Velocity factor solver

It is convenient or necessary sometimes to infer transmission line velocity factor from measurements of the first resonance of two significantly different lengths of the same transmission line. The advantage of this method is that it approximately nulls out the residual time offset of the instrument and in fact permits practical measurement fixtures for attaching the test sections to the instrument. The technique depends on there being only one difference between the uniform Zo test sections, and that is the length of transmission line.

The length values entered do not have to be the actual length of line end to end (including the line inside connectors), but can be measured for example from ends of the visible jacket provided the same connectors / adapters are used on both sections.

The method relies upon an assumption that velocity factor is independent of frequency (Zo is purely real). That assumption may introduce some small error for lossy lines at frequencies below about 10MHz, and is probably not suitable below 1MHz.

Already stated is an assumption that Zo is uniform. It may be the case that connectors used depart from Zo of the transmission line proper. To minimise the error introduced, the electrical length of these non-uniform Zo sections should be less than two electrical degrees, and the short test section should be much less than the long test section. This scenario might arise using 50Ω connectors (N, BNC, SMA etc) on 75Ω test cable, or UHF series connectors (uncontrolled Zo in the region of 30-40Ω) on 50Ω cable.

Since most analysers are better at measuring low impedances, use an O/C termination for quarter wave sections, and S/C termination for half wave sections. Be careful with loose collars used with coax connectors like UHF series.

The shorter section should be long enough to be able to measure its first resonance. The longer section needs to be short enough to be able to measure its first half wave resonance. Within those constraints, the greater the difference in length, the better. be consistent with how you measure length, and the S/C or O/C used, and measure frequency very carefully.

Inputs:

Electrical length (both sections)	Length (m)	Frequency of fundamental resonance (MHz)
Section #1
Section #2
Offset (ps)

Results:
Offset (ps)
Offset (m)
e-delay (ps)
Velocity factor (pu)
Velocity factor (%)
Phase velocity (m/s)

Version:

Offset is the time offset determined in the fixture, and which was deducted to obtain the velocity factor. If you leave Section #2 blank, the calculator will use the specified offset (which can be obtained from a paired measurement with the same fixture). Offset in m is at the calculated velocity factor. e-delay is the round trip fixture time, it is the figure you might plug into some VNA / client software.

The calculator does not do a lot of error checking, if you enter nonsense, it will probably produce nonsense.

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