# ESR of Ceramic Capacitor

I have been doing a bit research on ceramic capacitors, as I need one for the output of my synchronous buck converter. And as its very common that ESR is not straight forwardly given in the data sheets, we have to calculate it ourselves by Dissipation Factor value given at a certain frequency (normally 120 Hz) for a certain capacitance value.

$$ESR = \dfrac{D \cdot F}{2 \pi f C}$$

For e.g if i have this ceramic capacitor I can calculate the ESR as

$$\dfrac{0.05}{2 \pi \cdot 120 \cdot 470 \mu F} = 141m\Omega$$

(page 1 of data sheet, calculating for 470uF cap).

Now my question is, what if I am using this capacitor in my circuit at 100kHz? Its ESR should decrease right? As I think ESR should decrease with increasing the frequency. But the Dissipation factor increases with the increase in frequency as well. So how can one estimate the capacitor ESR at a high frequency? As there is no Frequency vs ESR OR Frequency vs D.F graphical relation given in the data sheets (I have gone through almost 100s of data sheets). So is there any way by which I can estimate the ESR of this capacitor at a higher frequency of 100kHz?

Actually I will be charging my battery cell with the help of my buck converter and I need the capacitor ESR to be less than 10mOhms, because that is my Battery cell's ESR (mentioned in the data sheet), so I am trying to look for a ceramic capacitor with a lower ESR than this, for minimizing my voltage ripple at the output.

Thankyou!

While ESR is not always given it is often easy to find on a better manufacturers website. Many have online or downloadable tools that will show you all of the information you could ever want about a cap. With the rise of the need to simulate PDN for everyday boards, people have been demanding exactly this kind of information.

For example take a look at Murata's simsurfing tool It's free of course and all you do is select a capacitor from the list and among other things you can see the graph of ESR and impedance vs frequency. If you're simulating it's easy to extract a simple RLC model from the data.

If you are using that capacitor at 100kHz I might be interested in it's ESL - series inductance - it's a leaded part and quite large and this may swamp the resistance and give you horrible resonance problems: - I'd be looking for a capacitor that was specified more fully and it would more likely be a radial electrolytic. I would also consider the benefits of having it in parallel with a 1uF ceramic capacitor and maybe a 100nF - these sorts of devices are usually quite well specified by for high frequencies.

My advice is find a more appropriate solution.

Now my question is, what if I am using this capacitor in my circuit at 100kHz? Its ESR should decrease right?

No, dissipation factor applies at a specific frequency - you can't just calculate ESR at F1 and expect it to become a different value at F2. Wiki tells us: -

DF will vary depending on the dielectric material and the frequency of the electrical signals.

The ESR equation works so long as you are below the resonant frequency of the cap. If you take a look at the impedance "notch" curve, the ESR should decrease up to the point where the cap is at its resonant point, after which you'll see the parasitic ESL begin to become more pronounced. This is where the equation above is incomplete (at the resonant frequency and above).

I know this very old question has best answer by some hardware guy. I end up here because I was looking for same question. I will really try what some hardware guy has suggested and I think it's the best way to make sure your capacitor will work for your specific application.

However, I found out very interesting note from Richard Fiore (38 years of experience in RF engineering). The note says:

ESR is typically expressed in milliohms at specific frequencies by most manufacturers. The standards most frequently used as a guideline are EIA RS483 and MIL-C-55681. The measurements are performed at various frequencies between 30 MHz and 1 GHz. Therefore, it is necessary to consider the ESR value at your specific design frequency. If, for example, you are designing for a 900 MHz wireless application, and the ESR is specified at 150 MHz, the ESR at 900 MHz may be calculated by multiplying the specified ESR at 150 MHz by √ 900/150 . This relationship is well behaved at RF and accounts for the "skin effect". The ESR is the main loss element of the capacitor and is used to determine the power loss i.e.; P = I²*ESR.

According to him, the ESR increases with frequency (even I used to think that). However, in case you don't have access to manufacturer tools or graphs, I think I will be considering his formula to calculate ESR at my desired frequency.