Measuring Resistors with an Impedance Analyser

[trewmac]

Resistors
Resistors have electrical length which translates to inductance. They also have some unwanted capacitance. We are going to look at the real world behavior of resistors using a TE3001 Network Analyser with a tweezer tip.
The resistor can be modeled by the diagram below including these unwanted stray elements.

A typical metal film axial resistor might have: Lstray=5nH and Cstray=0.5pF

Unlike the inductor and capacitor, it is the magnitude of R, not the frequency that tends to determine which parasitic takes effect;
Small valued resistors appear inductive.
Large valued resistors appear capacitive.

The tipping point for surface mount resistors is somewhere between 50 and 100 Ohms depending on the size and brand.

On the smith chart below is a plot of 6 different Vishay 0805 surface mount resistors illustrating this shift from inductive to capacitive behaviour.
Resistor values are 0R, 10R, 50R, 100R, 1K and 1M.

For those small values of R with inductive reactance, the stray capacitance has a negligible effect and can be ignored.  This simplifies the real world model to just R and L in series which can easily be measured using the series RL format.

Below is a plot of the 0R, 10R and 50R resistors in series RLC format showing their parasitic inductor value.

For 0R, stray L=2.2nH,
For 10R, stray L=2.3nH.
For 50R, stray L=1.35nH.
The larger values of R have capacitive reactance. If we ignore the stray inductance (because its effect is negligible) the model simplifies to the parallel combination of R and C.

This is best viewed with the parallel RC format.

For 100R, stray C=0.15pF
For 1k, stray C=0.47pF
For 1M, stray C=0.45pF

So a better model of the 10R 0805 resistor at 100MHz would be:

Similarly, a better model for the 1K 0805 resistor at 100MHz would be:


Done!

[Mechatrommer]

interesting subject but... one port TE3001 Network Analyser is 3,950.00 USD http://www.impedanceanalyzer.com.au/online_store.php , even though it can nicely go to 300MHz, but again i aint see no display there, so i believe your imageries are aided from another equipments? we have alot cheaper poorman mechanism for this, ie an dso and fg and simple diy circuit. and btw, you dont have to separate R and L in different threads imho, they are all the same to me at least, ie RLC in some combination. interesting subject nevertheless, esp in your analysis description, both threads are bookmarked keep posting useful info, hi-f parasitics Z is always still a mistery to me.

[Mechatrommer]

oh now i just realized the relation between the OP and the site i linked

[trewmac]

Thanks for the feedback Mechotrommer.
The analyser has an on board LCD for individual impedance measurements and also connects to purpose built PC software via USB. That is why there are both LCD screen shots from the unit and sweep charts from the software. It is useful to use both and no extra equipment needed.

It is true that R,L and C are all combinations of R,L and C at high frequencies. I've separated them in an attempt to simplify the discussion. The parasitic effects are a mystery to lots of people! We get asked questions about it quite a lot, so if you have anything specific, you can ask and I will see if I know the answer.. In the meanwhile, hope the article helped a bit! 

[KJDS]

In practice, with modern small surface mount resistors, the biggest issue is the pad capacitance, especially on multilayer boards with thin dielectric.

[trewmac]

Yeah that's right. The pads and tracks used to mount a component can have a dramatic effect on it's ability to function as intended.
Using the impedance probe it is possible to characterize the entire circuit on the PCB from any given point.

This way you know exactly how the input of one device looks from the output of another, including any track and pad reactance.
(sometimes I have to cut tracks to take a measurement and then rejoin them)