Measuring Capacitors with an Impedance Analyser

[trewmac]

Have you discovered that the impedance of your capacitor has positive phase?
We're going to explore the real world behaviour of  capacitors using a TE3001 analyser with a tweezer tip.
Capacitors are subject to parasitic issues just like the inductors described in the previous post.
Below is the measured capacitance of a 1nF 0805 X7R Ceramic chip capacitor manufactured by AVX.

Once again, the low frequency response makes sense but around 107MHz the capacitance sharply rises before becoming negative!

Just like inductors, capacitors have unwanted stray elements inherent in the physical construction of the component that come into effect at high frequencies.

107MHz is the self resonant frequency for this capacitor and above this frequency it appears inductive.

Real world capacitor model
Capacitors are constructed by layers of conductors and insulators that inherently contain resistance and inductance. They can be modelled electrically by the diagram below.

R stray is often referred to on data sheets as equivalent series resistance or ESR.

Low Frequency Response

At low frequencies (far below the self resonant frequency) the impedance of L approaches a short circuit so it can be removed from the model. Further more, the impedance of C is so large compared to R, R can also be removed.

The value of C can be read straight from the LCD screen in R-L-C format. I chose to view it at 1MHz.

C=1.04nF

High frequency response
Above the resonant frequency the impedance of C approaches a short circuit so it can be removed from the model.  Further more, the impedance of L is so large compared to R, R can also be removed.

Now L can be measured using the equivalent circuit format at a frequency well above the resonant frequency. I had to go all the way to 300MHz to get a reasonable impedance to measure.

L=1.86nH

Self resonance
At the self resonant frequency f, the measured reactance is zero because the reactance of the stray inductance L cancels out the reactance of the capacitance C. With L and C gone, this leaves only R.


Viewed in the parallel equivalent RC chart the resistance will reach a minimum value at self resonance, and this value is R stray.

Reading from the chart,  R ~ 0.05 Ohms.

The value of f can be taken from the location of this minimum or the zero crossing of reactance as we did before. Both ways of finding f should yield similar values.

Reading from the chart, f ~ 107MHz.



The same formula for self resonance that we used for the inductor model can be to test the validity of our capacitor model.

This time, we rearrange the formula to get L in terms of C and f:   

Plugging in our values of C and f , we get

Not perfect, but for our simple model it’s not far off the measured 1.86nH.

So now we have a real world model that more accurately describes the high frequency behaviour of this capacitor.

To summarise the technique:


  Just resistors to go now...