Zip Cord Feed Line
We were looking to feed a 40m Horizontal Loop antenna which had a feed-point impedance of 130 Ω. We wanted to use a balanced feed line, but for that impedance it would need to be very thin, narrower than 300 Ω TV ribbon in fact. So we investigated the properties of zip cord (otherwise know as "figure-8", or "twin-lead"). This type of cable is used for DC, speakers and small, double-insulated appliances. Although reported to be lossy at higher frequencies, the results here looked promising.
Introduction
We will try two different methods to find the characteristic impedance of zip cord. Method 1 uses a NanoVNA and a 200 Ω miniature preset potentiometer. Method 2 uses a NanoVNA, wire diameter and spacing measurements, a velocity factor calculation and an on-line loss calculator.
Method 1:
- Zip-tie one end of the zip line to the calibrated NanoVNA Port 1
- Solder a 200 Ω miniature preset potentiometer to the other end of the line
- Drape the full length of the zip chord over some wooden chair back to keep it away from metal
- Set nanoVNA Display to Smith.
- Set nanoVNA Stimulation Start to 50 kHz
- Set nanoVNA Stimulation Stop to 30 MHz
- Set the potentiometer to approximately 200 Ω
- Display the Smith chart on the NanoVNA. The sweep will resemble a circle. Note the diameter of the circle.
- Set the potentiometer to approximately 50 Ω
- Display the Smith chart on the NanoVNA. The sweep will resemble a circle. Note the diameter of the circle.
- Adjust the potentiometer to minimise the diameter of the circle
- Set the NanoVNA Cursor to the horizontal mid-point of the circle
- Read the resistance component of the impedance. This is the characteristic impedance of the cable.
- Measure the conductor diameter and centre to centre distance using digital-calipers for accuracy.
- Zip-tie one end of the zip line to the calibrated NanoVNA Port 1
- Measure the frequency at which a given length (L) of line is one quarter-wavelength using a nanoVNA.
- Note: The impedance of the line at the nanoVNA will be a minimum at a quarter wavelength from the open circuit end.
- Set nanoVNA Display to Smith.
- Set nanoVNA Stimulation Start to 50kHz (min).
- Set nanoVNA Stimulation Stop to just above the frequency where the impedance hits its first minimum.
- Measure the frequency at the first minimum.
- Calculate the Velocity Factor of the one quarter-wavelength, length (L), of cable:
- λ = C / ƒ in free space, where λ = Wavelength, C = Speed of Light and ƒ = Frequency
- λ = V C / ƒ in a conductor, where V = Velocity Factor of conductor
- V = λ ƒ / C, but λ = 4 L since L is one quarter wavelength
- V = 4 L ƒ / C
- Calculate the line impedance and loss using Owen Duffy's on-line calculator.
We tried the following zip cords:
- Type: 15AWG Ultra Heavy Duty Figure 8 Cable
- Conductor Diameter: 1.7 mm
- Centre-to-centre distance: 3.3 mm
- Relative Permittivity of the PVC insulation (from on-line reference): 4 F/m
- Length: L =7.875 m
- Quarter Wavelength Frequency: ƒ = 6,347,000 Hz
- Speed of light: C ~ 300,000,000 m/s
- Velocity Factor = 4 L ƒ / C = 0.666
- Length of feed line required = 12 m
- Operating Frequency = 7.1 MHz
Method 1:
Method 2:
- Type: 18AWG Red / Black Speaker Cable
- Conductor Diameter: 1.1 mm
- Centre-to-centre distance: 2.7 mm
- Permittivity of the PVC insulation (from on-line reference): 4 F/m
- Length: L =4.550 m
- Quarter Wavelength Frequency: ƒ = 11,163,000 Hz
- Speed of light: C = 300,000,000 m/s
- Velocity Factor = 4 L ƒ / C = 0.677
- Length of feed line required = 12 m
- Operating Frequency = 7.1 MHz
Method 1:
Method 2:
Results
The line impedance is very sensitive to the conductor diameter and centre-to-centre distance. The smaller the diameter or larger the centre-to-centre distance the higher the impedance. It it not so sensitive to the relative permittivity or velocity factor. The measurement of the Velocity Factor here is only approximate. See here and here and here for measurement errors and alternative approaches.
| Altronics W4050 | Altronics W2121 | |
Method 1 | 90 Ω | 108 Ω |
Method 2 | 103 Ω | 126 Ω |
Conclusion
Method 2 returns a characteristic impedance about 15% higher than Method 1. The reason for this is unknown. Method 2 is still required if the line loss is to be calculated, however we know that the line loss will be negligible in any case. Method 1 is much easier in practice to work out and so is our preferred method.