Conductors for a Guanella 1:1 balun – discussion

This article discusses some design factors that should be considered when designing / implementing a Guanella 1:1 balun (often known as a common mode choke).

The behavior of a Guanella 1:1 balun can conveniently be separated into its concurrent common and differential modes.

It is the differential mode that is of most interest when it comes to conductors.

Let’s recall the meaning of InsertionVSWR:

Insertion VSWR is the VSWR looking into the balun with a matched load (termination) on its output, it is a measure of imperfection of the balun.

Low InsertionVSWR applications

If the application is one where the transmission line has low standing wave ratio, then you might not want the transmission line embedded in the balun to not degrade that, and the simplest solution is to use the same Zo line within the balun.

Most comonly, it is low InsertionVSWR wrt 50Ω that is the target. The simplest way to achieve 50Ω line in the balun is to use commercial coax. Analysing transmission line loss is relatively simple, use a good line loss calculator.

Ordinary solid polyethylene dielectric coax works fine up to 60°, and with good braid cover even seems to survive being bent to half the specification radius.

PTFE coax has higher temperature withstand, but is typically much stiffer.

Another option is Cujack.

I would avoid ANY foamed dielectric cable, ANY foil shield cables, ANY copper clad steel centre conductors.

Though lots of authors show ways to create nominal 50Ω lines with two or four wires, they are rarely close to 50Ω or uniform, and they are likely to not have the voltage withstand of most practical coaxes. See On use of enameled wire in transmitting baluns for more discussion.

A low Insertion VSWR high Zcm Guanella 1:1 balun for HF – more detail #2 discusses an example where even quite small pigtails on the coax produce measurable InsertionVSWR. For most transmitting purposes, the small defect is not an issue, but may be more important in a measurement system.

Other applications

For other applications, inherent impedance transformation it a low priority issue, often because it can be offset somewhere else, like in an ATU. When such a balun is used with an ATU, is will often be the case that on the transmission line within the balun for different loads:

  • V/I on the balun transmission line may range from very low to very high;
  • I may range from very low to very high; and
  • V may range from very high to very low.

Damage may occur due to overheating, core loss and wire loss are the ‘long term’ contributors. Damage may also result from insulation breakdown. Some insulation breakdowns do not cause permanent damage and some do by creating a carbon track in not much more than an instant which degrades the breakdown voltage, often substantially.

It is wise to design to wire insulation to withstand the expected working voltage and a substantial safety margin.

See On use of enameled wire in transmitting baluns for more discussion.

I would avoid tinned copper wire (or any structure with lower conductivity coating), wires with low conductivity cores (eg CCS), highly stranded wires, unsolderable wires.

Dielectric loss

Dielectric loss for most good insulators at HF is approximately proportional to frequency, the length of line and applied voltage.

PVC insulated wires of used by lots of authors, but PVC dielectric loss tends to become significant towards 30MHz. In my experience, its LossFactor ranges widely and would seem to depend on pigments, plasticisers and fillers used in manufacture. It is not a good choice, especially at the high end of HF for 5 stacked cores (ie long line section) at 1500W on a high Z / unkown load.

Conductor loss

Conductor loss is fairly straight forward, it includes skin effect and in the case where two conductors are very close together, proximity effect. Broadly, doubling wire diameter halves effective RF resistance, but this is modified by proximity effect.

A base scenario for discussion

Lets model a scenario:

  • #14 (1.6mm) conductor;
  • PVC insulation (most varieties of the cited Davis Flex-weave use PVC insulation);
  • 5 stack of FT240 cores;
  • 190mm/turn ;
  • 16t;
  • transmission line length 3.1m including an allowance for pigtails; and
  • 30MHz.

Firstly let’s model it with a 50+j0Ω load, this is what you might expect if you measured the line section between Port 1 and Port 2 of a VNA.

1.6mm (#14) PVC twin 5 x FT240

Parameters
Conductivity 5.800e+7 S/m
Rel permeability 1.000
Diameter 0.001600 m
Spacing 0.002500 m
Velocity factor 0.800
Loss tangent 5.000e-3
Frequency 30.000 MHz
Twist rate 0 t/m
Length 3.100 m
Zload 50.00+j0.00 Ω
Yload 0.020000+j0.000000 S
Results
Zo 97.93-j0.22 Ω
Velocity Factor 0.8000
Twist factor 1.0000
Rel permittivity 1.562
R, L, G, C 7.362168e-1, 4.098371e-7, 4.027604e-5, 4.273420e-11
Length 139.597 °, 0.387768 λ, 3.100000 m, 1.293e+4 ps
Line Loss (matched) 0.154 dB
Line Loss 0.182 dB
Efficiency 95.89 %
Zin 7.286e+1-j4.992e+1 Ω
Yin 0.00934021+j0.00639912 S
VSWR(50)in, RL(50)in, MML(50)in 2.41, 7.660 dB 0.817 dB
Γ, ρ∠θ, RL, VSWR, MismatchLoss (source end) -5.648e-2-j3.076e-1, 0.313∠-100.4°, 10.097 dB, 1.91, 0.447 dB
Γ, ρ∠θ, RL, VSWR, MismatchLoss (load end) -3.240e-1+j1.014e-3, 0.324∠179.8°, 9.789 dB, 1.96, 0.482 dB
V2/V1 -3.543e-1-j5.677e-1, 6.692e-1∠-122.0°
I2/I1 -1.083e+0-j4.735e-1, 1.182e+0∠-156.4°
I2/V1 -7.087e-3-j1.135e-2, 1.338e-2∠-122.0°
V2/I1 -5.416e+1-j2.367e+1, 5.910e+1∠-156.4°
S11, S21 (50) 3.014e-1-j2.838e-1, -6.223e-1-j6.382e-1

Let’s get s21(50) into polar form.

Because Zo is not 50+j0Ω, there is impedance transformation and Zin is 73-j50Ω, |s11|=-7.7dB |s21|=0.999dB. There are two contributions to |s21|:

  • input mismatch loss 0.817dB; and
  • (transmission) loss 0.182dB, 4.1% of input power is converted to heat due to conductor resistance and dielectric loss.

High impedance, high voltage, low current scenario

Now let’s model it with a 2000Ω load to evaluate high voltage conditions.

1.6mm (#14) PVC twin 5 x FT240

Parameters
Conductivity 5.800e+7 S/m
Rel permeability 1.000
Diameter 0.001600 m
Spacing 0.002500 m
Velocity factor 0.800
Loss tangent 5.000e-3
Frequency 30.000 MHz
Twist rate 0 t/m
Length 3.100 m
Zload 2.000e+3+j0.000e+0 Ω
Yload 5.000e-4+j0.000e+0 S
Results
Zo 97.93-j0.22 Ω
Velocity Factor 0.8000
Twist factor 1.0000
Rel permittivity 1.562
R, L, G, C 7.362168e-1, 4.098371e-7, 4.027604e-5, 4.273420e-11
Length 139.597 °, 0.387768 λ, 3.100000 m, 1.293e+4 ps
Line Loss (matched) 0.154 dB
Line Loss 1.421 dB
Efficiency 72.09 %
Zin 1.604e+1+j1.159e+2 Ω
Yin 0.00117212-j0.00846881 S
VSWR(50)in, RL(50)in, MML(50)in 20.13, 0.864 dB 7.439 dB
Γ, ρ∠θ, RL, VSWR, MismatchLoss (source end) 1.552e-1+j8.611e-1, 0.875∠79.8°, 1.160 dB, 15.00, 6.301 dB
Γ, ρ∠θ, RL, VSWR, MismatchLoss (load end) 9.066e-1+j2.016e-4, 0.907∠0.0°, 0.851 dB, 20.42, 7.496 dB
V2/V1 -1.298e+0-j7.233e-2, 1.300e+0∠-176.8°
I2/I1 -6.217e-3-j7.577e-2, 7.603e-2∠-94.7°
I2/V1 -6.490e-4-j3.617e-5, 6.500e-4∠-176.8°
V2/I1 -1.243e+1-j1.515e+2, 1.521e+2∠-94.7°
S11, S21 (50) 3.014e-1-j2.838e-1, -6.223e-1-j6.382e-1

(transmission) Loss is now considerably higher than the base model at 1.4dB, 28% of input power is converted to heat due to conductor resistance and dielectric loss.

Low impedance, high current, low voltage scenario

Now let’s model it with a 5Ω load to evaluate high current conditions.

1.6mm (#14) PVC twin 5 x FT240

Parameters
Conductivity 5.800e+7 S/m
Rel permeability 1.000
Diameter 0.001600 m
Spacing 0.002500 m
Velocity factor 0.800
Loss tangent 5.000e-3
Frequency 30.000 MHz
Twist rate 0 t/m
Length 3.100 m
Zload 5.00+j0.00 Ω
Yload 0.200000+j0.000000 S
Results
Zo 97.93-j0.22 Ω
Velocity Factor 0.8000
Twist factor 1.0000
Rel permittivity 1.562
R, L, G, C 7.362168e-1, 4.098371e-7, 4.027604e-5, 4.273420e-11
Length 139.597 °, 0.387768 λ, 3.100000 m, 1.293e+4 ps
Line Loss (matched) 0.154 dB
Line Loss 1.231 dB
Efficiency 75.31 %
Zin 1.121e+1-j8.120e+1 Ω
Yin 0.00166894+j0.01208536 S
VSWR(50)in, RL(50)in, MML(50)in 16.38, 1.062 dB 6.638 dB

(transmission) Loss is now considerably higher than the base model at 1.2dB, 25% of input power is converted to heat due to conductor resistance and dielectric loss.

In summary, the high current and high voltage application both have much higher loss than the base 50 configuration that might be measured with a VNA (though it is not simply -|s21|).

Variations

This design above is notable for having a very large number of turns on a 5xFT-240 core stack. It is an unusual design and the long embedded transmission line with low grade PVC dielectric contributes to poor performance.

By contrast, a single FT240 with 11t of 1.6mm (#14) PTFE insulated wire and 2000Ω load would have transmission line loss closer to 0.1dB or 2% of input power converted to heat in the transmission line component.

The base design might be thought of as massive and capable of very high power, but whilst piling turns on might tend to reduce core losses, transmission line conductor and dielectric losses become more significant. Losing more than 25% of input power to transmission line loss with extreme loads on a 5x stack does not make for a kilowatt balun!