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Understanding MF and HF chokes and transformers.

This web page will look into measurements of coils, chokes and transformers in the range of 1 to 50Mhz (covering the ITU definition of MF and HF ranges from 300kHz to 30MHz). The following sections are covered:

• Terminology
• Balanced and Unbalanced
• Balun
• Choke
• Transformer
• Transmission line
  
• Differential and Common mode currents
  
• Measuring inductors/capacitance/resistance of coils made with different Coax cables, bi(parallel)/monofilar wire, twisted wire
• Calibrating NanoVNA
  
• Measurement setups for (coupled) coils, Transformers and Chokes
  
• Coil measurements using NanoVNA and simulations using LTspice
• Transformers, Chokes and Hybrid configurations
• VSWR of Transformers, Chokes and Hybrids
• Common Mode Rejection (CMR) of Transformers, Chokes and Hybrids
• Conclusion
• Openstanding questions
• References
• Acknowledgements

Introduction

The aim of this web page is to determine which Hybrid Choke/Transformer to use for a 40m OCFD. The compenents making up the Hybrid are also individually measured, using different devices and different metholdogies. Also the properties of the OCFD are measured and compared with other people's measurements and literature. A conclusion will be provide where the synthesis of these compents is discussed (to provide a design and implementation template).

Terminology

Work in progress: Hopefully I will gain more knowledge to use proper naming.

Choke and Transformer look to have clear meaning/function to me and I think these can cover some/all of the bullets (as an added property) in the Balanced and Unbalanced section.

I will use the word balun on this webpage only to pointout a physical device. How the device is configured/used, determines if it is a Choke or Transformer.  Additional input and output properties are added to define if the configuration is Balanced/Symmetrical or Unbalanced/Asymmetrical.

Proper naming is important, and it has to be consistent and understood by me and others;-) To accomodate others, I have included in the below sections alternative terms used by others.
Anyway this web page should be build in such a way, that if a name changes it will be simply changing strings of letters.

Balanced and Unbalanced

Several (closely related) directions are refered to, when using the terms Balanced (bal) and Unbalanced (un):

• Sometimes Balanced and Unbalanced is refering to respectively symmetrical/balanced (two signals referenced to each other, not necessarily the earth: like a dipole antenna); and asymmetrical/unbalanced (one signal reference to the earth: coax based source) sources. Most (lower) MF and HF antennas/sources/sinks are, with variable degree, asymmetrical in real life.
• Sometimes Balanced and Unbalanced is refering to respectivley the differential; and common mode currents or voltages.
• Sometimes Balanced and Unbalanced is refering to respectively the currents are through two conductors and are equal and opposite; and has one driven conductor and the other conductor will be through multiple paths (another conductor, the earth, the air and then earth, etc.).
• Sometimes Balanced and Unbalanced is referring to respectively noise will have effect on both lines (and thus cancel each other out due to differential sensing); and noise has only effect on one line and thus can't be cancelled out.
• Sometimes Balanced is referring to balanced voltage (on the two conduction two precisely opposing voltages) and current balance (on the two conduction two precisely opposing currents). And Unbalanced to unbalanced voltage (one conductor has precisely zero volt [braid] and the other conductor passes the voltage) and balanced current (on the two conduction two precisely opposing currents): like coax.
  

It is sometimes not clear what is meant with the terms Balanced and Unbalanced, so asking/digesting the meaning is important. The last bullets sounds the most clear...
One can have un-un, bal-un and bal-bal.

Balun

IEV definition: Balun: device for transforming a balanced voltage to an unbalanced voltage or vice-versa.
I am still strungling with the term balun in many publications. For now: I don't look at this abbreviation of BALanced/UNbalanced, but see it as a string of five letters (aka an icon).
On this web page, a balun (not using a capital...) is defined as a 4 port device (2 input and 2 output ports). It is constructed with 2 or more tightly coupled coils. The coils (twisted pairs, mono, bifilar or twin, coax, stripline, etc.) can have different layouts (toroid, tube, λ/4 or λ/2, etc., around/inside a material) and core material (air, iron, NiZn, MnZn, dielectric, etc.). The interconnection/configurations of the coils determines its function, resulting in a Choke or Transformer.

Voltage balun

According to W7EL (page 159): A voltage balun causes equal an opposite voltages [defined from Earth] to appear at the balanced port regardless of load impedances

Current balun

According to W7EL (page 159): A current balun causes equal an opposite currents to appear at the balanced port regardless of load impedances

Choke

IEV definition: Choke: an impedance transforming device for preventing energy within a given frequency band from taking an undesired path.
Other terminology: 1:1 balun, current balun, common mode choke, sheath current choke, Tranmission Line-Transformer (TLT).
The aim of a Choke is to make sure that on each of the two outputs equal but opposing currents exist (there is no transforming aspect, so always 1:1).
If the socalled 1:1 balun chokes the Common Mode Currents (CMC), I call it on this webpage a Choke.

Transformer

IEV definition: Transformer: electric energy converter without moving parts that changes voltages and currents associated with electric energy without change of frequency.
Other terminology: x:1 balun, voltage balun, voltage/impedance/current transformer, Tranmission Line-Transformer (TLT), autotrafo.
The aim of a Transformer is to make sure that the voltage and thus impedance/current is transformed: these three are of course directly coupled through Ohm's law.

Transmission line

IEV definition: One-dimensionally distributed two-terminal-pair circuit element characterized by lineic inductance l, lineic capacitance c, lineic resistance r and lineic conductance g which may all be functions of the same space coordinate x, where the voltage u(x, t) and the electric current i(x, t), where t is the time, are related by partial differential equations
Other terminology:  feed lines, feeders, coax, twin-pair
Can be balanced (twisted pair, twin-pair, bifilar) or unbalanced (coax).

Differential and Common mode currents

Assume a current in each of the two wires (resp. i₁ and i₂). Looking at the same point along their length, one measures i₁ and i₂; the Differential mode current in each wire is (i₁ - i₂)/2 and the Common mode current in each wire is (i₁ + i₂)/2.
A 'nice' explanation of Common mode current is in many case by done looking at Coax cable. Where the in- and outside of the Coax braid are seen as two conductors. The TEM mode can only exist between the inside of Coax braid and the outside of the Coax inner conductor (the Differential mode current). While the outside of the Coax braid can be 'utilised' for something else (like Common mode current).
I have a few issues with this 'nice' explanation:

• If it is a CMC, it should flow through both conductors of coax (correct?), in the explanation it flows on the outside of the Coax braid, but where does it flow on the Coax inner conductor?
  
• The wavelength in the in- and outside of Coax braid are different (at the same frequency). The velocity factor (vf) of the inside Coax braid is around 60 to 80%, while on the outside Coax braid it will be closer to 97%.
• What kind of currents would this difference in vf give between in- and outside (within the Coax braid)?
• An explanation of CMC in a symmetrical cable can be seen in this presentation (slide 8 and 9).
  

A  more general explanation of how common mode current works in all types of cables could be the following:
At this moment the simple explanation of muRata works for me best: part of the energy (current) goes through stray capacitances from the antenna through the Earth or antenna feed to the earth of the rig. Beside this, noise sources can also intorduce common mode currents. These currents through Earth are resulting in a common current in the cable (be it symmetric or asymmetric cable).
I am open to other explanations.

Measuring inductors/capacitance/resistance of coils made with different Coax cables, bi(parallel)/monofilar wire, twisted wire

The aim is to understand if theory and pactice match.

Measurements done with GM328A Component tester (version 1.12k), NanoVNA-H 3.5 (software version 1.0.64, kernel 4.0.0) and NanoVNA Saver (version 0.3.9).

Only using one (composite) coil of the Chokes/Transformer (but not really checking the full Choke/Transformer function, that is for a later section): just to make some basic measurements of a coil's (mutual) induction, capacitance, resistance. These basic measurements are to to learn the test tools (Component tester and NanoVNA). The measurements are using Reflection measurements.

1. C_t = 10¹²/((2*π*f₁*10⁶)²*(L+M)*10^-6) [pF] (formulas a and b need to be done iteratively)
   
2. M = L - 10⁶/((2*π*f₂*10⁶)²*(C_w+C_t)*10^-12) [µH] (formulas a and b need to be done iteratively)
   
3. Z_f[1,2] (or Comon Mode Impedance [CMI]) = 2*R₀*(10^{(-S21_f[1,2]/20)}-1) [Ω] (on this page: R₀ = 50Ω, remember that in passive networks S21_f[1,2] in dB is negative [or -CMR])
   This formula is also used in e.g. NanoVNA Saver (between S21 LogMag and S21 |Z| series) and https://www.dl4zao.de/_downloads/Balun_dl4zao.pdf, slides 61-62.
   
4. "Using twisted pair wire to wind baluns [is] simpler and is good enough for MF and HF bands; there is no huge benefit in using bifilar windings, which are much harder to wind." (from DJ0IP, and my emphasis).
   I have totally no problems with winding bifilar coils, so I would use bifilar instead of twisted (for me it is an extra activity to make twisted PTFE). So this is a personal preferance.
5. The coax cable (RG58A/U and RG316) was wound with a smaller bend radius (resp ~1cm and ~0.75cm) than allowed by specification (resp. 2.54cm and 1.5cm). According to amateure radio sources this would not be a problem for coax cable with (hard) (resp. PE and PTFE) inner dielectric insulation. See also here. IMHO, one should try to align with the specified minimum bend radius, to be able to withstand the higher differential-mode voltages (Hunt, 2015).
   
6. On this web page 4:1 Sevick is used for naming, instead of 4:1 single core Guanella (as called by other authors): as Guanella always talks about multiple cores (Fig. 2b).
   

Inductance (L_ct and L_NV) evalutation

Inter coil capacitance (C_w) evaluation

AL (AL_ct and AL_NV) evaluation

Calibrating NanoVNA

It is important to calibrate my NanoVNA (one direction two ports calibration) using the SOL (Short-Open-Load) method (for Reflection [somethimes called Shunt] measurements) or the SOLTI (Short-Open-Load-Through-Isolation) method (for Series-through and Shunt-through measurements);

The SOLTI devices used are seen in below picture:

Different setups with VNA

The three different setups can be used for three different ranges of impedance (see alos this link, page 10):

1. Reflection
   For impedances between 15 and 200Ω
   The NanoVNA is more sensitive then the system described in above link. Looking at the NanoVNA the impedance range (for 7% error) is between 1 and 3kΩ; more or less an order larger on both sides.
   
2. Shunt-through
   For impedances smaller than 75Ω
   Assuming that the above accuracy of NanoVNA also happens for this setup: impedances smaller than 750Ω will be accuractely measured in Shunt-through. This matches somewhat this error analysis (Table 2).
   Probably the same issue with systematic error as with Series-through?
   
3. Series-through
   For impedances greater than 15Ω
   Assuming that the above accuracy of NanoVNA also happens for this setup: impedances larger than 1Ω will be accuractely measured in Series-through. This matches somewhat this error analysis (Table 2).
   When measuring (using NanoVNA-H 3.5, software version 1.0.64, kernel 4.0.0) impedance with series-through, a considerable systematic error was found in Z_DUT (in order of 9%). This error can be removed by included the derived impedance of port 1 (Z_source), which was for this particular NanoVNA close to 43.7+3iΩ. No significant influence is seen (for this particular NanoVNA) by including the derived impedance of port 2 (Z_load); which was very cose to 50+0iΩ.
   see for some more detail on this, this web page.
   

Measurement setups for (coupled) coils, Transformers and Chokes

In some cases one needs to include a connector setup which are not easy to include in above calibration (also called de-embedding the connectors).
For this web page the NanoVNA numbers have not been de-embedded. Another alternative (in case the extension is behaving as a 50Ω transmission line) is using the Calibrate -> Offset delay feature on NanoVNA Saver or Display -> Scale -> Electrical delay on the NanoVNA.

1. Common mode (CM)
2. Differential mode (DM)
3. Open-cicuit mode (OC)
   This setup is used by several people as their socalled CM measurements, but this OC setup does in some way a combination of the DM and CM setup. So be aware of that aspect when evaluating!
   This can also be seen as a Series-through measurement.

• CM3: a star (with each (R₀/3)Ω), as in above picture
• CM2: balanced resistors (each of (R₀/2)Ω) (see below) (from. https://www.dl4zao.de/_downloads/Balun_dl4zao.pdf, slide 49).
  
  The CM measurements on this web page are based on CM2.
• CM0: all resistors are 0Ω (aka L₁ and L₂ are in parallel).
  CM0 is the easiest to measure.

There is no real difference between these three CM-variants (see below simulation in LTspice): upto 400MHz there is only 3dB difference in S₂₁ between CM3 and CM0, and below 100Mhz there is no significant different.

• OC (Open circuit), L2 is open circuit, as in above picture
  OC is the easiest to measure.
• CC (Closed Circuit): L2 is shortened.
  In this case one measures the leakage inductance.
  

When we are looking a Transformers and Chokes, f₁ and f₂ become f_OC1 and f_OC2 for the OC mode. In most cases Z_f1 and Z_f2 will be Z_cm and Z_dm.
I think G3TXQ uses OC measurements. He warns that the reactance of a Choke should be at least more than several positive kΩs (to overcome the negative reactance of the antenna feeder, which is several negative 100Ωs). But it is anyway important to have a large resistance for a Choke. This garantees that the |Z| is high (several kΩs).

Coil measurements using NanoVNA and simulations using LTspice

To see if a simulation is close to the Series-through (in this case also OC mode) measurements, bi-2r2r-43 (bifilar PFTE coil with 10 windings) has been used.
As the Series-through measurements is also an OC mode test: Z_f[1,2] become R_[cm,dm].
Two different type of equivalent circuit models have been worked out: power-supply choke (two monofilar multi layer coils) and MF and HF choke (transmission line: one bifilar/coax single layer coil).

The coil measurements

The Series-through measurements using NanoVNA Saver gives (power, impedance and frequency axes are logarithmic, phase axis is liniair):

The coil simulation: power-supply and MF & HF choke

All circuit are based around RLGC models.

Power-supply choke

The equivalent circuit (for simulation in LTspice and from the reference discussed here) of a power-supply choke is below (send me an e-mail if you want the LTspice model files):

<The above circuit has been changed somewhat from the original article: R_CM and R_DM (capital letter subscripts) have been replaced by 2*R_cm and 2*R_dm (small letter subscripts) to match the above definition of R_cm and R_dm>

Using this power-supply equivalent circuit in LTspice XVII and the parameters measured of power-supply chokes in the above article (Tabel III), one can fully reconstructed the paper's results over the frequency range of 0.1 and 10MHz.

And the simulation results (from LTspice) are (power, impedance and frequency axes is logarithmic and phase axis are liniair):

• The frequency of the peaks in Zin(V1) (and Zout(V1)) match more or less the peak in S11 |Z| and the peak in S21 |Z| series.
  
• I don't think that Zin(V1) and Zout(V1) are comparable with S11 |Z| and S21 |Z| series. If I plot the S-parameters Z11(V1) and Z21(V1) in LTspice, I get very erratic results.
• Zin(V1) and Zout(V1) are the same when doing a Series-through measurement.
• The simulated curves have this spike at f_CO2 and the S21 LogMag and S21 Phase are faster changing in mid frequency range.
• The S21 LogMag at f_CO1 and f_CO2 also looks way too low (and does not follow the formula)

• A paper by Nomura&Kojina&Hattori, 2018, which looks at RCL ladders.
  
• Another more extensive equivalent circuit: https://hal.archives-ouvertes.fr/hal-01886795/document [Kotny]
  
  

MF and HF choke

• Guanella's equivalent circuit (TLT) is based on a tranmission line for the DM mode and a inductor for the CM mode [Guanella, 1944]
  
• Owen Duffy made models of 1:1 Guanela Choke and 4:1 Ruthroff Transformer. These will be included in the research I am doing

Here are inductor impedance (green top curve in each pane) simulations (just for illustration) of four different models:

Evaluation

The responce of Guanella equivalent circuit is closest (no spike around f_CO2) to the measurements of the above 1:1 Guanella choke. The reason is that the power-supply chokes are (multi layer) monofilar inductors, while the MF and HF chokes (TLT) are a (single layer) bifilar/coax transmission line for the DM and a inductor for the CM.
Let me know if you have further improvements.

Simulating antenna, Choke and feeder

An equivalent circuit for antenna, Choke and feeder can be found here.

Transformers, Chokes and Hybrids

• FT240-31
  160m to 30m, 80m to 40m
  
• FT240-43
  160m to 10m, 40m to 30m
  
• FT240-52
  40m to 10m, 30m to ~17m
  
• FT240-61
  30m to 10m, ~17m
  

• Zc>=4kΩ ≍ -32dB
• if Zc<4kΩ
• 'several' meaning 3 or more times, aka larger than Xc>3kΩ
• Rc>=Xc

Theoretical approach to a Choke wound on toroid

Several #43 parameters (FT140-43, 14 turns, C_stray=0.3pF)

Several #31 parameters (431173551, 9 turns, C_stray=1.1pF)

The two simulated chokes were build and the CMR was measured.
The comparison of #43 is here:

The black curve is the CMR measured by V. Reijs from a FT140 with 14 turns RG316, and the red curve is the simulated one (with C_stray of 0.3pF). The C_stray in the simulation is adjusted in such a way that the 'dip CMrej_eff' in simulated has similar frequency to 'dip CMrej_eff' in measured. The green curve is the simulated phase.

The comparison of #31 is here:

The black curve is the CMR measured by Nico Veth (Common mode chokes: Info, maken, meten, Electron, April 2022, page 172) from a 431173551 toroid with 9 turns 6.3mm twin wire, and the red curve is the simulated one (with C_stray of 1.1pF). The C_stray in the simulation is adjusted in such a way that the 'dip CMrej_eff' in simulated has similar frequency to 'dip CMrej_eff' in measured. The green curve is the simulated phase.

The simulated and measured CMR match quite well.

Another comparison was done with RG58 cable, the above graph of G3TXQ was also analysed using the simulation. Remember that the C_stray in my simulation is adjusted in such a way that the 'peak |Z_eff|' in simulated has similar frequency to 'peak |Z|' in G3TXQ's measuremets.

The bold (somewhat darker) and underlined numbers (to see a larger picture; right click the above image) indicate when R_eff > |Z_eff|.

One can compare these simulations with G3TXQ measurements:

The differences are slight. So we can conclude that the simulation is ok-ish.
To align the above two graph (using RG58), it looks that the more turns gives a (almost linear) higher C_stray is seen (for most materials C_stray = 0.087*N, measured for N≥9).

In some references C_stray looks to be decreasing with increasing number of turns as described here (for wire up to 1.6mm) and here. Another study (Fig. 6 using RG58 airwound; wire diameter 8mm) shows an (almost linear) increase in C_stray with the number of turns. This last study aligns with my earlier described simulations.

Quenstions asked to Fair-Rite (after a month; no answers received yet):

• The formula of Snoek in this Fair-Rite paper (page 52, Equation 1) looks to be calculating in kHz instead of Hz. What is correct?
  
• With increase of temperature: an increase of permeability, but a decrease of impedance is shown in Fair-Rite catalogue (e.g. page 16, Figure: Percent of Original Impedance vs Temperature and Figure: Initial Permeability vs. Temperature). When looking at the formula: Inductance (Fair-Rite catalogue, page 138) one would expect also an increasing impedance. Or is the resistivity (μ") also changing with temperature?
  
  The above μ" dependendy of #43 is found if assuming that μ'-curve is only propertionally depending on μ_i (at 10kHz?) and there is no additonal temperature dependency of μ' on frequency (beside the normal dependency). With my methodology temperatures above 80C μ" dependency becomes undetermined (R would become negative...). A pity no other frequency behavoir (say 2.5 or 5MHz) is in the #43 specs. For #31 there is shown a 5MHz frequency dependency of μ", which is more or less between 10 and 25MHz, so perhaps the same yields for #34?
  Or should μ'-curve have an additional temperature dependency on frequency? If μ" has it, why not μ'? This addional μ' dependency on freqeuncy, could also 'overcome' the negative resistance...
  EPCOS has a Ferrites and Accessories data book (page 54-55) where for some ferrites the tan(δ)/µ' is given (for freq<700kHz) from which one can easily derive µ" (= (tan(δ)/µ')*(µ')²); K8 and K10 have somewhat similar ferrite as #43. Below is the complex permeability as a function of temperatue (at 0.5MHz) for K8 (for comparison it shows also the µ'(T) of #43):
  
  
• The temperature dependency of inductance (at 0.1MHz) has been measured by putting a 1:1 Guanella Choke into an oven and change the temperature from 145 to 20C (over a period of some 90 minutes). This gave the below change in inductance (and inductance should in theory be proportional to μ'):
  
  This behavoir is though totally different from the μ' dependency on temperature as given by Fair-Rite #43 (or other ferrite manufactures):
  
  Inductance and μ' should have a similar curve form, IMHO, but they are quite different. What do I do wrong? The measured AL_NV of the ferrite used at 25C is close to the specs (so no large deviation there).
• Impedance depency on temperature is also measured for several amateur bands:
  
  Also this is different from the behavior specified by Fair-Rite #43:
  
  These graphs are quite different. What do I do wrong? The measured AL_NV of the ferrite used at 25C is close to the specs (so no large deviation there).
• A decrease of resonance frequency with increased N is shown in Fair-Rite catalogue, Figure 25 on page 152. Some documents on self capacitance show a decrease of resonance freq. due to decreasing stray capacitance with N (of wire upto 1.6mm). Although I myself find an increase of resonance frequency with increasing N (of cable RG319/RG58). This C_stray looks to be quite important for designing a Choke. Do you have a formula/directions for C_stray?
  Documentation of Laird (page 10) provides some input on influence of the number of turns. Their material 28 is closest to Fair-Rite #43 (although Owen Duffy has a different μ_i' [around 600] for Laird material 28!).
  
• In the #73 permeability CSV file one sees a negative μ'. How is this possible? Is this now a capactive instead of a inductive load?
  

Equivalent circuit with fix value components

The above model for the Choke is based on variable L(f) and R(f) and constant C_stray. To simulate this in a more simplified way (e.g. in LTspice), one could use an equivalent circuit that approaches the Choke behavior with parallel components which have fixed values: L_cm, R_par and C_par. The values can be derived from toroid simulation or from a VNA.
L_cm is the inductance at low frequency, aka with μ'_i. Or one can determine it from the low frequency S₂₁ LogMag of a VNA.
R_par is the highest value of |Z_eff|. Or one can determine it in the S₂₁ |Z|, when the S₂₁ Phase=0 of a VNA. The frequency belonging to this highest |Z_eff| is F_res.
C_par is now:
C_par = 1/((2*π*F_res)²*L_cm)

The resulting CMrej_eqv (dB, blue curve) below F_res (dashed blue line) is comparable to the CMrej_eff (dB, red curve) model, but for frequencies above F_res the simplified model has too much CMR.

Constructing Chokes and Transformers

Name	R0wire [Ω]g	Type	R0in [Ω]	R0out [Ω]	R0opt [Ω]h	Source	Configuration	Picture
1:1 DG0SA (is of the 1:1 Guanella type)	50 (100||100)	Choke	50	50	50	DG0SA https://www.dg0sa.de/341_343.pdf https://www.youtube.com/watch?v=P7wW4TtXmc8&t=2029s	twice 11 turns bifilar PTFE onto a FT140-43 core.
1:1 Guanella	50	Choke	50	50	50	DJ0IP https://www.dj0ip.de/vertical-antennas/rf-chokes/1-1-guanella-choke/	14 turns RG316 onto a FT140-43 core.
4:1 Ruthroff	100	Transformer	200	50	100	DJ0IP and VK6YSF http://vk6ysf.com/balun_4-1.htm	16 turns twisted PTFE onto a FT140-61 core.i
4:1 Sevick	100	Transformer	200	50	100	DG0SA https://www.dg0sa.de/341_343.pdf https://www.youtube.com/watch?v=P7wW4TtXmc8&t=2029s https://www.nonstopsystems.com/radio/pdf-ant/antenna-article-trnsmn-lines-2fmi.pdf (page 30-32)	twice 11 turns bifilar PTFE onto one FT140-43 core.
4:1 dual core Guanella	100	Choke/Transformer	200	50	100	VK6YSF https://vk6ysf.com/balun_guanella_current_1-4.htm	11 turns bifilar PTFE onto two FT140-43 core.

7. Best if R_0wire = R_0opt
8. R_0opt = √ (R_0in*R_0out)
9. 4:1 Ruthroff uses a different ferrite material (FT140-61) then the other devices (FT140-43).
   

The hybrid configuration consists of a Transformer and Choke defined above.
A picture of a bench-setup for the 4:1 Ruthroff (left) and 1:1 Guanella (right) hybrid configuration (input and output are terminated with resp. 200Ω and 50Ω; one can conect Earth to the wiper contact of potmeter, so simulaed resistive antenna):

Measuring Transformers, Chokes and Hybrids with VNA

VSWR of Transformers, Chokes and Hybrids

1 port VNA measurements are presented.

For each device the following graphs are shown:

• S₁₁ Smith chart
• LogMag of S₁₁ and S₂₁ (LogMag axis linear and freq. axis logarithmic)
• S₁₁ |Z| (|Z| and freq. axis logarithmic)
• S₂₁ |Z| series (|Z| series and freq. axis logarithmic).
  Not relevant for 1 port measurement
• S₁₁ VSWR [(Voltage) StandWave Ratio] (VSWR and freq. axis linear)
• S₂₁ Phase (Phase axis linear and freq. axis logarithmic)
  Not relevant for 1 port measurement
  

Transformer (A)	Choke (B)	Hybrid (A+B)
4:1 Ruthroff	1:1 Guanella	4:1 Ruthroff + 1:1 Guanella
4:1 Sevick		4:1 Sevick + 1:1 Guanella
4:1 dual core Guanella		4:1 dual core Guanella + 1:1 Guanella

• The 4:1 Sevick's VSWR is slightly better than the 4:1 dual core Guanella's VSWR
• The 4:1 Ruthroff's VSWR is 'worst' of the three (also discussed by G3TXQ, section C).ⁱ
• The VSWR of the Transformer determines mostly the VSWR of the Hybrid configuration
• The 4:1 Sevick and dual core Guanella + 1:1 Guanella's VSWR are better than the 4:1 Ruthroff + 1:1 Guanella's VSWR.ⁱ
• The 4:1 Sevick + 1:1 Guanella's VSWR is smallest of the three.ⁱ

The VSWR can be changed with e.g. a capacitor on 50Ω side of the Transformer, not on the Hybrid configuration input.

Common Mode Impedance (CMI) of Transformers, Chokes and Hybrids

2 port VNA measurements (CM2) are presented.

Below CM2 measurements were done. For each device the following graphs are shown:

• S₁₁ Smith chart
• LogMag of S₁₁ and S₂₁ (LogMag axis linear and freq. axis logarithmic)
• S₁₁ |Z| (|Z| and freq. axis logarithmic)
• S₂₁ |Z| series (|Z| series and freq. axis logarithmic)
  This is also the CMI (Z_f in Ω)
  
• S₁₁ Phase (Phase axis linear and freq. axis logarithmic)
  
• S₂₁ Phase (Phase axis linear and freq. axis logarithmic)

Transformer (A)	Choke (B)	Hybrid (A+B)
4:1 Ruthroff	1:1 Guanella	4:1 Ruthroff + 1:1 Guanella
4:1 Sevick		4:1 Sevick + 1:1 Guanella
4:1 dual core Guanella		4:1 dual core Guanella + 1:1 Guanella

• G3TXQ (section: 'Why reactive chokes are undesirable') warns that the reactance of a Choke should be at least more than several positive kΩs (to overcome the negative reactance of the antenna feeder, which is several negative 100Ωs). But it is anyway important to have a large resistance for a Choke. Both garantees that the |Z| is high (several kΩs). All the shown Hybrid align to that for most of the frequency range.
  
• The 4:1 Sevick's and 4:1 Ruthroff's CMI (in Ω: S₂₁ |Z| series) are much lower than the 4:1 dual core Guanella's CMI (as described by G3TXQ, Section D).ⁱ
• The Hybrid combination's CMI (in Ω: S₂₁ |Z| series) is something(?) like the sum of Choke's and Transformer's CMI.
• The 4:1 Sevick + 1:1 Guanella's CMI is similar to the 4:1 Ruthroff + 1:1 Guanella's CMI.ⁱ
• The 4:1 dual core Guanella + 1:1 Guanella's CMI is similar to the other two upto some 8MHzⁱ
• The 4:1 dual core Guanella + 1:1 Guanella's CMI is the largest of the three at higher frequncies in HF range.ⁱ

Some other sensitivity test:

• If he number of coax windings of the 1:1 Guanella Choke is decreased from 14 to 11, the S₂₁ is increased with ~3dB
• If the 1:1 Guanella Choke is cross-wound instead of straight-wound (as described here); no significant differences appear in the above CM2 parameters upto 30MHz. The cross-wound Choke has the advantage that the input and output are at opposing sides of the toroid.
  
• If the 4:1 Ruthroff (15 turns) was wound on a FT140-43 core instad of on a FT140-61 core (although that one has 16 turns); no significant differences appear in the above CM2 parameters upto 30MHz.

Comparing Hybrid configurations

Transformer	Choke	Curve color	CMI (CM2 setup)	VSWR (1-port)
4:1 Ruthroff	1:1 Guanella	red
4:1 Sevick	1:1 Guanaella	black
4:1 Sevick	1:1 DG0SA	purple
4:1 Sevick	1:1 Guanella	without hand (red)
4:1 Sevick	1:1 Guanella	with hand some 3cm below setup (under table) (black)
4:1 Ruthroff	1:1 Guanella	without hand (red)
4:1 Ruthroff	1:1 Guanella	with hand some 3cm below setup (under table) (black)
4:1 Sevick	1:1 Guanella	5cm beside each other (red)
4:1 Sevick	1:1 Guanella	stacked (black)

Low frequency simulation of Transformers and Chokes with LTspice.

1:1 Guanella Choke

Drawing 3 of G3TXQ in LTspice

4:1 Ruthroff Transformer

Drawing 5 of G3TXQ needs a slight change to depict reality. The Earth symbol at point c of the coil needs to be removed, and c needs to be connected to b (the coaxial braid). This is reality, as there is normally no Earth available at the location of the Transformer/antenna (if there would be a seperate Earth, Ruthroff Transformer would perform worse looking at CMC).

Adjusted drawing 5 of G3TXQ in LTspice

4:1 Sevick Transformer

By a lot of people also called 4:1 single core Guanella Transformer.

Drawing 7 of G3TXQ in LTspice

4:1 dual core Guanella Transformer/Choke

Drawing 6 of G3TXQ in LTspice

Evaluation of simulations in LTspice

Three parameters are varied: antenna's Earth's impedance (Re=100 or 1000Ω; which is higher than seen in the Z₃ variation of my 40m OCFD measurements), antenna'a inbalance (OCF=50 or 75%, a balance of 1:3; which is slightly higher Balance than measured in my 40m OCFD [1:2.4]) and the resistance of source towards Earth (RsourceEarth=1mΩ or 100MΩ). This gives the below averages in current (I_CMC=i(r1)-i(R2)), voltage (V3) and R_in:

Type	Re = {100,1000} Ω			OCF = {50,75} %			RsourceEarth = {1m,100M} Ω
	i(R1)-i(R2) [A]	V3 [V]	Rin [Ω]	i(R1)-i(R2) [A]	V3 [V]	Rin [Ω]	i(R1)-i(R2) [A]	V3 [V]	Rin [Ω]
1:1 Guanella	7u	7m	49.994	0.8u	80u	50	0	0	50
4:1 Ruthroff	75n	16u	50.001	1.7m	165m	48	70n	7u	50.001
4:1 Sevick	1.8m	400m	47.7	1.7m	165m	48.2	1.7m	165m	48
4:1 dual core Guanella	25u	25m	49.97	4.4u	440u	49.996	0	0	50.1

So the 1:1 Guanella and the 4:1 dual core Guanella devices have (regardless of the Re, OCF or R_sourceEarth) the lowest I_CMC and V3 and the R_in is also most stable.
The 4:1 Ruthroff device is relative low influenced by Re or R_sourceEarth. It is though heavily influenced by OCF (similar as 4:1 Sevick).
The 4:1 Sevick device has (regardless of Re, OCF or R_sourceEarth) the highest I_CMC and V3 and the lowest R_in.
These simulations' results also map the VNA measurements of the built devices. This also maps the table of page 9 and 10 of G3TXQ's paper.

Measurements of impedance and VSWR

In Owen Duffy's web page (section Measurements and Examples), five |Z|/VSWR tests are defined to test if a 4:1 current Choke is a 4:1 Choke. W8JI (section Basic Balance Quality Test for Current Baluns) 's similar tests evaluate more components (like voltage devices and 1:1 current devices). This extension has been evaluated below.
My own (above) evaluation does something similar for different components. Test 3 are the average numbers (R_in) mentioned in the table. Test 4 and 5 are the variations (ΔR_in ) seen due to varying the balance (OCF) and the resitance to the earth (R_e). Beside this, one can also see the difference in CM current (I_CMC ± ΔI_CMC) and voltage change due to OCF: V₃ ± ΔV₃.
The tests were performed on the components designed for my OCFD from 40m (from 7MHz):

Name

Type device

test 1

3.95MHz <freq. too low for the components tested>

6.9MHz

14MHz

comments

test 2a (T) |Z|>???Ω VSWR>150

test 3 (T) |Z|~50Ω VSWR<1.2

test 4 (C) |Z|~50Ω VSWR<1.2

test 5 (C) |Z|~50Ω VSWR<1.2

test 2a |Z|>???Ω VSWR>150

test 3 |Z|~50Ω VSWR<1.2

test 4 |Z|~50Ω VSWR<1.2

test 5 |Z|~50Ω VSWR<1.2

test 2a ||Z|>???Ω VSWR>150

test 3 |Z|~50Ω VSWR<1.2

test 4 |Z|~50Ω VSWR<1.2

test 5 |Z|~50Ω VSWR<1.2

1:1 Guanella

current

oke

744/inf

47.6/1.06

47.6/1.06

47.3/1.08

424/inf

48.1/1.08

48.1/1.08

47.8/1.09

206/inf

49.9/1.12

49.9/1.12

49.6/1.12

Test applicable according W8JI, not according Owen Duffy (not a 4:1 current). Test results are good for a Choke.

4:1 Ruthroff

voltage

oke

1.8k/175

48.0/1.06

2.5/1278

13.5/30.0

819/168

48.0/1.08

4.3/137

23.2/13.9

372/161

48.0/1.14

8.6/44.9

45.9/5.98

Test applicable according W8JI, not according Owen Duffy (not a 4:1 current). Test results are bad for a Choke.

4:1 Sevick

current?

oke

892/353

48.3/1.05

49.9/1.3

21.2/7.6

486/344

48.5/1.05

51.3/1.19

32.8/3.7

232/433

49.4/1.08

52.3/1.13

48.0/2.05

Test applicable. Test results are bad for a Choke.

4:1 dual core Guanella

current

oke

1.3k/178

48.2/1.06

45.9/1.17

48.1/1.07

826/181

48.4/1.08

46.6/1.16

48.4/1.09

307/177

49.7/1.15

48.1/1.19

49.6/1.14

Test applicable. Test results are good for a Choke.

a: W8JI (section Basic Balance Quality Test for Current Baluns) states that the VSWR has be as high as possible (VR proposes threshold VSWR=150, equivalent to |S₁₁|=|Γ|=0.987). E.g. 1:1 Guanella and the 4:1 dual core Guanella have high VSWR (>150), but mostly a low |Z| (<1kΩ) . So looking at the above results, this looks to be more realistic than having a |Z|>1kΩ (as Owen Duffy defined in his test 2).

Like in my simulations: the standalone 4:1 Ruthroff and 4:1 Sevick show a bad Choke performance, while 4:1 dual core Guanella performs well as a Choke. They all perform as a Transformer (test 3).

OCFD with Transformer and Choke

Resonance frequencies and VSWR

An OCFD (Off Centre Fed Dipole: short leg=6.4m and long leg=14.9m of AWG=#12) was fed through a 4:1 Ruthroff Transfomer and 1:1 Guanella Choke (15windings) Hybrid. The VSWRs measured (low resoluation scan with NanoVNA @ ~1dBm) with this hybrid were:

Blue VSWR curve where all antenna is around 1m from ground. The red VSWR curve shows when the antenna height goes from 4m (long leg) to 1m (short leg). The black VSWR curve is when the antenna is at a traditional windmill (the centre around 5m height [stage height] and the long and short legs at around 4m).
Adjusting the length of the short and long leg at the traditional windmill location (total length 19.3m: short 5.64m and long 13.67m: 29.2%) so that a low VSWR happens in the 40m amateur band.
The theoretical length calculated by KK1CW for this adjusted OCFD (40m base band, 29.2%, poor ground conditions, insulated solid copper #12 and 5m height of feedpoint) is 20.1m. While the measured optimum at the traditional windmill is 19.3m. So there is a difference of 0.8m. This could be due to not-ideal antenna environment (like buildings and stage of mill) and not being an inverted V (more a straight arrangement).

Measurements at traditional windmill

The following frequencies and their VSWRs are found (using a higher resolution VNA scan, and the feeder was RG-58C/U):

Band	measureda VSWRmin by PE1ATN height=5m ~5m feeder	measuredc VSWRmin by PE1ATN height=5m ~5m feeder	measuredd VSWRmin by PE1ATN height=5m ~5m feeder	measuredc VSWRmin by PE1ATN height=5m repeat ~5m feeder	measuredc VSWRmin by PE1ATN height=5m ~13m feeder	measuredd VSWRmin by PE1ATN height=5m ~13m feeder	measuredd VSWRmin by PE1ATN height=5m ~13m feeder outsidestage	calculatedb VSWRmin by K8BA height=6m
40m	1.77@7.1M	1.92@7.2M	1.68@7.1M	1.82@7.2M	1.73@7.2M	1.86@7.1M	1.75@7.1M	2.40@7.1M
20m	1.91@13.9M	1.82@14.5M	1.64@14.3M	1.96@14.4M	1.87@14.4M	1.78@14.3M	1.85@14.3M	1.84@14.0M
15m	2.89@21.4M	3.25@21.3M	2.62@21.4M	3.59@21.3M	3.43@21.7M	2.56@21.4M	3.73@21.3M	4.69@21.1M
10m	3.00@28.3M	1.65@28.7M	1.22@28.8M	1.58@28.7M	1.57@29.0M	1.43@28.9M	1.13@28.9M	1.80@28.2M

a: The measured VSWR is the VSWR of OCFD+hybrid (4:1 Ruthroff Transfomer and 1:1 Guanella Choke)
b: The calculated VSWR is only the OCFD.
c: The measured VSWR is the VSWR of OCFD+hybrid (4:1 Sevick Transfomer and 1:1 Guanella Choke)
d: The measured VSWR is the VSWR of OCFD+hybrid (4:1 dual core Guanella Transfomer and 1:1 Guanella Choke)

In graphical form:

Measurements at home location

A lot of measurements were done at the home location. Here is the setup of the 40m OCFD antenna (29.2%) and feeder depcited:


Many test runs (some 70) were done at this home location over several days (6 days in total). The setup was at least rebuild a few times. Some measurements were repeated (to check reproducebility) or slightly adjusted (to see variability due to e.g. device reversing and earthing). In the below overview of test runs, the average over frequencies has been given by default (as it is assumed that the antenna will be used at 7, 14 and 28MHz). If one clicks on these test run graphs, one can see the split out over frequencies. The data is available in Excel(pivot) file.

Measuring the impedance of an OCFD antenna

By using the method of Kevin Schmidt (2004, Fig. 4 and Appendix), the T equivalent circuit of the 40m OCFD(+41dualcore Guanella(+feeder))  and 200Ωload+41dualcore Guanella(+feeder) has been determined (using three times the Reflection setup).
Z_c, Z_a and Z_b are measured as follows:

• Z_c: connect wire 1 and wire 2 of the twinlead together and measuring the impedance to ground;
  
• Z_a: connect wire 2 to ground and measure the impedance between wire 1 and ground;
  
• Z_b: connect wire 1 to ground and measure the impedance between wire 2 and ground.
  

RG58C-U feeder some 13m long, and the Earth system is a wire of some 3m from the NanoVNA to an Earth rod which is 3m long/deep (nothing else connected to this Earth).

Setup

R0 [Ω]

Freqa [MHz]

Zc [Ω] (measured twice)

Za [Ω] (measured twice)

Zb [Ω] (measured twice)

ZD [Ω] (averaged)

ZU [Ω] (averaged)

Z1 [Ω] (averaged)

Z2 [Ω] (averaged)

Z3 [Ω] (averaged)

|Zo=Z1+Z2|  [Ω] / VSWR(R0)

Balance |Za / Zb|

OCFD+41dualcore Guanella+  +feeder

50

7.05874

614-142i / 598-136i

40.4-5.27i / 40.5-5.28i

41.3+1.4i / 42+2i

38+0i

-30-94i

4-47i

34+47i

554-102i

38/1.3

1.0

14.1984

348-25.1i / 359-33.1i

47.5-19.5i / 47-19.3i

46.6-14.1i / 47.3-14i

48-18i

11-37i

29-28i

18+9i

337-30i

51/1.0

1.0

27.8941

272-4.8i / 278+17.2i

19.7+10.6i / 19.5+10.6i

19.5+7.43i / 19.4+7.79i

19+10i

151+35i

17+23i

2-13i

266+20i

22/2.3

1.1

OCFD+41dualcore Guanella

50

7.05874

1970-251i / 1970-258i

38.3+5.39i / 37.8+5.32i

41.8+9.45i / 42.1+9.52i

42+18i

-236-210i

-97-96i

139+114i

2227+208i

46/1.1

0.9

14.0212

1830-1450i / 1820-1460i

26.5+5.72i / 26.4+5.78i

26+3.24i / 26+3.27i

24+9i

159+147i

92+78i

-68-69i

2013-1048i

26/1.9

1.0

27.9510

360-841i / 367-963i

37.9-39.6i / 38.7-39.1i

44.6-39.9i / 44.5-39.9i

45-39i

-99+50i

-27+5i

72-45i

403-903i

59/1.2

0.9

OCFD

200

7.05874

1020-934i / 962-921i

142+209i / 165+217i

317-307i / 275-282i

89+50i

87+657i

88+353i

1-304i

195-184i

102/2.0

0.6

14.1984

250-12.7i / 249-9.42i

106-173i / 107-172i

97.8+80.1i / 97.4+77.2i

104-46i

-23-280i

41-163i

64+117i

55-43i

114/1.8

1.6

27.8941

708+59.9i / 595-122i

1090+85.1i / 1090+66.4i

127-436i / 125-437i

421-436i

568+658i

495+111i

-73-547i

293+259i

606/3.0

2.4

200Ω+41dualcore Guanella+  +feeder

50

7.05874

1020-179i / 1070-164i

46.3+17.5i / 46.3+17.5i

44.7+16i / 44.7+16i

46+17i

47+12i

47+15i

-1+3i

1045-174i

49/1.0

1.0

14.1984

177+47.1i / 174+44.7i

42.3+27.8i / 42.3+27.8i

32.7+24.7i / 32.6+24.8i

41+28i

44-3i

42+12i

-1+15i

172+32i

50/1.0

1.2

27.8941

186-0.761i / 191+0.59i

66.4+37.8i / 66.4+37.7i

49.3+32.2i / 49.4+32.4i

63+39i

54-13i

58+13i

4+26i

178-19i

74/1.5

1.3

200Ω+41dualcore Guanella

50

7.05874

553-2840i / 551-2830i

53+21.3i / 53+21.4i

53+20.8i / 53+20.8i

53+21i

27-5i

40+8i

13+13i

541-2843i

57/1.1

1.0

14.1984

606-1690i / 605-1690i

57.4+41.8i / 57.4+41.8i

57.3+40.9i / 57.3+40.7i

57+42i

24-9i

40+16i

17+5i

592-1703i

71/1.4

1.0

27.8941

165-942i / 165-942i

71.9+76.5i / 71.9+76.6i

72.7+75.2i / 72.7+75i

70+76i

15-2i

42+37i

27+39i

148-962i

103/2.1

1.0

Some evaluation points:

• There are a few negative resistances in Z₁ and Z₂ (yellow-ish background) of the T equivalent circuit. LTspice is able to simulate a negative resistance and I also see such negative values in Schmidt's article (2004, Fig. 8), so I expect it is ok.
• The S₁₁ of Z_c of OCFD+41dcGuanella and 200Ω+41dualcore Guanella are very flat and close to 0dB (even after two re-measurements).
• OCFD has been fully repeated, similar results.
• OCFD shows (as expected) an unbalance of around 1:2.5 at ~28MHz.
  
• |Z₃| shows an impedance between 70 and 2.5kΩ toward Earth, this matches somewhat the statement of G3TXQ (page 1): "Z₃ can be anything from a few Ohms to many thousands of Ohms depending on the particular system."
  

Advice or feedback on these measurements are welcome?

Remark: A small unclarity in Kevin Schmidt's article: The picture of Fig. 2 belogs to caption text of Fig. 1; the picture of Fig. 3 belongs to caption text of Fig. 2; and the picture of Fig. 1 belogs to the caption text of Fig. 3.

SVWR

Here is an overview of some 40 runs to determine the VSWR (averaged over 7, 14 and 21Mhz and explicit feeder paths), looking at different standalone and hybrids devices at the home location (home: heights; long@4m, centre@2m, short@1m, feederlength ~11.6m):

The best choice for VSWR depends if transmitter or ATU can handle it: so without ATU a VSWR between 1 and 2 and with ATU no real issues for above data. Beside this, a smaller difference between the two different feeder paths is preferred.
Looking only at VSWR that would result in preferred devices: 41Ruthroff, 41Sevick+11Guanella, 41Guanella or 41Guanella+11Guanella.

CMR and Bandwidth

CMC has been measured (repeatedly) for these hybrid configurations at another site (home location: heights; long@4m, centre@2m, short@1m, feederlength ~11.6m and on the ground). Transmitter power was 5W@7041250Hz (38.5V on RF meter)

xxx-Transformer + Guanella Choke (nth repeat measurement)	RFcable [V]  at different locations on RG-58C/U feeder from receiver
	~0.5m	~5.8m	~11.5m
4:1 Ruffroth (1st)	0.5	0.6	0.8
4:1 Ruffroth (2nd)	0.5	0.3	0.7
4:1 Ruffroth (2nd) (device reversed)	0.7	0.4	0.6
4:1 Sevick (1st)	0.7	0.6	0.7
4:1 Sevick (2nd)	0.7	0.2	0.4
4:1 Sevick (2nd) (device reversed)	0.4	0.3	0.7
4:1 dual core Guanella (1st)	0.8	0.5	0.5
4:1 dual core Guanella (2nd)	1.2	1.0	0.5
4:1 dual core Guanella (2nd) (device reversed)	0.8	0.5	0.8
4:1 dual core Guanella (3rd)	1.0	0.8	0.5
4:1 dual core Guanella (3rd) (device reversed)	0.9	0.6	0.5

Repeatability (1σ) of RF_cable was around  ~0.2V. Have no indication that standing waves happened for this frequency (or at 14 or 28MHz).

CMR frequency dependency

Location: home.
The below is assuming a 50Ω load for the CMC (due to RF_cableavg).
4:1 Ruffroth Transformer + Guanella Choke is (device reverse):

Freq. [MHz]	RFout [V]	RFcableavg [V]	CMR (field) [dB]*	CMR (VNA) [dB]
7.0	35.5	0.5	37	36
14.1	31.8	1.2	28	37
28.1	24.5	0.5	34	35

* The CMR is calculated assuming similar loads for the RF_cableavg (≡CMC) and the RF_out (≡transmitter power). This was also done by W7EL (balance equation on page 160).

4:1 Sevick Transformer + Guanella Choke is (device reverse):

Freq. [MHz]	RFout [V]	RFcableavg [V]	CMR (field) [dB]*	CMR (VNA) [dB]
7.0	31.8	0.4	37	36
14.1	29.4	1.3	27	37
28.1	20.9	0.6	31	35

4:1 dual core Guanella Transformer + Guanella Choke is:

Freq. [MHz]	RFout [V]	RFcableavg [V]	CMR (field) [dB]*	CMR (VNA) [dB]
7.0	38.5	0.7	35	37
14.1	15.5	0.8	26	42
28.1	24.4	0.3	38	41

Freqeuncy dependency of CMR in graphical form:


Here is an overview of some 25 runs to determine the CMR (averaged over 7, 14 and 21Mhz and explicit feeder paths), looking at different standalone and hybrids devices at the home location (home: heights; long@4m, centre@2m, short@1m, feederlength ~11.6m):

The best choice is a device with a higher CMR value.
Looking only at CMR that would result in preferred devices: 41Ruthroff+11Guanella, 41Sevick+11Guanella, 41Guanella or 41Guanella+11Guanella.
These results can be compared with W7EL results (experiments 1: differen between 'current balun' [11Guanella] and 'voltage balun' [11Ruthroff, 1959, Fig. 2]), like W7EL these is some 15dB difference between Choking (current) devices and Transforming (voltage) devices.

The CMR in the field is in general less than the VNA measured CMR for these hybrids.

All in all: the theory (antenna lengths), simulations and measurements (of VSWR and CMC) of individual components (OCFD antenna, Transformer, Choke, Hybrid) and the combination are somewhat different. The VSWR of the OCFD+Hybrid looks as expected from component measurements. The CMR in the field is less than determined with standalone Hybrids (using the NanoVNA).

Bandwidth frequency dependency

The bandwidth of the return loss at home location (for 40 and 20m it was measured between two -2dB point, while for 10m it was measured at one 2dB point and multiplied by two):

Type	40m			20m			10m
	Freq. [MHz]	Bandwith (2dB) [MHz]	Q2dB	Freq. [MHz]	Bandwith (2dB) [MHz]	Q2dB	Feq. [MHz]	Bandwith (2dB) [MHz]*	Q2dB
4:1 Ruffroth + 1:1 Guanella	6.98	0.57	12.2	14.17	1.14	12.4	28.54	2.48	11.5
4:1 Sevick + 1:1 Guanella	7.01	0.51	13.7	14.20	1.11	12.8	28.50	2.52	11.3
4:1 dual core Guanella + 1:1 Guanella	6.98	0.49	14.1	14.14	1.14	12.4	28.46	1.84	15.5

The Q_2dB factor (Freq/Bandwidth) does not change very much for the 40 (the fundamental band) and 20m bands and types of device. Except for the 10m band the 4:1 dual core Guanella has a slightly higher Q_2dB than the other two.

Here is an overview of some 40 runs to determine the Q_2dB (averaged over 7, 14 and 21Mhz and and explicit feeder paths), looking at different standalone and hybrids devices at the home location (home: heights; long@4m, centre@2m, short@1m, feederlength ~11.6m):

The best choice is a device that has a flatest VSWR curve; aka lower Q_2dB value. Beside this a smaller difference between the two different feeder paths is preferred.
Looking only at Q_2dB that would result in preferred devices: 41Ruthroff+41Guanella, 41Sevick+11Guanella, 41Guanella or 41Guanella+11Guanella.

Feeder angle influence

The effect of the feeder angle on VSWR (yellow curve) and Q_2dB (purple curve) has been determined for a device combination with high CMR (41Guanella+11Guanella: dashed curve) and a single device with low CMR (41Sevick: dotted curve). The feeder angle is defined as the angle between the feeder (at feedpoint) with the plumb line (to ground), see also the setup at home. This gives the following picture:

When the device has a low CMR (dotted: 41Sevick), the VSWR (yellow) and certainly the Q_2dB (purple) varies significantly.

The frequency of the VSWR dip (F_r; for 41Sevick) also changes with the amount of CMC, see below picture where the CMC increases due to increasing feeder angle for the 41Sevick device:

Differences due to devise reversal and feeder path

Device reversal:

• VSWR: stdev is a bit smaller for reversed than for not reversed device, but the averages of reversed and not reversed devices are not significantly different
• Q_2dB:  stdev is a bit smaller for reversed than for not reversed device, but the averages of reversed and not reversed devices are not significantly different
• CMR: stdev is a bit smaller for reversed than for not reversed device, but the averages of reversed and not reversed devices are not significantly different

Different feeder path:

• VSWR: stdev and average of the different paths are not significantly different.
  
• Q_2dB: stdev and average of the different paths are for 41Ruthroff and 41Sevick devices significantly larger for nearby long leg (mainly occuring for 7MHz), For all others the different paths show no significantly difference
• CMR: stdev and average of the different paths are not significantly different.

Effects of high CMC (low CMR/CMI)

There are several effects of high CMC due to low CMR/CMI:

• feeder acting as antenna:
• feeder of TX antenna acting as radiator
• feeder of RX antenna picking up unwanted signals (QRM).
• influencing measurements (NanoVNA, SWR-meter, etc.)
• changing CMC:
  
• proximity of body/metal
• narrowing of the VSWR dip (according to DJ0IP, section When CMC flows on the coax): broadening)
• increasing frequency (F_r) of the VSWR dip
• an additional VSWR dip: according to DJ0IP, section When CMC flows on the coax (not seen by myself. This could be because the feeder length [19.6m with vf=0.97] is close to half 40m band)
• changing the VSWR curve
• different routing of feeder:
• different length of feeder: according to DJ0IP, section When CMC flows on the coax (not checked by myself)
  

RF meter

An RF meter was constructed to be able to measure the CMC. This design (as described by Roy Lewallen on Jan 21st, 2003) was utilised.

The above current source was implemented in real life through a 1:10 Transformer (ferrite snap-on cable core) over the feed line.

The implementation resulted in the below sensitivity (measuring the DVMvoltage through the coax core and coax core current [proxy for a CMC] by scope using a 50Ω dummy):

Make sure that the leads (e.g to DVM) are not alongside the feeder line, otherwise they migth pick up (additional) CMCs.
Converting DVMvoltage (RF_out [V_tt]) into CMC [A_rms] is:
CMC = 0.0086*DVMvoltage

Threshold value for CMC

It is expected that the CMC is linear depending on the transmitter current/power. Transmitter power (P_tx) will be (within Dutch limits) around 10W (QRP), 100W upto 400W. So between 40 and 56dBm.
A CMR of a typical Choke is from 34dB (see earlier parts of this web-page).
So the question is what CMC (: CMC = P_tx - CMR, all in dB[m]) can be an acceptable CMC_thres before it becomes experienced as a nuisance?
According to DJ0IP (Single-Core Vs, Dual-Core 4: Guanella BALUN: A direct comparison of a real life antenna. 2013, page 6) this CMC_thres is around 30mA (15 dBm).
Using a typical Choke, this would give a P_tx of 49 dBm (=15+34) ~ 80W.

Conclusion

Openstanding questions

Bold purple and underlined text needs to be studied more. If you can help solve these outstanding questions, let me know. Thanks
Outstanding questions:

1. Why does the component tester not quantify inductors (consisting of tighly coupled coils) well?
   
2. How the optimum ferrite mix matches on G3TXQ tables, needs to be investigated?
3. 
   

References

Acknowledgements

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