Capacitor parameters

[Centmo]

Hi, I need some help deciphering some capacitor parameters. I am trying to model a specific capacitor in PSPICE:

EKZE101ELL331ML25S
**broken link removed**
(near the bottom right of the last page)

Voltage Rating: 100V
Capacitance: 330uF
Impedence: 0.038 Ohm @ 100kHz
Dissipation Factor (tan(d)): 0.08 @ 120Hz

Now, I'd like to model this capacitor in PSPICE. As I understand, it needs to be modelled as a capacitor, resistor and inductor in series. How would I derive the values of the resistor and inductor?

Thanks.

 

[FvM]

You can't model unknown parameters. Series inductance isn't specified in the datasheet. Loss factor/real impedance is frequency dependant and would need to be represented by a RC ladder network for exact modelling, For a simplified model, refer to the specified ESR.

 

[Centmo]

Ok, I would be happy with a simple model of C in series with R. So, now I just need to determine ESR. The datasheet specifies 'Impedence' but I assume this is complex impedence (Z). How would I determine ESR from these parameters? Is it relatively constant through frequency?

 

[FvM]

The 100 kHz impedance value can be used as good estimation for the ESR.

 

[albbg]

If you want to model the capacitor as series RLC, I think you can proceed as follow:

at low frequency the series inductor can be neglected, the you can apply:

tan(delta)=R/Xc where Xc is the reactance of the capacitor and R the series resistance (i.e.: the ESR)

from your parameters: Xc=1/(2•Π•f•C) ==> Xc=1/(2•Π•120•330u)≈4 ohm, then

R=0.08•4=20 mOhm

The modulus of the impedance of a series RLS is given by: Z=sqrt[R²+(XL-XC)²], using the parameters you gave:

Xc=1/(2•Π•100000•330u)≈0.0048 ohm

0.038=sqrt[0.02²+(XL-0.0048)²] ==> XL≈0.037 ohm

since XL=2•Π•f•L, then L≈59 nH

 

[FvM]

Nice calculation, but it hasn't to do with real electrolytic capacitors. Assuming same ESR at 120 Hz and 100 kHz leads to wrong conclusions.

Without an Z versus frequency diagram, you can't reliably derive parameters. My statement, that Z(100 kHz) effectively represents the ESR isn't based on the shown sparse datasheet rather more informative data sheets of similar capacitors, e.g. from Panasonic. It's particularly impossible to estimate ESL without a Z diagram that shows a clear inductive edge. See below a respective example.

 

[albbg]

As far as I know the ESR is quite (not perfectly) constant over frequency. Then I think a model calculated as I suggested should be accurate enough for most of the simulation. Of course the complete model would be more complicated, from simply adding the plate leakage resistor to parallelize many RLC branches. But I intended Centmo asking about a quite simple model.

Z(100 kHz) cannot be a reliable estimation of ESR due to the presence of a non-negligible series inductor. Furthermore, but I'm not sure, I remember the ESR is slightly lowering when the frequency increase (but I could be wrong).

By the way tan(delta)=ESR/Xc by definition.

 

[FvM]

Apart from the said problems involved with your calculation, there's a calculation error, that I overlooked.

R=0.08•4=20 mOhm
should be
R=0.08•4=320 mOhm

In other words, the ESR estimated from the 120 Hz loss factor is already larger than the specified 100 kHz impedance. So there's surely no ESL effect included in the 100 kHz number. For a visual explanation why the calculation fails, see below the tan d versus frequency plot of real electrolytic capacitor. I added a blue line that shows tand ~ f (constant ESR).



P.S.:

Z(100 kHz) cannot be a reliable estimation of ESR due to the presence of a non-negligible series inductor.

As long the reading represents the impedance minimum, see the impedance curves in my previous post, it is a good estimation.

 

[albbg]

Yes, FvM you are right, thank you for the correction. There is an error in the calculation that, of course, invalidate all the other steps. It's my fault.

Your estimation of ESR at 100 kHz frequency is correct as far as that point is close enough to the SRF of the capacitor.

 

[The Electrician]

I have some Panasonic low impedance capacitors, specifically intended for switching power supplies. I don't have a 330 uF unit, but I do have a 470 uF 35 volt one, and that should be close enough to demonstrate parameter variations with frequency.

Here are a couple of images made with an impedance analyzer showing the result of a frequency sweep of this capacitor from 100 Hz to 5 MHz. Both the horizontal and vertical scales are logarithmic. The first image shows the impedance (green) and the ESR (yellow). The SRF is plainly indicated by the minimum of the impedance curve. The ESR is equal to the impedance at the SRF, where the two curves touch. Marker A is at 100 kHz, and we can see that the impedance is nearly equal to the ESR at that frequency.

The ESR curve is not completely flat with frequency, but it doesn't vary too much. Keep in mind that the vertical scale is logarithmic. The ESR at 100 kHz is 27.98 milliohms, and at 100 Hz is about 75 milliohms.

This image shows the impedance and the ESL. Note that the apparent ESL is negative below the SRF and goes off scale in the negative direction. Above the SRF we see the ESL (yellow) approach its true value of 11.5 nH.

These curves are typical for a modern low impedance aluminum electrolytic.

- - - Updated - - -

Here's a sweep of DF and ESR for the same capacitor:

 

[FvM]

Thanks for the detailed measurements. Once you have the complex impedance characteristic over the full frequency range, you are able to fit an equivalent circuit like the below one. Depending on the intended accuray, two to four ladder elements are usually suffcient to represent the impedance.

A bad thing, that reveals in the diagram in post #8 is the strong temperature dependency of loss (ESR elements).

 

[Centmo]

Thanks for the input everyone. Appreciate the spectrum analysis plots too, those are great. It's interesting to compare the similarities and differences of those plots to the diagram in this document:
https://www.illinoiscapacitor.com/pdf/papers/impendance_dissipation_factor_esr.pdf