# PVC speaker twin – loss model applied

One of the many gems of ham lore that I was fed as a beginner almost sixty years ago was that 23/0.076 (0.67mm^2) PVC insulated twin flex was suitable as an RF transmission line at HF, and that it had a Characteristic Impedance Z0 close to 75Ω.

It seems that these claims have been extended to apply to lighter gauge cables often called speaker cable or bell wire.

This article explores two cases of the application of a light grade of speaker twin to a G5RV antenna. The scenarios is a G5RV Inverted V with 7m of speaker twin from dipole to the coax section, and loss is calculated for the speaker twin section at 14.1 and 3.6MHz.

## PVC speaker twin copper / PVC 0.2mm^2 characteristics

The following articles report measurement of a sample of speaker twin, and derivation of a simple loss model:

From those articles, the loss model is copied for reader convenience.

Above is a plot of the calculated MLL (red dots) based on the s11 measurements, and a curve fit to the model $$MLL = k_1\sqrt f+k_2f \text{ dB/m}$$.

Allowing for the scatter at the lower frequencies as we are measuring 1m of line with an inexpensive hobby grade VNA, $$MLL=\text{3.26e-5} \sqrt{f}+\text{1.39e-9}f \text{ dB/m}$$ is a pretty good estimator.

It is my experience that such cables vary greatly in parameters, conductor construction and particularly dielectric parameters which seem to depend on the PVC itself, plasticisers, fillers and pigments added. Nevertheless, this example shows that a wide range in performance may be experience with a multi band dipole.

### 14.1MHz

Load impedance is taken (from an NEC model) to be 90+j0Ω and loss under standing waves calculated using RF Arbitrary Transmission Line Loss Calculator.

# RF Arbitrary Transmission Line Loss Calculator

## PVC speaker twin copper / PVC 0.2mm^2

Parameters
Ro 150.00000
vf 0.660
k0 0.000000e+0
k1 3.260000e-5
k2 1.390000e-9
Frequency 14.100 MHz
Length 180.0000 deg
Results
Zo 150.09-j3.96 Ω
Length 180.000 °, 3.142 ᶜ, 0.500000 λ, 7.013972 m, 3.546e+4 ps
Line Loss (matched) 0.996 dB
Line Loss 1.101 dB
Efficiency 77.61 %
Zin 1.003e+2-j5.928e-1 Ω
Yin 9.973e-3+j5.896e-5 S
VSWR(50)in 2.01
VSWR(50)in, RL(50)in, MML(50)in 2.01, 9.510 dB 0.516 dB

Loss under standing waves is not wonderful, but at 1.1dB might well be acceptable to a user on a budget. Impact on SYSTEM performance would be small.

### 3.6MHz

Load impedance is taken (from an NEC model) to be 10-j340Ω and loss under standing waves calculated using RF Arbitrary Transmission Line Loss Calculator.

# RF Arbitrary Transmission Line Loss Calculator

## PVC speaker twin copper / PVC 0.2mm^2

Parameters
Ro 150.00000
vf 0.659
k0 0.000000e+0
k1 3.260000e-5
k2 1.390000e-9
Frequency 3.500 MHz
Length 45.0000 deg
Results
Zo 150.34-j8.70 Ω
Length 45.000 °, 0.785 ᶜ, 0.125000 λ, 7.054679 m, 3.571e+4 ps
Line Loss (matched) 0.464 dB
Line Loss 7.852 dB
Efficiency 16.40 %
Zin 1.142e+1-j5.860e+1 Ω
Yin 0.003204+j0.016440 S
VSWR(50)in 10.53
VSWR(50)in, RL(50)in, MML(50)in 10.53, 1.655 dB 4.990 dB

Loss under standing waves is moderately high at 7.8dB and probably not acceptable to most users. Impact on SYSTEM performance would be moderately high.

## Conclusions

• Use of small PVC insulated twin cables is popular on HF.
• Matched line loss of small PVC insulated twin cables can be high to very high, worse at the higher end of HF due to significant dielectric loss.
• The effect of standing waves is to increase loss, and so use of these cables for high VSWR feed lines such as with multi band dipoles may be a low performance option.