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Modeling >> Passive Devices >> Modeling ESR variation of Capacitor
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Message started by Faisal on Apr 17^th, 2007, 9:30am

Title: Modeling ESR variation of Capacitor
Post by Faisal on Apr 17^th, 2007, 9:30am

Hi,

The ESR (Equivalent Series Resistance) is specified the capacitor data-sheets. It varies over the frequency range. How can I model this behavior within Spectre ??

At this moment, I use a low frequency value of ESR in my simulation, but as the LDO stability depends upon ESR, I think its a good idea to consider ESR variation with frequency.

Title: Re: Modeling ESR variation of Capacitor
Post by Ken Kundert on Apr 17^th, 2007, 11:22am

You might want to take a look at the capacitor modeling papers in the "Modeling" section of this website. In particular the one on modeling dielectric absorption and the fracpole suite.

-Ken

Title: Re: Modeling ESR variation of Capacitor
Post by Faisal on Apr 18^th, 2007, 5:15am

Thank you for this link. I have now couple of related questions.

1) I am in the process of choosing the capacitor while looking at their datasheets. Is their a quick way to dervie a crude di-electric absorpiton model from the data-sheet ?

2) The ESR, impedance is specified starting from 10 or 100 Hz, but not some lower number like 0.1 or 1 Hz. From certain data-sheets it seems that the value of ESR will increase as we approach dc. What is the reason behind this behavior?

Title: Re: Modeling ESR variation of Capacitor
Post by Ken Kundert on Apr 18^th, 2007, 3:34pm

The way I do it is to plot the resistance and reactance of the capacitor on a log-log chart. Then I use straight-line asymptotes to represent the idealized components in the model. The reactance due to a capacitor will have a slope of -1, for an inductance the slope will be +1. Resistors will have a slope of 0. A capacitive fracpole will have a slope of -1/2. I then move these lines up or down, left or right, in order to fit the data from the capacitor. Once you get the best fit, you convert their reactance to their component values.

The dielectric absorption is responsible for the series resistance changing with frequency. This effect is described in the paper.

-Ken

Title: Re: Modeling ESR variation of Capacitor
Post by Faisal on Apr 25^th, 2007, 8:09am

On pg 11 of the document, "Modeling Absorptive Capacitors", the parametes τ and C∞ are derived, while "only looking at Fig 2". Can some one explain how the author calculates τ = 1 sec and C∞ = 12.5nF from Fig 2.

Title: Re: Modeling ESR variation of Capacitor
Post by Ken Kundert on Apr 25^th, 2007, 12:37pm

The 12.5nF can be extracted from the low frequency reactance (X). The reactance of a C_∞ = 12.5nF capacitor is 1/2πfC = 1.27kΩ at 10kHz.

The value of τ is more of a judgment call. The resistive part of dielectric absorption is a slowly curved line, as shown in the bottom part of Fig. 4. You can determine α from the distance between the real and imaginary parts of the curve at the inflection point (1/τ). But as α approaches 1 the curve becomes so gently sloped that it is difficult to determine where the inflection point is. I somewhat arbitrarily chose it to be 1 because I felt the inflection point was well below the lowest value shown. But frankly, the value of τ is not critical.

-Ken

Title: Re: Modeling ESR variation of Capacitor
Post by martinm_de on Jun 18^th, 2014, 8:54am

Hi Ken,

thanks for answering all these questions instead of leaving
us in desparation!

Here is my question, also related to fracpoles and
ESR modelling:

in your paper on page 8
http://www.designers-guide.org/Modeling/suite.pdf ,

the software asks for an ESR.
When looking at the generated subcircuit,
the ESR is added to the inductor model.
So, we have a constant ESR.

My understanding was that ESR is ~1/f , and is modelled
by the fracpole.

So, why is ESR appearing as a constant resistor?

Thanks.

Title: Re: Modeling ESR variation of Capacitor
Post by Ken Kundert on Jun 19^th, 2014, 8:47am

There are multiple components to the ESR. One part is the dielectric absorption. It goes to 0 as f goes to 0. Another part is contact and lead resistance, which presumable is constant over frequency. When the program refers to ESR it is only referring to the contact and lead resistance.

This is kind of a "if you can't fix it, feature it" situation. Dielectric absorption is expensive to model, and I cannot maintain the model over all frequencies, so I use the fact that the dielectric absorption model breaks down at lower frequencies to model the contact and lead resistance.

-Ken

Title: Re: Modeling ESR variation of Capacitor
Post by martinm_de on Jun 20^th, 2014, 12:05am

Hi Ken,

thanks a lot, it is clear now.
You are the man.

Regards

Martin