An interesting study in the effect of fixture on impedance measurement

A chap posted a pic and some mini VNA measurement results of a resistor which he reported has a DC resistance of 80Ω.

Above is part of the pic, focusing on the ‘fixture'. The chap reports that the VNA was OSL calibrated, and we might assume that was at the SMA(M) connector (it is difficult to explain the results if the reference plane was at the VNA jack).

So, when I look at this, I guess:

• an SMA(F)-N(F)… probably Zo close to 50 ohms and lets say 15mm long;
• then a N(M)-UHF(F)… probably Zo close to 35 ohms and lets say 10mm long;
• then looks like a UHF(F) jack… probably Zo close to 35 ohms and lets say 2mm long; and
• then a resistor, and with some unavoidable inductance to it and its pigtails pigtails, and some distributed capacitance which is probably very small.

Above is his table of measured Z looking in from the reference plane.

Mapping these values on a Smith chart gives insight. Above is a zoomed in view of these points on a Smith chart normalised to 80Ω. The locus gives a strong hint of a possible cause in the measured impedance variation.

Lets build a Simsmith model that transforms the measured values back to the nominal 80Ω (assuming that the resistor has very low self inductance, nH).

So, above is the Simsmith model where L uses a file of impedances being the table above. All the component values have negative signs to back them out, and the expectation is that if these all caused an 80Ω resistor to measure as in the table, then backing them out should give us something very close to 80Ω at all the measured frequencies.

The red locus is that of the measurements, and the blue is the ‘corrected' value. With a little tweaking of the length guesses made earlier, the impedance is very close to 80Ω, all points falling within the VSWR(80)=1.03 circle.

Most of the variation in measurement (the red plot) is explained by this model. Indeed, it is the underlying curved nature of the red plot that strongly hints contribution of a transmission line section of Zo less than 50Ω, and experienced practitioners know that the Zo of UHF series connectors is not controlled, and commonly in the range 30-40Ω… the UHF connectors are the smoking gun.

There is one main lesson to be learned from this, the fixture is EVERYTHING.