As pointed out in the articles, the solutions cannot be simply extended to real antenna scenarios. Nevertheless, it might provoke thinking about the performance of some types of socalled balanced ATUs, indeed the naive nonsense of an “inherently balanced ATU”.
(Witt 2003) goes to some length to calculate his IMB figure of merit based on a similar load of two not necessarily equal series resistors with the mid point grounded to the ATU chassis. Witt’s IMB is equivalent to the factor 2Ic/Idthat was calculated in earlier articles in this series, and equally useless in inferring behavior in a real antenna system.
(Duffy 2010) gives an explanation of the behavior of baluns in an antenna system, and it becomes apparent that simple linear circuit solutions of a couple of resistors does not give insight into the behavior in real antenna systems.
The bottom line though is that while NEC models might be informing, there is no substitute for direct measurement of common mode current (Duffy 2011)… and it is so easy.
This article reports the same asymmetric load using the MFJ949E internal voltage balun.
The test circuit is an MFJ949E T match ATU jumpered to use the internal balun and resistors of 50Ω and 100Ω connected from those terminals to provide a slightly asymmetric load.
The voltage between ground and each of the output terminals was measured with a scope, and currents calculated.
Above are the measured output voltage waveforms at 14MHz.
Lets work out the current amplitudes. Above, V1 (yellow) is 5.9divpp, V2 (cyan) is 7.2divpp. I1=V1/50=5.9*0.2/50=23.6mApp. I2=V2/100=7.2*0.2/100=14.4mApp.
Expanding the timebase allows better measurement of the phase difference.
V2 lags by a half cycle less 8.25µs, so V2 phase is 180+8.25e9*14e6*360=180+42=138°.
Lets calculate the common mode and differential component of current in each load resistor. We will use Python as it handles complex numbers.
>>> i1=0.0236
>>> i2=0.0144*(math.cos(138/180*math.pi)+1j*math.sin(138/180*math.pi))
>>> ic=(i1+i2)/2
>>> abs(2*ic)
0.016100289594275147
>>> id=(i1i2)/2
>>> abs(id)
0.01781446515461856
>>> abs(2*ic)/abs(id)
0.903776198417105
>>> 20*math.log(abs(2*ic)/abs(id))/math.log(10)
0.8787820061070818
So, the differential component of current is 17.8mApp, and the total common mode current is 16.1mApp, the total common mode current is 90% of the differential current or 0.9dB less than differential current.
By any standard, this is appalling balance, and demonstrates why voltage baluns are unsuited to the application.
The fact that the “inherently balanced” topology is only 1.8dB better that this voltage balun experiment speaks volumes for the failure of the “inherently balanced” topology.
The measurements reported here are for a specific scenario (components, frequency and load), and should not be simply extrapolated to other scenarios.
The calculated imbalance if you like applies to the specific test circuit, and cannot really be extended to use of this balun in an antenna system scenario.
]]>This article reports the same equipment reversed so that the common mode choke is connected to the output of the MFJ949E.
The test circuit is an MFJ949E T match ATU followed by A low Insertion VSWR high Zcm Guanella 1:1 balun for HF. A banana jack adapter is connected to the balun output jack, and resistors of 50Ω and 100Ω connected from those terminals to provide a slightly asymmetric load.
The voltage between ground and each of the output terminals was measured with a scope, and currents calculated.
Above are the measured output voltage waveforms at 14MHz.
Lets work out the current amplitudes. Above, V1 (yellow) is 4.0divpp, V2 (cyan) is 8.0divpp. I1=V1/50=4.0*0.2/50=16.0mApp. I2=V2/100=8.0*0.2/100=16.0mApp.
Expanding the timebase allows better measurement of the phase difference.
V2 lags by a half cycle and 1.0µs, so V2 phase is 1801.0e9*14e6*360=1805=185°.
Lets calculate the common mode and differential component of current in each load resistor. We will use Python as it handles complex numbers.
>>> i1=0.016
>>> i2=0.016*(math.cos(185/180*math.pi)+1j*math.sin(185/180*math.pi))
>>> ic=(i1+i2)/2
>>> abs(2*ic)
0.0013958203956907485
>>> id=(i1i2)/2
>>> abs(id)
0.015984771545309726
>>> abs(2*ic)/abs(id)
0.0873218858170239
>>> 20*math.log(abs(2*ic)/abs(id))/math.log(10)
21.177537875409207
So, the differential component of current is 16.0mApp, and the total common mode current is 1.40mApp, the total common mode current is 9% of the differential current or 21.2dB less than differential current.
Calculation of the common mode component of current involves the addition of two almost equal and almost opposite phase currents and is very sensitive to uncertainty in each of the measurements using this measurement method. This balun should achieve 2Ic/Id>35dB in this scenario, but it would take a higher accuracy measurement system to measure it.
The fact that the “inherently balanced” topology measures 18dB worse that this experiment speaks volumes for the failure of the “inherently balanced” topology.
The measurements reported here are for the specific scenario (components, frequency and load), and should not be simply extrapolated to other scenarios.
The calculated imbalance if you like applies to the specific test circuit, and cannot really be extended to use of this balun in an antenna system scenario.
Continued at Inherently balanced ATUs – part 3 .
]]>LB Cebik in 2005 in his article “10 Frequency (sic) Asked Questions about the AllBand Doublet” wrote
In recent years, interest in antennas that require parallel transmission lines has surged, spurring the development of new inherently balanced tuners.
Open wire lines require current balance to minimise radiation and pick up, the balance objective is current balance at all points on the line.
Cebik goes on to give examples of his “inherently balanced tuners”.
Above, Cebik’s “inherently balanced tuners” all have a common mode choke at the input, and some type of adjustable network to the output terminals.
Cebik was not the originator of the idea, many others had written of the virtue of the configuration, but I cannot recall seeing meaningful measurement to support the claims.
Lets take the last circuit, and simulate it using A low Insertion VSWR high Zcm Guanella 1:1 balun for HF followed by an MFJ949E T match ATU. The MFJ949E stands on its insulating feet on a large conductive sheet to serve as the ground, the balun in connected to the ATU input jack and the input jack of the balun is grounded to the aluminium sheet. A banana jack adapter is connected to the ATU Coax 1 output jack, and resistors of 50Ω and 100Ω connected from those terminals to provide a slightly asymmetric load.
The voltage between ground and each of the output terminals was measured with a scope, and currents calculated.
Above are the measured output voltage waveforms at 14MHz.
The meanings of currents used here is given at Differential and common mode components of current in a two wire transmission line.
Lets work out the current amplitudes. Above, V1 (yellow) is 4.8divpp, V2 (cyan) is 7.4divpp. I1=V1/50=4.8*0.2/50=19.2mApp. I2=V2/100=7.4*0.2/100=14.8mApp.
Expanding the timebase allows better measurement of the phase difference.
V2 lags by a half cycle and 7.5µs, so V2 phase is 1807.5e9*14e6*360=18038=218°.
Lets calculate the common mode and differential component of current in each load resistor. We will use Python as it handles complex numbers.
>>> i1=0.0192
>>> i2=0.0148*(math.cos(218/180*math.pi)+1j*math.sin(218/180*math.pi))
>>> ic=(i1+i2)/2
>>> abs(2*ic)
0.011825300356025956
>>> id=(i1i2)/2
>>> abs(id)
0.016089765935912277
>>> abs(2*ic)/abs(id)
0.7349578858466762
>>> 20*math.log(abs(2*ic)/abs(id))/math.log(10)
2.674750918136747
So, the differential component of current is 16.1mApp, and the total common mode current is 11.8mApp, the total common mode current is more than a two thirds the differential current or 2.7dB less than differential current.
By any standard, this is appalling balance.
The measurements reported here are for a specific scenario (components, frequency and load), and should not be simply extrapolated to other scenarios.
The calculated imbalance if you like applies to the specific test circuit, and cannot really be extended to use of this balun in an antenna system scenario.
The problem starts with that it is near impossible to build such an ATU with perfect symmetry, meaning the distributed inductances and capacitances to ground are symmetric so that with a symmetric load, the entire system was symmetric and there was very low common mode load current.
Achieving that symmetry does not guarantee symmetric currents in an asymmetric load. Fig 4 and the associated text at Balanced ATUs and common mode current deal with this problem.
“Inherent balance” is a belief of the very naive… and snake oil salesmen who would relieve them of their money whilst selling the satisfaction that they have something rather special!
Superlatives like “true balanced tuner”, “fully balanced tuner”, “superb current balance” are bait for naive hams who do not test the claims, hams who do not measure the balance objective… common mode current.
Continued at Inherently balanced ATUs – part 2 .
]]>Above is Ruthroff’s equivalent circuit, Fig 3 from his paper (Ruthroff 1959). Focusing on the left hand circuit which explains the balun as a transmission line transformer (TLT), and taking the node 1 as the reference, the loaded source voltage appears at the bottom end of the combined 4R load, and transformed by the transmission line formed by the two wires of the winding, and inverted, at the top end of the combined 4R load.
It is the transformation on this transmission line that gives rise to loss of symmetry.
The complex ratio Vout/Vin is dependent on the complex reflection coefficient Gamma at both ends of the line and the line propagation constant gamma, all of which are frequency dependent complex quantities.
Vout/Vin=(1+GammaLoad)/(1+GammaSource)*e^(gamma*l)
In baluns, the real part is often close to unity, the phase is more significant.
TWLLC and family tools calculate this quantity in the long output, but I do not recall seeing it calculated in other tools. Values for Gamma may be shown in other tools, but again I have not seen gamma shown directly.
Astute readers will realise that a more correct balun could be made by including another TLT to supply the noninverted output. By then, it looks like a Guanella 4:1 balun with the output centre tap grounded (so it behaves like a voltage balun) and has better balance… on symmetric loads.
In the first article, the measurements at the input of around 7m of 50Ω line were adjusted to move the reference plane to the load end of the coax using the add/subtract cable feature of Antscope to deembed the transmission line.
The second article used a FAVA5 analyser and VNWA software to make the measurements and to some extent, deembed the transmission line. In this case the transmission line was quite short at 370mm, and whilst the facility adjusted for propagation time, it did not adjust for attenuation though that was very small in this case and of little consequence. The FAVA5 analyser and VNWA software combination would not suit the scenario in the first article as will be demonstrated.
This article examines the response to a 6m length of RG58 with O/C load at 30MHz.
We can see that although the phase of Gamma (phase of 0.85+j0.01) is close to zero the magnitude is 0.85 when the magnitude should be 1.00 for an O/C load.
The reason for this is that the port extension facility does not deembed the attenuation of the line.
I can use TLLC to calculate the ratio of Vout/Vin for that scenario as 1.182e+0∠2.3°, so Vin/Vout=0.868 which reconciles well with the measured Gammaof 0.85.
In this case the attenuation is significant, and the port extension facility falls short in modelling the effect.
By contrast, Rigexpert’s Antscope use for the first article does include attenuation in the cable add/subtract facility and gives acceptable results.
Antscope’s cable add/subtract facility which includes a database of common cable parameters provides a convenient means of backing out the transmission line when measurements are made remotely, and whilst dependent on the accuracy of the line characteristics, it is a very useful facility not found universally.
]]>Above is the top view of the balun, and the test termination comprised two 100Ω 1% resistors clamped between the screw terminals, so pigtails were just 3mm in length.
Above is a view of the interior.The coax pigtails are quite short, they exist at the input and output.
Because of the pigtails inside the box, and on the termination, there is some unavoidable lead inductance.
Measurements were made with a FAVA5 and VNWA PC software.
A measurement of impedance looking into the balun is obtained by using port extension to subtract the effect of the known length of RG316 transmission line.
To be more correct, it deembeds the propagation time of the additional line but it does nothing to deembed the attenuation which is quite small for the line in this case, so the error is small.
Above is the scan from 1 to 31MHz. The existence of some inductance at both ends of the transmission line complicate the results, but it appears that the port extension correction is approximately correct and Insertion VSWR reaches 1.1 at 30MHz, some of which is due to imperfection in the termination used. Nevertheless it is a good result, partly due to keeping pigtails short, partly that the screw terminals allow a short termination. Equivalent series inductance would appear to be perhaps 30nH.
Classic baluns for antenna use tend to have screw terminals that are widely spaced, often on opposite sides of the box, seemingly to suit wider spaced transmission lines. Of course when used with such lines, Insertion VSWR is not relevant, but where they are used with say, a HF Yagi, wide spacing is sub optimal.
]]>The Ruthroff 1:1 voltage balun can be seen as two back to back Ruthroff 4:1 voltage baluns with the redundant winding removed… and that prompts the thinking that the cascade of two baluns back to front might cancel the phase delay.
Let’s measure a popular Ruthroff 1:1 voltage balun.
Above, the RAK BL50A was a quite popular balun, and probably the balun of choice for half wave dipoles… well until the message about current baluns escaped.
Above is a scope capture of the terminal voltages with a 100Ω centre tapped load, the centre tap is bonded to the coax shield terminal.
The red trace is CH1+CH2.
Lets put those numbers into a calculator as unscaled divisions from the scope.
Above, the calculated phase difference is 10.9° which reconciles well with the estimate from the scope trace delay above.
The ratio 2Ic/Id is 20%, this is pretty awful current balance on a symmetric load.
Now this balun is worse at higher frequencies because the attenuation in the balun transmission line increases, and the phase delay increases almost proportional to frequency.
So, whilst ideal voltage baluns deliver equal but opposite currents into a perfectly symmetric load, practical Ruthroff 1:1 voltage baluns might not be all that good.
Voltage symmetry is poor, predictable, and it is load dependent, and it gives rise to significant common mode current, even in a symmetric antenna system.
If you think your balun is working well… it is probably because you have not measured common mode current.
Above is Ruthroff’s equivalent circuit, Fig 3 from his paper (Ruthroff 1959).
If one looks carefully at the transmission line form, there is effectively a two wire line wound into a helix (usually on a magnetic core) and connected from the unbalanced source to one half of the load inverting the connection for the necessary phase reversal.
Ideally, Vout of this line is equal to Vin, ie Vout/Vin should be 1∠0°. That is unlikely as it implies a zero length transmission line which provides the decoupling of the phase inverting line.
This article looks at the Ruthroff 4:1 balun balance using the very popular MFJ949E as an example.
Above is a pic of the MFJ949E Ruthroff 4:1 balun. The transmission line is not uniform, but let’s make an approximation to predict its behavior with a centre tapped 100Ω load, the centre of which is connected to the ground terminal.
The following is a model using TWLLC of a similar transmission line with 50+j0Ω load (one half of the load is connected to the transmission line). We will assume that Zcm of the TLT is very high.
Approximate MFJ949E Ruthroff balun TL 

Parameters  
Conductivity  5.800e+7 S/m 
Rel permeability  1.000 
Diameter  0.000600 m 
Spacing  0.002000 m 
Velocity factor  0.750 
Loss tangent  0.000e+0 
Frequency  7.000 MHz 
Twist rate  0 t/m 
Length  0.600 m 
Zload  50.00+j0.00 Ω 
Yload  0.020000+j0.000000 S 
Results  
Zo  170.52j2.02 Ω 
Velocity Factor  0.7500 
Twist factor  1.0000 
Rel permittivity  1.778 
Length  6.725 °, 0.018680 λ, 0.600000 m, 2.669e+3 ps 
Line Loss (matched)  1.22e2 dB 
R, L, G, C  7.976649e1, 7.666990e7, 0.000000e+0, 2.637228e11 
Line Loss  4.12e2 dB 
Efficiency  99.06 % 
Zin  5.113e+1+j1.854e+1 Ω 
Yin  0.01728488j0.00626760 S 
Γ, ρ∠θ, RL, VSWR, MismatchLoss (source end)  5.288e1+j1.322e1, 0.545∠166.0°, 5.271 dB, 3.40, 1.531 dB 
Γ, ρ∠θ, RL, VSWR, MismatchLoss (load end)  5.466e1+j4.146e3, 0.547∠179.6°, 5.247 dB, 3.41, 1.541 dB 
Vout/Vin  8.582e1j3.457e1, 9.252e1∠21.9° 
Iout/Iin  1.006e+0j3.533e2, 1.006e+0∠2.0° 
S11, S21  4.334e2+j1.754e1, 9.561e1j2.102e1 
Y11, Y21  1.168e3j4.917e2, 1.168e3+j4.951e2 
NEC NT  NT t s t s 1.168e3 4.917e2 1.168e3 4.951e2 1.168e3 4.917e2 ‘ 0.600 m, 7.000 MHz 
k1, k2  7.679e6, 0.000e+0 
C1, C2  2.428e1, 0.000e+0 
Mhf1, Mhf2  2.340e1, 0.000e+0 
dB/m @1MHz: cond, diel  0.007679, 0.000000 
γ  2.339e3+j1.978e1 
Among all that detail is an estimate of Vout/Vin, it is 9.252e1∠21.9°. That is to say that if there is 1.0V on the ‘direct’ balun terminal, the other terminal via the transmission line will be 0.9252∠21.9° V.
Since the current in each of our 50Ω 1% load resistors is V/50, we can calculate the common mode current by summing them, and it will not be zero because of the lower voltage and particularly the significant phase delay of the ‘indirect’ terminal.
Connecting a scope to the terminals and measuring the voltage applied to each of the 50Ω resistors, we can see that the orange trace is lower in amplitude (about 90%) and delayed by about 8ns (20.2°)
We can also use the scope to add the waveforms to find the common mode component.
The red trace is CH1+CH2.
Lets put those numbers into a calculator as unscaled divisions from the scope.
Above, the calculated phase difference is 22° which reconciles well with the estimate from the scope trace delay above. It also reconciles well with the theoretical prediction earlier.
The ratio 2Ic/Id is 40%, this is pretty awful current balance on a symmetric load.
Now this balun is worse at higher frequencies because the attenuation in the balun transmission line increases, and the phase delay increases almost proportional to frequency.
This is quite a small balun physically, larger baluns will have longer transmission line and greater phase delay, so even worse performance on a perfectly symmetric load.
So, whilst ideal voltage baluns deliver equal but opposite currents into a perfectly symmetric load, practical Ruthroff 4:1 voltage baluns might not be all that good.
Measured behavior of the Ruthroff 4:1 voltage balun accords with prediction using Ruthroff’s transmission line model of the device.
Voltage symmetry is poor, predictable, and it is load dependent, and it gives rise to significant common mode current, even in a symmetric antenna system.
If you think your balun is working well… it is probably because you have not measured common mode current.
Pickup most handbooks, and even text books, and antennas and often antenna systems are described in this way.
That model is quite inadequate for many or most antenna systems installed in proximity of natural ground. For example, a two terminal dipole and feed line system representation cannot have feed line common mode current, and it follows that thinking in terms of two terminal models denies a full understanding of the antenna system.
(Schmidt nd) sets out a three terminal model of an antenna system in presence of ground using quite conventional linear circuit theory.
Above is Schmidt’s Y network based on values of three intermediate impedances, ZD, ZU, and ZC. These are found from measured values Za, Zb and ZC as explained by Schmidt:
I measure ZC by connecting both leads of the twinlead together and measuring the impedance to ground. Next I connect wire 2 to ground and measure the impedance between wire 1 and ground and call this Za. Reversing the connections, by grounding wire 1 and measuring between wire 2 and ground gives Zb.
An adapter was used to allow measurement of Zz, ab, and Zc reported below. Above, it is attached to a FAVA5 antenna analyser… the worst instrument I have ever used, but never mind, it might get fixed with firmware updates over the coming years… though experience says that is probably wishful thinking.
Measurements were confirmed with a Rigexpert AA600.
The antenna system is a reasonably symmetric Inverted V configuration of the G5RV with tuned feeders, where the feed line to the point of measurement is 10m of 560Ω open wire line.
Above are the direct measured values and calculated results.
The calculations are a bit tedious, a handy online calculator can perform them more conveniently.
The unbalance impedance Zu is not trivial, though the real component is small, the imaginary component is significant suggesting that although the wires are symmetric, there is some asymmetry perhaps due to ground height variation, soil type, soil water content, vegetation etc.
The antenna system is a reasonably symmetric Inverted V configuration of the G5RV with tuned feeders, where the feed line to the point of measurement is 10m of 560Ω open wire line.
Above are the direct measured values and calculated results.
The unbalance impedance Zu is not trivial, and worse that the previous case. again a significant imaginary component suggesting that although the wires are symmetric, there is some asymmetry perhaps due to ground height variation, soil type, soil water content, vegetation etc.
Readers will often see back of the envelope calculations of the effectiveness of a common mode choke. The article Using Ohms law on antenna baluns deals with some of the junk science that masquerades as fact. Some back of the envelope analyses assume the common mode driving voltage is that of a 50Ω unbalanced source, and the load is simply a common mode choke whereas if an ATU is between the 50Ω point and feed line, voltages and currents are transformed, the series common mode impedance of the ATU and any balun(s) are relevant as is ZC of the antenna system as measured above.
To obtain valid results, the model must be valid, and that starts with including all of the elements that are relevant. Such a model can give a good prediction of the impact of a common mode choke of known Zcm at the point at which the measurements were made.
Such models are complex, and mathematical (high school maths + complex numbers), but solvable with the requisite knowledge.
A simpler approach is to simply directly measure the common mode current, and try common mode chokes with high Zcm to reduce it to an acceptable level. In most cases, the priority in addressing high common mode current is to examine the root cause, can the system symmetry be improved?