Today I wanted to measure the characteristic impedance of a unknown transmission line; in this case, it was a Hi-Fi stereo line I bought from the local hardware store.

Measuring the impedance with miniVNA is quite simple: as we know, when a transmission line is correctly loaded, it should return a fixed resistance value and no reactance, no matter of what frequency we are using.

Therefore, my idea was to put a variable resistor at the end of the line (in this case 4m long) and try to get the flattest response as possible.

This is the setup:

 

I used a 2.2K trimmer with a 470K resistor in parallel to lower the range.

This is the result with a badly regulated trimmer:

As we can see, the reactance and resistance change very heavily by changing the frequency.

In the following picture, the best result I’ve been able to achieve with my setup:

Sure it is not perfect, but it looks good.

The resistance line (cyan) reports values around 100Ω.

Let’s read with the multimeter the exact value of the load:

It confirms the readings! Note that I’m using a tiny 2.2K trimmer with a 470Ω resistor in parallel: I don’t have a lot of resolution so I consider these reading accurate enough for my setup.

Using the math formulas

The formula to calculate the characteristic impedance Z₀ of a transmission line is well known.

It usually requires the relative permettivity of insulator between the conductors, but this value can be calculated using the velocity factor.

Fortunately, our miniVNA is able to calculate the velocity factor of any line with a pretty good precision, so here it is the formula that uses the velocity factor:

Z₀ = 276 * V_f * log₁₀ (d/r)

Where:

• V_f is the velocity factor
• d is the distance between the center of the conductors
• r is the radius of each conductor

Note that d and r must be expressed in the same unit, no matter which one: mm, inch or whatever you like as far as they are measured with the same unit.

My wire had the following characteristics:

• V_f = 0.73 (measured directly by miniVNA)
• d = 4 mm
• r = 1.25 mm

The resulting Z₀ value is 101.7Ω, which matches quite accurately what I have measured.

Time-domain measurement

[Updated on Aug. 21th, 2016] – I later on sold my miniVNA a invested into a great VNWA3. This equipment can perform time-domain measurement, thus read the characteristic impedance at every point in a transmission line. This the result on a piece of the same wire:

The impedance is a bit variable because my cable had bends and did some curve. However its impedance varied from 99.6 to 102.9Ω, with an average impedance of 100.86Ω. This value mathces the calculated one (101.7Ω) with a less than 1% error.

Try on coax cable

Just to have a confirmation, let’s try the same test with a length of RG-58.

This is when it is not correctly terminated (in this case load was a 680 Ω resistor):

While this is the case of a 50Ω terminator at the end of the RG-58 cable:

By the way, the miniVNA measured a cable velocity factor of 0.73 for the stereo line (that has heavy insulation) and 0.65 for RG-58 (which is pretty accurate, since the “formal” value is 0.66).

73 de IZ2UUF