purpose. In either case, the common mode current is reflected to a large extent by the inductive reactance back where it originated. Installation of a balun at the feedpoint of a doublet does not make the CM currents go away, it just establishes a ‘fence’ for those currents between non-antenna associated currents (on the outside of the feedline) and the radiating structure.

Let us explore some NEC models with three ‘devices’ to attempt to confine current to the lower conductor:

- a gap;
- a large pure inductive reactance;
- a large pure resistance.

The first is at 10MHz a vertical conductor over a perfectly conducting earth, and space 0.1m above it, another vertical conductor.

Above is the current distribution showing phase and amplitude, the gap is at one third the height. It is not totally clear from the 2D rendering of a 3D characteristic, but the phase in the upper two thirds is opposite to the phase in the lower third, and this is by virtue of the lengths which are approximately a quarter and half wavelength.

So, even where there is a substantial gap, the upper conductor is coupled to the lower conductor and the current is not confined to the lower conductor.

The gap in the above model was filled with a conductor loaded with Z=0+j1000Ω.

Above is the current distribution showing phase and amplitude, the gap is at one third the height.

A view from the zenith of current magnitude and phase plot shows the phase in the upper part is about 120° out of phase with the lower third.

So, even where there is a large pure inductive reactance, the upper conductor is coupled to the lower conductor and the current is not confined to the lower conductor.

The gap in the first model was filled with a conductor loaded with Z=1000+j0Ω.

Above is the current distribution showing phase and amplitude, the gap is at one third the height. In this case the phase in the upper two thirds is close to opposite that in the bottom third.

So, even where there is a large pure resistance, the upper conductor is coupled to the lower conductor and the current is not confined to the lower conductor.

None of these simple structures isolate the current to the lower element only, there is significant current in the upper element, indeed greater current moment in the latter two cases by virtue of its length.

These experiments suggest that behavior is not simply as set out in the quote.

]]>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.

]]>A significant difference in the two wire line is that we want the line to operate in balanced mode during the test, that there is insignificant common mode current. To that end, a balun will be used on the nanoVNA.

Above, the balun is a home made 1:4 balun that was at hand (the ratio is not too important as the fixture is calibrated at the balun secondary terminals). This balun is wound like a voltage balun, but the secondary is isolated from the input in that it does not have a ‘grounded’ centre tap. There is of course some distributed coupling, but the common mode impedance is very high at the frequencies being used for the test.

Above, the underside of the terminal block has a 2 pin machined pin socket to allow convenient OSL calibration using the parts shown in

Antenna analyser – what if the device under test does not have a coax plug on it?. The screw terminals are not quite on the reference plane, but the small error will be adjusted out by the Velocity factor solver.

The fixture was OSL calibrated before measuring the line sections.

Using the method described at Velocity factor solver the quarter wave resonance was measured for each of the test cables with the same adapters.

Above is measurement of the long cable. The long cable measured 8.240m end to end, the short cable measure 4.104m.

Above is the calculation which tells us that the velocity factor of the coax itself is 0.85.

Be aware that velocity factor is frequency dependent, though the error is small for practical low loss cables above 10MHz.

You can now cut the cable based on the measured velocity factor, allowing for the electrical length of connectors and adapters as appropriate.

]]>In summary, though G3TXQ expected the antenna system to have good balance, on measurement it was not all that good. The analysis showed that even a moderate impedance common mode choke reduced the common mode current Icm substantially more than no balun, or an ideal voltage balun.

This article performs similar analysis of the case of an ideal voltage balun applied to my own antenna system documented at Equivalent circuit of an antenna system at 3.6MHz.

In this article I will use notation consistent with (Schmidt nd).

Above is the equivalent circuit.

Above is a schematic of the antenna equivalent circuit driven by equal but opposite phase voltages (ie, an ideal voltage balun).

From that we can write a set of mesh equations and solve them.

\(1=(z1+z3) \cdot i1 -z3 \cdot i2\\

1=-z3 \cdot i1+(z2+z3) \cdot i2\\

\)

This is a system of 2 linear simultaneous equations in 2 unknowns. In matrix notation:

\(\begin{vmatrix}i1\\i2 \end{vmatrix}=

\begin{vmatrix}

z1+z3 & -z3\\

-z3 & z2+z3

\end{vmatrix}^{-1} \times

\begin{vmatrix}1\\1\end{vmatrix}\\

\)

Let’s do that in GNU Octave.

desc="3.6MHz case from https://owenduffy.net/blog/?p=14267"; printf("%s\n\n",desc); #transform measurements Za=26.7+68.1i Zb=23.9+64.5i ZC=59.0+167i #Schmidt, Kevin. nd. Putting a Balun and a Tuner Together: http://fermi.la.asu.edu/w9cf/articles/balun/index.html S=Za*ZC*(2*Zb**2-Za*ZC)+Za*Zb*(2*ZC**2-Za*Zb)+Zb*ZC*(2*Za**2-Zb*ZC); ZD=4*Za**2*Zb**2*ZC/S; ZU=4*ZC**2*Za*Zb*(Za-Zb)/S; z1=(ZD+ZU)/2 z2=(ZD-ZU)/2 z3=ZC+(ZU**2-ZD**2)/(4*ZD) #sources v1=1 v2=1 #equations of mesh currents #v1=(z1+z3)*i1 -z3*i2 #v2=-z3*i1+(z2+z3)*i2 #solve mesh equations A=[z1+z3,-z3;-z3,z2+z3] b=[v1;v2] x=A\b; i1=x(1); i2=x(2); #scale to 100W input pr=100; printf("@%0.1fW input:\n",pr); p=real(v1*i1)+real(v2*i2); i1=i1*(pr/p)**0.5 i2=i2*(pr/p)**0.5 #calculate differential and common mode components of current ic=(i1-i2)/2 id=(i1+i2)/2 ica=abs(ic) ida=abs(id) icrel=2*abs(ic)/abs(id) i1a=abs(i1) i2a=abs(i2) i12a=2*abs(ic)

The console output is…

3.6MHz case from https://owenduffy.net/blog/?p=14267 Za = 26.700 + 68.100i Zb = 23.900 + 64.500i ZC = 59 + 167i z1 = 18.002 + 41.924i z2 = 10.426 + 31.757i z3 = 52.296 + 148.891i v1 = 1 v2 = 1 A = 70.30 + 190.82i -52.30 - 148.89i -52.30 - 148.89i 62.72 + 180.65i b = 1 1 @100.0W input: i1 = 0.67231 - 1.72300i i2 = 0.67684 - 1.79004i ic = -0.0022646 + 0.0335163i id = 0.67458 - 1.75652i ica = 0.033593 ida = 1.8816 icrel = 0.035707 i1a = 1.8495 i2a = 1.9137 i12a = 0.067185 >> >>

The comparative statistic I will use is | 2*ic| (total common mode current) relative to |id|, it is given by the variable icrel above which has a calculated value of 0.0357 for this scenario.

Note that differential current and common mode current will almost always each be standing waves and their phase velocity may differ.

The last three values calculated are those that would be measured by a clamp on RF ammeter around the 1, 2 and 1+2 wires together. These values could be plugged into Resolve measurement of I1, I2 and I12 into Ic and Ic to resolve the measurements into common mode and differential mode components.

Above, the calculator results reconcile with the results of the Octave script.

You don’t need complicated maths to asses an installed antenna system, measurements with a clamp on RF ammeter can be resolved into the common mode and differential mode components using the calculator.

In this case, Icm with a voltage balun is not too bad, a consequence of very good balance of the antenna system. The measured Icm with the installed common mode choke is 20mA, about 10.5dB better than the calculated 67mA for an ideal voltage balun.

Good voltage baluns deliver good current balance on very symmetric loads, good current baluns deliver good current balance on ALL loads

Above is Hunt’s equivalent circuit of his antenna system and transmitter. It is along the lines of (Schmidt nd) with different notation.

He made measurements that led to calculation of these components for the dipole which he states is visually fairly symmetric.

Above are the calculated values he gives at Leg a and Leg b. Lets assume that the measurements are made at the tuner interface with respect the the unbalanced tuner ground connection. Note that Za and Zb are not close to equal, so the antenna system is hardly symmetric or balanced.

Above is a schematic of the antenna equivalent circuit driven by equal but opposite phase voltages (ie, an ideal voltage balun).

From that we can write a set of mesh equations and solve them.

\(1=(za+zc) \cdot ia -zc \cdot ib\\

1=-zc \cdot ia+(zb+zc) \cdot ib\\

\)

This is a system of 2 linear simultaneous equations in 2 unknowns. In matrix notation:

\(\begin{vmatrix}ia\\ib \end{vmatrix}=

\begin{vmatrix}

za+zc & -zc\\

-zc & zb+zc

\end{vmatrix}^{-1} \times

\begin{vmatrix}1\\1\end{vmatrix}\\

\)

Let’s do that in GNU Octave.

#equations of mesh currents #1=(za+zc)*ia -zc*ib #1=-zc*ia+(zb+zc)*ib za=15.1+79i zb=1.6-109i zc=30.7+110i A=[za+zc,-zc;-zc,zb+zc] b=[1;1] x=A\b ia=x(1) ib=x(2) ic=(ia-ib)/2 id=(ia+ib)/2 ica=abs(ic) ida=abs(id) icrel=2*abs(ic)/abs(id) #for calculator abs(ia) abs(ib) 2*abs(ic)

The console output is…

za = 15.100 + 79.000i zb = 1.6000 - 109.0000i zc = 30.700 + 110.000i A = 45.800 + 189.000i -30.700 - 110.000i -30.700 - 110.000i 32.300 + 1.000i b = 1 1 x = 0.0046179 + 0.0091411i 0.0049694 + 0.0242611i ia = 0.0046179 + 0.0091411i ib = 0.0049694 + 0.0242611i ic = -0.00017574 - 0.00756002i id = 0.0047937 + 0.0167011i ica = 0.0075621 ida = 0.017375 icrel = 0.87043 ans = 0.010241 ans = 0.024765 ans = 0.015124

The comparative statistic I will use is | 2*ic| (total common mode current) relative to |id|, it is given by the variable icrel above which has a calculated value of 0.870 for this scenario.

By way of comparison, the same scenario with the common mode choke (ie current balun) with Zcm=1500+j1500Ω, the same statistic is 0.0738 (Working a common mode scenario – G3TXQ Radcom May 2015). The modest current balun results in relative common mode current being 21dB lower than the ideal voltage balun.

Note that differential current and common mode current will almost always each br standing waves and their phase velocity may differ.

The last three values calculated are those that would be measured by a clamp on RF ammeter around the a, b and a+b wires together. These values could be plugged into Resolve measurement of I1, I2 and I12 into Ic and Ic to resolve the measurements into common mode and differential mode components.

Above, the calculator results reconcile with the results of the Octave script.

You don’t need complicated maths to asses an installed antenna system, measurements with a clamp on RF ammeter can be resolved into the common mode and differential mode components using the calculator.

This solution is based on Hunts measurements and equivalent circuit calculation, and the abject failure of a voltage balun on an antenna system that Hunt reported as apparently symmetric applies to this scenario, but it is not surprising as good current baluns will tend to be more effective in reduction of common mode current than voltage baluns.

- Duffy, O. nd. Find three terminal equivalent circuit for an antenna system
- Hunt, S. May 2015. High performance common mode chokes in Radcom
- Schmidt, Kevin. nd. Putting a Balun and a Tuner Together: http://fermi.la.asu.edu/w9cf/articles/balun/index.html

Above is Hunt’s equivalent circuit of his antenna system and transmitter. It is along the lines of (Schmidt nd) with different notation.

He made measurements that led to calculation of these components for the dipole which he states is visually fairly symmetric.

Above are the calculated values he gives at Leg a and Leg b. Lets assume that the measurements are made at the tuner interface with respect the the unbalanced tuner ground connection. Note that Za and Zb are not close to equal, so the antenna system is hardly symmetric or balanced.

Lets solve the network. We will set input power to 100W to find currents typical of a 100W transmitter. A bit of Python as a complex number calculator follows.

>>> import cmath >>> >>> za=15.1+79j >>> zb=1.6-109j >>> zc=30.7+110j >>> >>> yb=1/zb >>> yc=1/zc >>> >>> zi=(za+1/(yb+yc)) >>> zi (384.4354106617894-30.586235624203923j) >>> pi=100 >>> ia=(pi/zi.real)**0.5 >>> ia 0.5100212930349505 >>> ib=-ia*(yb)/(yb+yc) >>> ib (-0.5380158352758633-1.7202577832374206j) >>> abs(ib) 1.8024283286157343 >>> (ia-ib)/2 (0.5240185641554069+0.8601288916187103j) >>> (ia+ib)/2 (-0.0139972711204564-0.8601288916187103j) >>> abs((ia-ib)/2) 1.0071827866761451 >>> abs((ia+ib)/2) 0.8602427760789687 >>> abs((ia+ib)/2)/abs((ia-ib)/2) 0.854107901226052 >>> abs((ia+ib)) 1.7204855521579374

So, for ia=0.510+j0A , ib=-0.538-j1.72A, so the currents are quite unbalanced.

In fact the magnitude of the differential mode current is 1.01A (per conductor) and the magnitude of the common mode current is 0.860A (per conductor). So, for Ia=0.510A, the total common mode current Icm (ie the sum of the common mode component at Leg A and Leg B) is 1.72A. Common mode current is quite high… for a visually symmetric dipole, albeit driven by an unbalanced source.

Note that differential current and common mode current will almost always each be standing waves and their phase velocity may differ.

We can solve the network adding a quite modest common mode choke with Zcm=1000+j1000Ω and find that Icm is reduced to from 1.72 to 0.158A, a 20.7dB reduction.

Some experts would insist that based on series measurement on a VNA which would give |s21|=-23.4dB, the common mode rejection of such a balun is 23.4dB. Of course that is a quite misguided concept as this worked solution shows it is just 20.7dB in this scenario.

I reported a similar experiment at Equivalent circuit of an antenna system. In that case, the antenna was more symmetric than Hunt’s dipole.

- Duffy, O. nd. Find three terminal equivalent circuit for an antenna system
- Hunt, S. May 2015. High performance common mode chokes in Radcom
- Schmidt, Kevin. nd. Putting a Balun and a Tuner Together: http://fermi.la.asu.edu/w9cf/articles/balun/index.html

One expert advised that 100mm wire clip leads would work just fine.

Another expert expanded on that with When lengths approach 1/20 of a wavelength in free space, you should consider and use more rigorous connections.

At Antenna analyser – what if the device under test does not have a coax plug on it? I discussed using clip leads and estimated for those shown that they behaved like a transmission line segment with Zo=200Ω and vf=0.8.

So lets model the scenario of a perfect 50Ω load at 30MHz measured through λ/20 of clip lead with Zo=200Ω and vf=0.8.

The InsertionVSWR of the clip lead fixture is 3.

Note that Zo in this case is quite low because the wires are quite close together, Zo would easily exceed 200Ω with wider spacing and the transformation would be even worse.

Another expert opined as long as the lead is much shorter than about one tenth of a wavelength, it won’t matter much.

(Zo=200, VSWR=6.7)

In fact the InsertionVSWR of a λ/120 section exceeds 1.2 With a λ/120 fixture (80mm @ 30MHz), if the actual VSWR of the DUT was 1.5, you might read anywhere from 1.2 to 1.9 on the nanoVNA.

The outcome is ridiculous, the advice is ridiculous, this is the way we help beginners… or is it principally about inflating the egos of the experts?

At the time of writing this, the advice goes unchallenged… possibly because it is unsociable to call out BS.

A fair question is can accurate VSWR measurements be made of a CB antenna with UHF connector?

The article A check load for antenna analysers with UHF series socket

describes a low cost UHF 50Ω load that will outperform most other types of UHF load. Lets use that and a SMA-UHF(F) adapter to measure insertion loss of the fixture and load adapter.

Above the SMA load with UHF(M) adapter, and a UHF(F) to SMA(M) adapter. UHF connectors do not have a constant through impedance of 50Ω, but how bad are they in this test?

Above, a sweep from 1-200MHz suggests that the adapters are quite suitable for modest accuracy measurements to 200MHz. This is a lot better than improvising with clip leads.

A word of warning, using large connectors and heavy cables might subject the nanoVNA on-board jacks to damaging forces… be careful.

]]>The single most common factor in their cases is an attempt to use TDR mode of the VNA.

Well, hams do fuss over the accuracy of quarter wave sections used in matching systems when they are not all that critical… but if you are measuring the tuned line lengths that connect the stages of a repeater duplexer, the lengths are quite critical if you want to achieve the best notch depths.

That said, only the naive think that a nanoVNA is suited to the repeater duplexer application where you would typically want to measure notches well over 90dB.

The VNA is not a ‘true’ TDR, but an FDR (Frequency Domain Reflectometer) where a range of frequencies are swept and an equivalent time domain response is constructed using an Inverse Fast Fourier Transform (IFFT).

In the case of a FDR, the maximum cable distance and the resolution are influenced by the frequency range swept and the number of points in the sweep.

\(d_{max}=\frac{c_0 vf (points-1)}{2(F_2-F_1)}\\resolution=\frac{c_0 vf}{2(F_2-F_1)}\\\) where c0 is the speed of light, 299792458m/s.

Let’s consider the hand held nanoVNA which has its best performance below 300MHz and sweeps 101 points. If we sweep from 1 to 299MHz (to avoid the inherent glitch at 300MHz), we have a maximum distance of 33.2m and resolution of 0.332m.

Here is such a sweep of a cable of length around 1.2m.

The marker is close to the apparent peak of the response at about 11.8ns (1.17m), and each step of the marker is 1.3ns (0.129m).

If we sweep to 900MHz, we do get better resolution (albeit for shorter dmax).

The resolution is reduced to 0.435ns (0.043m)

If you want mm resolution for short line sections, you need a VNA that sweeps a much wider frequency range and / or much more sweep points.

Above, nanoVNA-saver results on the same DUT with smoothing of 100 sweeps produces a nice clean looking graph and a calculated distance to fault of 1.222m, mm resolution implied by the number format… but are you mislead?

We can do a s11 sweep of a short circuit or open circuit line section (just as in the FDR / TDR case), but make the sweep quite narrow (ie high resolution) around a quarter wave or half wave resonance.

Above is a very narrow sweep with 1kHz resolution at 40MHz, ie 0.0025% resolution. From the interpolated resonance frequency of 40.4MHz and previously measured vf, we can calculate the physical length to be 1.224m… with resolution of 0.0000306m.

Many analysers and VNAs sport a Distance to Fault mode, and it is commonly a FDR implementation. These can be very effective productivity tools in identifying not just cable opens and shorts, but loose connectors, pinched cable etc.

The foregoing discussion shows that FDR / Distance to Fault may not be adequate for tuning of critical line sections, but it often has sufficient resolution for identifying the locality and severity of a fault.

Things have come a long way in the around 150 years since Oliver Heaviside successfully applied his mind to location of faults in submarine telegraph cables.

Whilst the TDR mode of a VNA looks an appealing way to measure line length, with low end instruments like the nanoVNA it does not have adequate resolution for demanding applications.

]]>Two lengths of the same cable were selected to measure with the nanoVNA and calculate using Velocity factor solver. The cables are actually patch cables of nominally 1m and 2.5m length. Importantly they are identical in EVERY respect except the length, same cable off the same roll, same connectors, same temperature etc.

Above is the test setup. The nanoVNA is OSL calibrated at the external side of the SMA saver (the gold coloured thing on the SMA port), then an SMA(M)-N(F) adapter and the test cable. The other end of the test cable is left open (which is fine for N type male connectors).

Using the method described at Velocity factor solver the quarter wave resonance was measured for each of the test cables with the same adapters.

Above is measurement of the short cable. The short cable measured 1.150m between the insides of the crimp sleeves (which were hard up against the connector body), the long cable measure 2.450m and resonance was at 19.614MHz.

Above is the calculation which tells us that the velocity factor of the coax itself (having deducted the effects of adapters and connectors) is 0.66.

The calculator also reports that it calculated the offset to be 363.9ps, equivalent to 72mm of RG213 length in the adapter and connectors. This reconciles well with physical measurement (allowing that part of the internal path of N connectors is air dielectric, about 13mm in a mated pair so that appears to be 8.6mm equivalent at VF=0.66).

Be aware that velocity factor is frequency dependent, though the error is small for practical low loss cables above 10MHz.

You can now cut the cable based on the measured velocity factor, allowing for the electrical length of connectors and adapters as appropriate.

Warning: do not measure cable with a loose UHF series plug at an open end. The loose collar will cause unpredictable / unreliable results, install a UHF(F)-UHF(F) adapter to fix the problem. Likewise for plugs of similar construction (eg SMA).

]]>