There are many ways to get a good estimate of the characteristic impedance Zo of a transmission line.
One method is to measure the input impedances of a section of line with both a short circuit and open circuit termination. From Zsc and Zoc we can calculate the Zo, and the complex propagation constant \(\gamma=\alpha + \jmath \beta\).
Calculation of Zo is quite straightforward.
The solution for γ involves the log of a complex number \(r \angle \theta\) which is one of the many possible values \(ln(r) + j \left(\theta + 2 \pi k \right)\) for +ve integer k. Conveniently, the real part α is simply \(ln(r) \). The real part of γ is the attenuation in Np/m which can be scaled to dB/m, and the imaginary part is the phase velocity in ^{c}/m. The challenge is finding k.
Measurement with nanoVNA
So, let’s measure a sample of 14×0.14, 0.22mm^2, 0.5mm dia PVC insulated small speaker twin.
Above is the nanoVNA setup for measurement.
The transformer seen above is a 1:1 transformer as described at A 1:1 RF transformer for measurements – based on noelec 1:9 balun assembly. The system was OSL calibrated at the pin socket underneath the grey connector.
Scans were made from 160MHz of the 1m section of line with short circuit and open circuit termination.
Above is the short circuit scan which looks generally smooth.
Above is the open circuit scan which looks generally smooth.
Both scans were saved as .s1p files.
Calculations will be offered at 40 and 14MHz.
40MHz
Above, the results. Zo is 139.6+j0.7071Ω, and matched line loss MLL is 0.26dB/m. This MLL is quite a deal higher than you might expect, even of PVC insulated cables.
Because the line is well less than \(\frac{vf \: \lambda}{4}\) (guessing at the likely value of vf), we can calculate vf simply from the imaginary part of γ for k=0.
TWLLC model
PVC / copper speaker twin 0.22mm^2 @ 40.53MHz 

Parameters  
Conductivity  5.800e+7 S/m 
Rel permeability  1.000 
Diameter  0.000500 m 
Spacing  0.001700 m 
Velocity factor  0.660 
Loss tangent  3.500e2 
Frequency  40.530 MHz 
Twist rate  0 t/m 
Length  1.000 m 
Results  
Zo  150.82+j1.77 Ω 
Velocity Factor  0.6600 
Length  73.742 °, 0.204839 λ, 1.000000 m, 5.054e+3 ps 
Line Loss (matched)  0.262 dB 
Above, a TWLLC model was constructed to have about the same MLL. The model would suggest that dielectric loss is quite high. In my experience, PVC LossFactor ranges widely and would seem to depend on pigments, plasticisers and fillers used in manufacture.
14MHz
Above is a calc from the same sweep, but at 14MHz. MLL is pretty appalling for this sample, yet I see people recommending this stuff and stuff like it for feed line for a dipole, particularly for portable work. Larger size PVC twin lines are better, but never good. The figure8 cable / zip cord dipole of ham lore is one of those things that doesn’t pass analysis.
Footnote: This is a rework of an article using averaging of VNA calibration and measurements to reduce measurement noise. The results are only a little different to the original article, but accuracy is improved.