ResistorsResistors 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.
![](http://www.impedanceanalyzer.com.au/media/1/20130616-formula16.jpg)
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.
![](http://www.impedanceanalyzer.com.au/media/1/20130616-sweep9.jpg)
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.
![](http://www.impedanceanalyzer.com.au/media/1/20130616-formula17.jpg)
Below is a plot of the 0R, 10R and 50R resistors in series RLC format showing their parasitic inductor value.
![](http://www.impedanceanalyzer.com.au/media/1/20130616-sweep10.jpg)
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.
![](http://www.impedanceanalyzer.com.au/media/1/20130616-formula18.jpg)
This is best viewed with the parallel RC format.
![](http://www.impedanceanalyzer.com.au/media/1/20130616-sweep11.jpg)
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:
![](http://www.impedanceanalyzer.com.au/media/1/20130616-formula19.jpg)
Similarly, a better model for the 1K 0805 resistor at 100MHz would be:
![](http://www.impedanceanalyzer.com.au/media/1/20130616-formula20.jpg)
Done!